CN112818585B - Method and device for dividing iterative computation parallel particles of integrated circuit interlayer coupling - Google Patents

Method and device for dividing iterative computation parallel particles of integrated circuit interlayer coupling Download PDF

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CN112818585B
CN112818585B CN202110425202.0A CN202110425202A CN112818585B CN 112818585 B CN112818585 B CN 112818585B CN 202110425202 A CN202110425202 A CN 202110425202A CN 112818585 B CN112818585 B CN 112818585B
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唐章宏
邹军
王芬
黄承清
汲亚飞
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Beijing Wisechip Simulation Technology Co Ltd
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Abstract

The invention provides a partitioning method and a partitioning device for iterative computation parallel particles of integrated circuit interlayer coupling, which divide iterative computation into three types of computing units: a basic calculation unit, an integrated circuit layer-layer calculation unit and an electromagnetic field and current distribution calculation unit of each layer; secondly, dividing the iterative computation of the interlayer coupling of the integrated circuit into non-overlapping computation particles according to the three types of computation units; thirdly, based on one complete serial iterative computation, obtaining weighted CPU time and total CPU time of each computation particle, and combining the computation particles into different parallel particles according to the proportion of the weighted CPU time; and finally, classifying the parallel particles, wherein the similar parallel particles are mutually independent, and the corresponding calculation task sequences can be randomly disordered to form new calculation task sequences which are dynamically distributed to different calculation processes. The invention determines a parallel particle division method of efficient parallel computation of the interlayer coupling computation of the integrated circuit, and reduces the simulation time of the integrated circuit.

Description

Method and device for dividing iterative computation parallel particles of integrated circuit interlayer coupling
Technical Field
The invention relates to the technical field of integrated circuit interlayer coupling iterative computation, in particular to a method and a device for dividing iterative computation parallel particles of integrated circuit interlayer coupling.
Background
When the integrated circuit works, high-frequency alternating electromagnetic fields are formed on a multilayer layout of the integrated circuit due to transmission of high-speed signals, and the high-frequency alternating electromagnetic fields form high-frequency radiation sources, so that crosstalk and electromagnetic radiation are formed on other signal layers or other integrated circuits and chips, and normal work of the other signal layers or other integrated circuits and chips is influenced, and therefore, the influence of the spatial electromagnetic radiation among the layers of the integrated circuit needs to be calculated during design. In the traditional method, strict three-dimensional numerical calculation is generally adopted for solving the space electromagnetic radiation of the integrated circuit, but the multilayer super-large-scale integrated circuit has a complex structure and very complex three-dimensional numerical calculation, and the used CPU time and memory are very large. In the large-scale numerical calculation, different calculation examples have different structures, so that the calculation complexity of the different calculation examples is unequal, and for the unequal mass calculation, a high-efficiency parallel calculation method design is needed, the unequal calculation complexity of the different examples is fully considered, and the parallel calculation efficiency is improved as much as possible.
The conventional parallel computing is basically parallel to a single computing example, the parallel is realized in a large number of circulating computing parts, and parallel particles are usually fine, so that a large number of data exchange exists among different processes, and the parallel efficiency is reduced; secondly, due to different calculation schedules of different processes, a large amount of waiting is inevitable when data sharing and synchronization are needed, so that the overall parallel efficiency is low; moreover, since the calculation processes of a considerable part of the calculation processes of a single instance have a sequence and data have dependency, when the single calculation instance is parallel, the calculation of a considerable part cannot be parallelized, which also seriously reduces the overall parallel efficiency.
Disclosure of Invention
Objects of the invention
Based on the above, in order to reduce the influence of the point source described by the dyadic Green function on any point in space and approximate the coupling between each layer of the equivalent multilayer integrated circuit, the original three-dimensional electromagnetic field problem of the integrated circuit is reduced to the calculation complexity of the iterative method of the superposition of the two-dimensional electromagnetic field problem and the Green function. In order to reduce communication among processes to the maximum extent in the iterative computation process of interlayer coupling of a multilayer very large scale integrated circuit, avoid hard disk read-write bottleneck caused by the fact that a memory peak value is larger than an available physical memory during multi-process parallel computation, and perfectly solve the problem of process waiting caused by unequal complexity of different computation examples, thereby greatly improving the parallel computation efficiency, the application discloses the following technical scheme.
(II) technical scheme
As a first embodiment of the present invention, the present invention discloses a partitioning method for iterative computation parallel particles of integrated circuit interlayer coupling, comprising the following steps:
s1, dividing the iterative computation of the interlayer coupling of the multilayer ultra-large scale integrated circuit into three types of computation units: a basic calculation unit, a layer-to-layer calculation unit of an integrated circuit, and an electromagnetic field and current distribution calculation unit of each layer of the integrated circuit;
s2, dividing iterative computation of integrated circuit interlayer coupling into non-overlapping computation particles according to the three types of computation cells, wherein the computation particles are one or more computation cells executing all independent operations of the same type;
s3, obtaining the weighted CPU time and the total CPU time of each calculation particle based on one-time complete serial iterative calculation, and combining the calculation particles into different parallel particles according to the proportion of the weighted CPU time;
and S4, classifying the parallel particles, wherein the similar parallel particles are mutually independent, the corresponding calculation task sequences can be randomly disordered, in the process of executing the parallel particles, the sequences of all calculation tasks executed by the similar parallel particles are randomly disordered to form a new calculation task sequence, and the new calculation task sequence is dynamically distributed to different calculation processes to complete the parallel calculation of the calculation tasks.
Further, the basic computing unit includes two types: the first kind of basic calculation unit is used for calculating the field generated by the current in the simple polygon of the integrated circuit in any simple polygon on other layers of the integrated circuit by utilizing a dyadic Green function, and the second kind of basic calculation unit is used for calculating the grid unit in the single-layer two-dimensional finite element calculation of the integrated circuit; the calculation of the grid unit in the integrated circuit single-layer two-dimensional finite element calculation comprises the following steps: calculating the area of the grid unit, calculating the shape function of the grid unit, calculating the finite element rigidity matrix of the grid unit, and calculating the field intensity and the current density of any point in the grid unit.
Further, the first-class basic computing unit specifically operates as follows:
the method comprises the steps of firstly, calculating an electric field generated by a point current source at a field point, wherein the electric field generated by the point current source at the field point is a special analytical expression formed according to a special layered structure of an integrated circuit, and the current sources of a multilayer integrated circuit are layered, namely the current density distributed on each metal layer of an integrated circuit layout with a complex shape is only equal to that of each metal layerxAndyis related tozIndependently, the current density distribution is onlyx, yAs a function of (c).
And secondly, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the method comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 103176DEST_PATH_IMAGE001
；
wherein the content of the first and second substances,
Figure 331901DEST_PATH_IMAGE002
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure 721425DEST_PATH_IMAGE003
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure 555783DEST_PATH_IMAGE004
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 917625DEST_PATH_IMAGE005
is the weight factor corresponding to the gaussian integral point;
and thirdly, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields.
Further, the integrated circuit layer-layer computation unit includes: combining the first type of basic calculation units, and calculating fields generated by currents distributed on the complex integrated circuit layout filled by the simple polygons on the complex layouts of other layers of the integrated circuit based on the field linear superposition principle; the electromagnetic field and current distribution calculating unit of each layer of the integrated circuit comprises: and combining the second type of basic computing units, taking the influence of other layers on the source layer to be computed as an additional source item, and computing the electromagnetic field and current distribution of the source layer to be computed by adopting a two-dimensional finite element method.
Further, the calculation formula for calculating the weighted CPU time of the particle is:
Figure 536825DEST_PATH_IMAGE006
in the formula:
Figure 600596DEST_PATH_IMAGE007
is as followsiThe weighted CPU time of each calculated grain,
Figure 845501DEST_PATH_IMAGE008
is as followsiEach calculation particle has a single calculated CPU time,
Figure 311118DEST_PATH_IMAGE009
is as followsiThe number of particle executions was counted.
Further, the calculation formula of the total CPU time in the whole calculation process is:
Figure 851952DEST_PATH_IMAGE010
wherein, in the step (A),Tfor the total CPU time of the entire calculation process,mthe number of calculation particles divided for the entire calculation program,
Figure 403019DEST_PATH_IMAGE007
is as followsiThe weighted CPU time of the particles is calculated.
Further, the weighted CPU time of each calculation particle is sorted in descending order and accumulated in sequence until the accumulated sum exceeds 90% of the total CPU time, and each calculation particle in the accumulated sum is taken as a parallel particle.
The second embodiment discloses a partitioning device for iterative computation parallel particles of integrated circuit interlayer coupling, which comprises a computing unit partitioning module, a computing particle partitioning module, a parallel particle partitioning module and a parallel particle operation module,
the calculation unit division module is used for dividing the iterative calculation of the interlayer coupling of the multilayer ultra-large scale integrated circuit into three types of calculation units: a basic calculation unit, a layer-to-layer calculation unit of an integrated circuit, and an electromagnetic field and current distribution calculation unit of each layer of the integrated circuit;
the calculation particle dividing module is used for dividing the three types of calculation units into calculation particles which are not overlapped with each other;
the parallel particle division module obtains weighted CPU time of each calculation particle and total CPU time of an iteration method of integral multilayer ultra-large scale integrated circuit interlayer coupling based on one-time complete serial iterative calculation, the calculation particles are combined into different parallel particles according to the ratio of the weighted CPU time to the total CPU time, the similar parallel particles are mutually independent, and corresponding calculation task sequences can be randomly disordered;
the parallel particle operation module is used for randomly disordering the sequences of all the calculation tasks executed by the same type of parallel particles in the process of executing the parallel particles to form a new calculation task sequence, and dynamically distributing the new calculation task sequence to different calculation processes to complete the parallel calculation of the calculation tasks.
Further, the basic computing unit includes two types: the first kind of basic calculation unit is used for calculating the field generated by the current in the simple polygon of the integrated circuit in any simple polygon on other layers of the integrated circuit by utilizing a dyadic Green function, and the second kind of basic calculation unit is used for calculating the grid unit in the single-layer two-dimensional finite element calculation of the integrated circuit; the calculation of the grid unit in the integrated circuit single-layer two-dimensional finite element calculation comprises the following steps: calculating the area of the grid unit, calculating the shape function of the grid unit, calculating the finite element rigidity matrix of the grid unit, and calculating the field intensity and the current density of any point in the grid unit.
Further, the first-class basic computing unit specifically operates as follows:
the method comprises the steps of firstly, calculating an electric field generated by a point current source at a field point, wherein the electric field generated by the point current source at the field point is a special analytical expression formed according to a special layered structure of an integrated circuit, and the current sources of a multilayer integrated circuit are layered, namely the current density distributed on each metal layer of an integrated circuit layout with a complex shape is only equal to that of each metal layerxAndyis related tozIndependently, the current density distribution is onlyx, yA function of (a);
and secondly, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the method comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 936768DEST_PATH_IMAGE001
；
wherein the content of the first and second substances,
Figure 774668DEST_PATH_IMAGE002
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure 1250DEST_PATH_IMAGE003
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure 790345DEST_PATH_IMAGE004
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 862206DEST_PATH_IMAGE005
is the weight factor corresponding to the gaussian integral point;
and thirdly, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields.
(III) advantageous effects
The invention realizes different particle parallels in the iterative computation of the coupling between the integrated circuit layers, greatly reduces the communication between the processes and the waiting time caused by synchronization, simultaneously, adopts a random dynamic allocation method of the computation tasks, ensures that computation models with unequal complexity are randomly and uniformly distributed on each computation node, and avoids the bottleneck of hard disk read-write caused by virtual memory access due to overhigh peak value memory.
Drawings
The embodiments described below with reference to the drawings are exemplary and intended to be used for explaining and illustrating the present invention and should not be construed as limiting the scope of the present invention.
FIG. 1 is a block diagram of the main steps of a first embodiment of the present invention;
FIG. 2 is a principal flow diagram of a first class of basic computing unit of the present invention;
FIG. 3 is a block diagram of the modules of a second embodiment of the present invention;
fig. 4 is an exploded view of the electric field generated at the field point by the point current source of the present invention.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention.
It should be noted that: in the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described are some embodiments of the present invention, not all embodiments, and features in embodiments and embodiments in the present application may be combined with each other without conflict. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it is to be understood that the terms "central," "longitudinal," "lateral," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," and the like are used in the orientation or positional relationship indicated in the drawings, which are used for convenience in describing the invention and for simplicity in description, and are not intended to indicate or imply that the referenced device or element must have a particular orientation, be constructed and operated in a particular orientation, and are not to be considered limiting of the scope of the invention.
The following describes in detail a first embodiment of the partitioning method and apparatus for iterative computation of parallel grains for interlayer coupling of an integrated circuit according to the present invention with reference to fig. 1. The partitioning method for iterative computation parallel particles of integrated circuit interlayer coupling provided by the embodiment comprises the following steps:
s1, dividing the iterative computation of the interlayer coupling of the multilayer ultra-large scale integrated circuit into three types of computation units: a basic calculation unit, a layer-to-layer calculation unit of an integrated circuit, and an electromagnetic field and current distribution calculation unit of each layer of the integrated circuit;
s2, dividing iterative computation of integrated circuit interlayer coupling into non-overlapping computation particles according to the three types of computation cells, wherein the computation particles are one or more computation cells executing all independent operations of the same type;
before parallel computing, the number of processes needs to be determined manually, and one process is taken as a main process.
The calculation particles are defined according to the problem operation characteristics. The problem operation characteristics are different from industry to industry. For example, for large scale integrated circuit electromagnetic field distribution calculation, when a multilayer integrated circuit board with a certain structure and an external circuit thereof are subjected to field-path coupling, the operational characteristics comprise: the influence of the point source on any point in the space is along with the distance relation between the point source and the point, the number of separated medium layers, the electromagnetic field distribution and the current distribution of each layer, and the time point of the electromagnetic field distribution and the current distribution of the influenced layer is updated.
S3, obtaining the weighted CPU time and the total CPU time of each calculation particle based on one-time complete serial iterative calculation, and combining the calculation particles into different parallel particles according to the proportion of the weighted CPU time;
further, the calculation formula for calculating the weighted CPU time of the particle is:
Figure 567994DEST_PATH_IMAGE006
in the formula:
Figure 949166DEST_PATH_IMAGE007
is as followsiThe weighted CPU time of each calculated grain,
Figure 474825DEST_PATH_IMAGE008
is as followsiEach calculation particle has a single calculated CPU time,
Figure 101110DEST_PATH_IMAGE009
is as followsiThe number of particle executions was counted.
Further, the calculation formula of the total CPU time in the whole calculation process is:
Figure 661404DEST_PATH_IMAGE010
wherein, in the step (A),Tfor the total CPU time of the entire calculation process,mthe number of calculation particles divided for the entire calculation program,
Figure 229789DEST_PATH_IMAGE007
is as followsiThe weighted CPU time of the particles is calculated.
Further, the weighted CPU time of each calculation particle is sorted in descending order and accumulated in sequence until the accumulated sum exceeds 90% of the total CPU time, and each calculation particle in the accumulated sum is taken as a parallel particle.
Specifically, if the iterative computation of the interlayer coupling of the multilayer very large scale integrated circuit is divided into 3 computing particles of c1, c2 and c3 according to the definition of the computing particles, 3 computing particles can execute the computing task of the whole computing process; if c1 executes 500 operation tasks, c2 executes 200 operation tasks, and c3 executes 5 operation tasks; then 705 operation tasks constitute the whole operation process, which only needs 3 computation particles of c1, c2 and c 3. The whole operation process is executed by 3 computing particles of c1, c2 and c3, and each of c1, c2 and c3 comprises at least 1 independent operation (operation task).
Sorting according to the weighted CPU time obtained by each calculated particle operation, wherein if the c1 weighted CPU time is 0.1s, the c2 weighted CPU time is 100s and the c3 weighted CPU time is 0.2s, the final sorting result is c2> c3> c 1; the weighted CPU times for the 3 calculated particles add sequentially from large to small, i.e., T (c2) + T (c3) + … until the sum of times is greater than 90% of the total CPU time; if T (c2) + T (c3) > 90%, then c2, c3 are each as a parallel particle; if T (c2) > 90% of the total CPU time, then c2 is a parallel particle.
And S4, classifying the parallel particles, wherein the similar parallel particles are mutually independent, the corresponding calculation task sequences can be randomly disordered, in the process of executing the parallel particles, the sequences of all calculation tasks executed by the similar parallel particles are randomly disordered to form a new calculation task sequence, and the new calculation task sequence is dynamically distributed to different calculation processes to complete the parallel calculation of the calculation tasks.
Specifically, the way of randomly scrambling the operation task sequence is as follows:
firstly, the sequence of operation tasks
Figure 229362DEST_PATH_IMAGE011
Correspondingly generating random number sequences
Figure 908605DEST_PATH_IMAGE012
，m＝1,2,3,…,M. Then to the sequence
Figure 808559DEST_PATH_IMAGE012
The sequences are sorted from small to large, and the sorted sequences are
Figure 282266DEST_PATH_IMAGE013
. Finally, generating new non-repeated operation task sequence
Figure 516938DEST_PATH_IMAGE014
，
Figure 983560DEST_PATH_IMAGE015
Is composed of
Figure 987288DEST_PATH_IMAGE016
In that
Figure 897476DEST_PATH_IMAGE017
Of (c) is used.
The key point is to make all the operation tasks in the parallel particles in sequence
Figure 370176DEST_PATH_IMAGE018
Randomly disorganized to generate new non-repetitive operation task sequence
Figure 453539DEST_PATH_IMAGE019
Then distributing operation tasks according to the sequence, namely equivalently distributing the original operation tasks randomly, wherein the random distribution strategy is characterized in that the random distribution scheme can completely disturb the distribution sequence of all the operation tasks, thereby realizing that the sum of the peak value memory occupied by the tasks operated by all the operation nodes simultaneously is formed by the average value of the peak value memory occupied by the process number and all the models (calculation particles) rather than the highest valueAnd (4) determining the value.
And the main process distributes all the operation tasks required to be executed by the parallel particles to all the processes including the main process according to the formed new calculation task sequence, and completes the parallel operation of all the operation tasks executed by the parallel particles.
In addition, if a certain operation task in the parallel particles is distributed to a process, a mark file which is used for indicating that the operation task is already distributed to the operation task is generated; when applying for distributing a certain calculation task, the other process tries to generate a mark file of the calculation task, and automatically applies for distributing the next calculation task by the other process under the condition that the mark file exists.
In the multi-process parallel operation process, the chances of allocating a certain operation task to each process are equal, if no measure is taken, multiple processes may be allocated to the same operation task, and the waste of operation resources is caused, so that some measure must be taken, and all operation tasks are uniquely allocated to a certain process. The simplest and most intuitive measure for achieving this is to assign a task a time stamp, i.e. a task is assigned to a process at the same time as it is marked so that other processes are no longer assigned the task. However, because the variables of each process are generally independent of each other during parallel operation, the operation tasks are asymmetric, the operation states of each process are different, and information distributed by any process through the variable marking task cannot be immediately transmitted to other processes, an external explicit marking method is needed to be adopted so that all processes can obtain the information once the operation tasks are marked. Therefore, if the operation task in the parallel particles is distributed to the process, the mark file of the operation task is immediately generated; when a process applies for distributing a certain operation task, the process will try to generate a mark file of the operation task, if the mark file exists, the operation task is indicated to be distributed, and the process will automatically apply for distributing the next operation task.
The specific implementation steps for realizing the correct allocation of the operation tasks by utilizing the marker files are as follows:
step A1, a process applies for distributioniAn arithmetic task;
step A2, judgmentiSign file of individual operation taskFiIf the current state does not exist, jumping to the step A8, and if the current state does not exist, jumping to the step A3;
step A3, judging the mark fileFiWhether the lock is locked or not, jumping to the step A8 if the lock is locked, and jumping to the step A4 if the lock is not locked;
step A4, locking the logo fileFi；
Step A5, generating a logo fileFi；
Step A6, marking fileFiUnlocking;
step A7, completing the first stepiCalculating the operation tasks;
step A8, judging whether all the operation tasks in the parallel particles are completed or not, if not, determining whether all the operation tasks in the parallel particles are completedi＝i+1 and returning to step a1, if finished, jumping to step a 9;
all the operation tasks required to be executed by the parallel particles are all distributed to all the processes, and the distribution of the parallel particles is finished; it returns to executing all the computational tasks that the other parallel grains need to perform to distribute their respective execution.
Further, the basic calculation unit, the layer-to-layer calculation unit of the integrated circuit, and the electromagnetic field and current distribution calculation units of the layers of the integrated circuit can realize the coupling among the layers of the approximately equivalent multilayer integrated circuit through different combination modes.
Specifically, for example, each iteration method can select the parallelism of layer-layer computing units of the integrated circuit, calculate the influence of different layers on other layers in parallel, and apply two-dimensional finite elements to different layers by using other parallel particles to calculate the electromagnetic field distribution and the current distribution of the layers, so as to update the electromagnetic field distribution and the current distribution of the layers; the electromagnetic field distribution and the current distribution of each layer of the integrated circuit can be calculated in parallel, each parallel particle comprises the influence of other layers on the layer, and the influence is used as a source item of the layer to apply a two-dimensional finite element to the layer to calculate the electromagnetic field distribution and the current distribution of the layer.
Further, the basic computing unit includes two types: the first kind of basic calculation unit is used for calculating the field generated by the current in the simple polygon of the integrated circuit in any simple polygon on other layers of the integrated circuit by utilizing a dyadic Green function, and the second kind of basic calculation unit is used for calculating the grid unit in the single-layer two-dimensional finite element calculation of the integrated circuit; the calculation of the grid unit in the integrated circuit single-layer two-dimensional finite element calculation comprises the following steps: calculating the area of the grid unit, calculating the shape function of the grid unit, calculating the finite element rigidity matrix of the grid unit, and calculating the field intensity and the current density of any point in the grid unit.
Further, as shown in fig. 2, the first-class basic computing unit specifically operates as follows:
first, as shown in fig. 4, calculating an electric field generated by a point current source at a field point, where an electric field expression generated by the point current source at the field point is a special analytical expression formed according to a special structure of an integrated circuit layer, and a specific expression of the analytical expression is as follows: aiming at the frequency domain electromagnetic field of the multilayer integrated circuit layout, the electric field intensity generated by a point source at any layer field point is calculated by adopting a dyadic Green function, and the electric field intensity of nine azimuths of any point at any layer of the multilayer integrated circuit layout can be solved through the following formula to represent the electric field intensity.
The electric field generated by the point current source at the field point is expressed as:
Figure 614569DEST_PATH_IMAGE020
Figure 180811DEST_PATH_IMAGE021
Figure 390075DEST_PATH_IMAGE022
Figure 214812DEST_PATH_IMAGE023
Figure 176820DEST_PATH_IMAGE024
Figure 163231DEST_PATH_IMAGE025
Figure 859791DEST_PATH_IMAGE026
Figure 973372DEST_PATH_IMAGE027
wherein the content of the first and second substances,
Figure 806199DEST_PATH_IMAGE029
Figure 963511DEST_PATH_IMAGE031
Figure 399565DEST_PATH_IMAGE033
Figure 300524DEST_PATH_IMAGE034
Figure 987858DEST_PATH_IMAGE035
Figure 66803DEST_PATH_IMAGE036
iis the unit of an imaginary number,i 2=-1；
Figure 472377DEST_PATH_IMAGE037
representing a Bessel function of order 0;
Figure 442607DEST_PATH_IMAGE038
representing a Bessel function of order 1;
Figure 499294DEST_PATH_IMAGE039
expressed as a function of the Bessel integral coefficient,
Figure 263987DEST_PATH_IMAGE040
；x, y, zthe coordinates of the field points are represented,
Figure 173168DEST_PATH_IMAGE041
,
Figure 681510DEST_PATH_IMAGE042
,
Figure 609015DEST_PATH_IMAGE043
representing source point coordinates; angular frequency
Figure 796807DEST_PATH_IMAGE044
，
Figure 176973DEST_PATH_IMAGE045
Represents a frequency;
Figure 239738DEST_PATH_IMAGE046
indicating that the site is at the second
Figure 21749DEST_PATH_IMAGE046
A layer of a material selected from the group consisting of,
Figure 128245DEST_PATH_IMAGE047
is as follows
Figure 510554DEST_PATH_IMAGE046
At layer boundarieszCoordinates;
Figure 360698DEST_PATH_IMAGE048
,
Figure 747949DEST_PATH_IMAGE049
respectively represent
Figure 25346DEST_PATH_IMAGE050
The number of complex waves in the horizontal and vertical directions of the layer;
Figure 632301DEST_PATH_IMAGE051
respectively represent
Figure 286137DEST_PATH_IMAGE050
A layer horizontal dielectric constant, a vertical dielectric constant;
Figure 511582DEST_PATH_IMAGE052
,
Figure 710613DEST_PATH_IMAGE053
respectively representlHorizontal magnetic conductivity and vertical magnetic conductivity of the layer;
Figure 552667DEST_PATH_IMAGE054
is shown aslThe anisotropy coefficient of the layer;
Figure 744614DEST_PATH_IMAGE055
,
Figure 73833DEST_PATH_IMAGE056
respectively representlIntegral coefficients of complex wave numbers of the horizontal and vertical layers;
Figure 958612DEST_PATH_IMAGE057
respectively representlThe undetermined coefficient of a layer,A l , B l the following linear equation is solved:
Figure 22383DEST_PATH_IMAGE058
T1is 2n×2nThe complex number matrix of (a) is,
Figure 503174DEST_PATH_IMAGE059
is of length 2nA complex vector of (a);
Figure 703211DEST_PATH_IMAGE061
Figure 758892DEST_PATH_IMAGE062
Figure 573875DEST_PATH_IMAGE063
Figure 842046DEST_PATH_IMAGE065
Figure 162168DEST_PATH_IMAGE066
the following linear equation is solved:
Figure 139483DEST_PATH_IMAGE067
T2is 2n×2nThe complex number matrix of (a) is,
Figure 646688DEST_PATH_IMAGE068
is of length 2nA complex vector of (a);
Figure 984128DEST_PATH_IMAGE070
Figure 673604DEST_PATH_IMAGE072
Figure 539929DEST_PATH_IMAGE074
Figure 65588DEST_PATH_IMAGE075
the following linear equation is solved:
Figure 691873DEST_PATH_IMAGE076
T3is 2n×2nThe complex number matrix of (a) is,
Figure 986588DEST_PATH_IMAGE077
is of length 2nA complex vector of (a);
Figure 289393DEST_PATH_IMAGE079
Figure 820125DEST_PATH_IMAGE080
Figure 499368DEST_PATH_IMAGE082
Figure 664901DEST_PATH_IMAGE084
Figure 404187DEST_PATH_IMAGE085
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 153706DEST_PATH_IMAGE086
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 371061DEST_PATH_IMAGE087
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzA component;
Figure 656680DEST_PATH_IMAGE088
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 301288DEST_PATH_IMAGE089
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 23256DEST_PATH_IMAGE090
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzA component;
Figure 562078DEST_PATH_IMAGE091
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 685892DEST_PATH_IMAGE092
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 783292DEST_PATH_IMAGE093
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzAnd (4) components.
The current sources of the multi-layer integrated circuit are distributed in a layered manner, namely the current density distributed on each metal layer of the integrated circuit layout with a complex shape is only equal to that of the current sourcexAndythe axial direction is related tozAxial direction independence, current density distribution of onlyx，yAs a function of (c).
And secondly, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the method comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 992557DEST_PATH_IMAGE094
；
wherein the content of the first and second substances,E(x,y,z) At any point in space for the current source in the two-dimensional plane Sx,y,z) The field that is generated is,
Figure 66561DEST_PATH_IMAGE095
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (x,y,z) The expression of the dyadic green function of the generated field,
Figure 44881DEST_PATH_IMAGE096
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 562450DEST_PATH_IMAGE097
is the weight factor corresponding to the gaussian integral point;
and thirdly, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields.
Further, the integrated circuit layer-layer computation unit includes: combining the first type of basic calculation units, and calculating fields generated by currents distributed on the complex integrated circuit layout filled by the simple polygons on the complex layouts of other layers of the integrated circuit based on the field linear superposition principle; the electromagnetic field and current distribution calculating unit of each layer of the integrated circuit comprises: and combining the second type of basic computing units, taking the influence of other layers on the source layer to be computed as an additional source item, and computing the electromagnetic field and current distribution of the source layer to be computed by adopting a two-dimensional finite element method.
Further, the specific method for calculating the two-dimensional finite element comprises the following steps:
for the direct current electric field model, the three-dimensional model of the multilayer integrated circuit refers to the conductivity in the direct current electric field model
Figure 9743DEST_PATH_IMAGE098
Potential of the electrodeuAll the distributions of (A) and (B) are three-dimensional space coordinatesx,y,z) I.e.:
Figure 421526DEST_PATH_IMAGE099
，
Figure 254353DEST_PATH_IMAGE100
the function of the three-dimensional model satisfies the following equation (1):
Figure 677244DEST_PATH_IMAGE101
in the equation (1),
and boundary condition (2):
Figure 611833DEST_PATH_IMAGE102
in the formula
Figure 778373DEST_PATH_IMAGE103
Is a boundary of the first type and is,nis normal to the boundary of the second type,
Figure 980553DEST_PATH_IMAGE104
represents a potentialuAt the first kind boundary
Figure 839924DEST_PATH_IMAGE103
Value of above, using
Figure 245498DEST_PATH_IMAGE105
It is shown that,
Figure 232039DEST_PATH_IMAGE106
bulk current density for external circuits;
the dimension of an actual PCB or a chip packaged board in the multilayer super large scale integrated circuit is far larger than the thickness of the metal layer, so that the three-dimensional direct current field problem of the multilayer integrated circuit is simplified into a two-dimensional direct current field problem;
the field solving equation set established by the finite element method for the two-dimensional model is an equation set (3):
Figure 138992DEST_PATH_IMAGE107
in the formula (I), theI(u) In order to be a functional function,tis the thickness of the metal layer or layers,
Figure 716735DEST_PATH_IMAGE108
as a grid celleThe electrical conductivity of (a) a (b),
Figure 609604DEST_PATH_IMAGE109
as a grid celleThe potential of (a) is set to be,
Figure 101634DEST_PATH_IMAGE110
as a grid celleThe area of (a) is,
Figure 29139DEST_PATH_IMAGE111
as the density of the surface current, the current density,
Figure 715466DEST_PATH_IMAGE112
representing grid cellseThe edge of (1);
for the alternating electromagnetic field model, the three-dimensional model of the multilayer integrated circuit refers to the dielectric constant in the three-dimensional model of the electromagnetic response characteristic in the frequency domain simulation of the multilayer VLSI
Figure 95632DEST_PATH_IMAGE113
Magnetic permeability of
Figure 876506DEST_PATH_IMAGE114
Electric field intensityEMagnetic field intensityHAll the distributions of (A) and (B) are three-dimensional space coordinatesx,y,z) I.e.:
Figure 910715DEST_PATH_IMAGE115
,
Figure 17211DEST_PATH_IMAGE116
,
Figure 619094DEST_PATH_IMAGE117
，
Figure 219970DEST_PATH_IMAGE118
the function of the three-dimensional model satisfies the following equation:
Figure 856488DEST_PATH_IMAGE119
in the formulaJFor the purpose of the applied current density distribution,
Figure 133886DEST_PATH_IMAGE120
for the angular frequency simulated for the integrated circuit,
Figure 472332DEST_PATH_IMAGE121
indicating the strength of the magnetic fieldHThe degree of rotation of the screw is reduced,
Figure 126167DEST_PATH_IMAGE122
indicates the electric field intensityEThe degree of rotation of the screw is reduced,jis the unit of an imaginary number,j 2=-1；
the board size of the actual PCB or chip package in the multilayer VLSI is far larger than the metal layer spacing, the three-dimensional model of the electromagnetic response characteristics in the frequency domain simulation of the multilayer VLSI is simplified into a two-dimensional model, and the dielectric constant in the model is at the moment
Figure 617191DEST_PATH_IMAGE113
Magnetic permeability of
Figure 81802DEST_PATH_IMAGE114
Electric field intensityEMagnetic field intensityHAll the distributions are two-dimensional plane coordinates (x,y) I.e.:
Figure 923856DEST_PATH_IMAGE123
，
Figure 368000DEST_PATH_IMAGE124
，
Figure 713531DEST_PATH_IMAGE125
，
Figure 598310DEST_PATH_IMAGE126
distribution thereof andzindependent of and potential in the fielduAnd surface current densityJ sSatisfies the following conditions:
Figure 412814DEST_PATH_IMAGE127
in the formula (I), the compound is shown in the specification,
Figure 408452DEST_PATH_IMAGE128
respectively representx, y, zThe unit vector of the direction is,E zof electric field strengthzThe direction component of the light beam is,H xandH yrespectively of magnetic field strengthxAndythe direction component of the light beam is,his the metal layer spacing;
through the simplification from the three-dimensional model to the two-dimensional model, the two-dimensional finite element functional extreme value formula corresponding to the two-dimensional model is obtained as follows:
Figure 857756DEST_PATH_IMAGE129
in the formula (I), the compound is shown in the specification,
Figure 179016DEST_PATH_IMAGE131
in order to be a functional function,
Figure 464504DEST_PATH_IMAGE132
it is shown that the extreme value is taken for the functional,
Figure 14565DEST_PATH_IMAGE133
as a grid celliThe surface admittance of the first and second electrodes,
Figure 334688DEST_PATH_IMAGE134
is a boundary
Figure 813467DEST_PATH_IMAGE135
The boundary condition of the opening of (a),u kis a boundary
Figure 851831DEST_PATH_IMAGE136
The distribution of the electric potential on the upper side,
Figure 189271DEST_PATH_IMAGE137
indicating a position to the right of the boundary and infinitely close to the boundary,
Figure 114633DEST_PATH_IMAGE138
indicating a position to the left of the boundary and infinitely close to the boundary,
Figure 777695DEST_PATH_IMAGE139
representing grid cellsiThe area of (a) is,
Figure 287043DEST_PATH_IMAGE140
as a grid celliThe current density of (a) is,
Figure 162595DEST_PATH_IMAGE141
as a grid celliThe surface resistance of the glass substrate is higher than the surface resistance of the glass substrate,
Figure 457310DEST_PATH_IMAGE142
as a grid celliThe potential of (a) is set to be,kis referred to askAnd (4) a boundary.
The method can realize different particle paralleling in the coupled iterative calculation among the layers of the multilayer very large scale integrated circuit, greatly reduces the communication among the processes and the waiting time generated by synchronization, simultaneously, adopts a random dynamic allocation method of the calculation tasks, ensures that the calculation models with unequal complexity are randomly and uniformly distributed on each calculation node, and avoids the bottleneck of hard disk read-write caused by virtual memory access due to overhigh peak value memory.
A second embodiment of the partitioning method and apparatus for iteratively calculating parallel particles for interlayer coupling of an integrated circuit according to the present invention is described in detail with reference to fig. 3. The partitioning apparatus for iterative parallel particle computation in integrated circuit interlayer coupling provided in this embodiment comprises a computing unit partitioning module, a computing particle partitioning module, a parallel particle operation module,
the calculation unit division module is used for dividing the iterative calculation of the interlayer coupling of the multilayer ultra-large scale integrated circuit into three types of calculation units: a basic calculation unit, a layer-to-layer calculation unit of the integrated circuit, and an electromagnetic field and current distribution calculation unit of each layer of the integrated circuit.
The calculation particle dividing module is used for dividing the three types of calculation units into calculation particles which are not overlapped with each other.
The parallel particle division module obtains weighted CPU time of each calculation particle and total CPU time of an iteration method of integral multilayer ultra-large scale integrated circuit interlayer coupling based on one-time complete serial iterative calculation, the calculation particles are combined into different parallel particles according to the ratio of the weighted CPU time to the total CPU time, the similar parallel particles are mutually independent, and corresponding calculation task sequences can be randomly disordered;
the parallel particle operation module is used for randomly disordering the sequences of all the calculation tasks executed by the same type of parallel particles in the process of executing the parallel particles to form a new calculation task sequence, and dynamically distributing the new calculation task sequence to different calculation processes to complete the parallel calculation of the calculation tasks.
The calculation formula for calculating the weighted CPU time of the particles is as follows:
Figure 510848DEST_PATH_IMAGE143
in the formula:
Figure 523803DEST_PATH_IMAGE144
is as followsiThe weighted CPU time of each calculated grain,
Figure 937467DEST_PATH_IMAGE145
is as followsiEach calculation particle has a single calculated CPU time,
Figure 350605DEST_PATH_IMAGE146
is as followsiThe number of particle executions was counted.
The calculation formula of the total CPU time in the whole calculation process is as follows:
Figure 824311DEST_PATH_IMAGE147
wherein, in the step (A),Tfor the total CPU time of the entire calculation process,mthe number of calculation particles divided for the entire calculation program,
Figure 793404DEST_PATH_IMAGE144
is as followsiThe weighted CPU time of the particles is calculated.
And sequencing the weighted CPU time of each calculation particle according to the descending order and sequentially accumulating until the accumulated sum exceeds 90% of the total CPU time, and taking each calculation particle in the accumulated sum as a parallel particle.
Specifically, if the iterative computation of the interlayer coupling of the multilayer very large scale integrated circuit is divided into 3 computing particles of c1, c2 and c3 according to the definition of the computing particles, 3 computing particles can execute the computing task of the whole computing process; if c1 executes 500 operation tasks, c2 executes 200 operation tasks, and c3 executes 5 operation tasks; then 705 operation tasks constitute the whole operation process, which only needs 3 computation particles of c1, c2 and c 3. The whole operation process is executed by 3 computing particles of c1, c2 and c3, and each of c1, c2 and c3 comprises at least 1 independent operation (operation task).
Sorting according to the weighted CPU time obtained by each calculated particle operation, wherein if the c1 weighted CPU time is 0.1s, the c2 weighted CPU time is 100s and the c3 weighted CPU time is 0.2s, the final sorting result is c2> c3> c 1; the weighted CPU times for the 3 calculated particles add sequentially from large to small, i.e., T (c2) + T (c3) + … until the sum of times is greater than 90% of the total CPU time; if T (c2) + T (c3) > 90%, then c2, c3 are each as a parallel particle; if T (c2) > 90% of the total CPU time, then c2 is a parallel particle.
The parallel particle operation module is used for randomly disordering the sequences of all operation tasks executed by the same parallel particle to form a new operation task sequence, and distributing all operation tasks executed by the parallel particle to all processes according to the new operation task sequence to complete the parallel operation of the operation tasks.
Specifically, the way of randomly scrambling the operation task sequence is as follows:
firstly, the sequence of operation tasks
Figure 27071DEST_PATH_IMAGE148
Correspondingly generating random number sequences
Figure 30799DEST_PATH_IMAGE149
，m＝1,2,3,…,M. Then to the sequence
Figure 675407DEST_PATH_IMAGE149
The sequences are sorted from small to large, and the sorted sequences are
Figure 646643DEST_PATH_IMAGE150
. Finally, generating new non-repeated operation task sequence
Figure 667688DEST_PATH_IMAGE151
，
Figure 791502DEST_PATH_IMAGE152
Is composed of
Figure 357744DEST_PATH_IMAGE153
In that
Figure 301429DEST_PATH_IMAGE154
Of (c) is used.
The key point is to make all the operation tasks in the parallel particles in sequence
Figure 126166DEST_PATH_IMAGE155
Randomly disorganized to generate new non-repetitive operation task sequence
Figure 356683DEST_PATH_IMAGE156
And then distributing the operation tasks according to the sequence, namely equivalently distributing the original operation tasks randomly, wherein the random distribution strategy is characterized in that a random distribution scheme can completely disturb the distribution sequence of all the operation tasks, so that the sum of the peak value memory occupied by the tasks operated by all the operation nodes at the same time is determined by the average value of the process number and the peak value memory occupied by all the models (calculation particles) rather than the maximum value.
And the main process distributes all the operation tasks required to be executed by the parallel particles to all the processes including the main process according to the formed new calculation task sequence, and completes the parallel operation of all the operation tasks executed by the parallel particles.
In addition, if a certain operation task in the parallel particles is distributed to a process, a mark file which is used for indicating that the operation task is already distributed to the operation task is generated; when applying for distributing a certain calculation task, the other process tries to generate a mark file of the calculation task, and automatically applies for distributing the next calculation task by the other process under the condition that the mark file exists.
In the multi-process parallel operation process, the chances of allocating a certain operation task to each process are equal, if no measure is taken, multiple processes may be allocated to the same operation task, and the waste of operation resources is caused, so that some measure must be taken, and all operation tasks are uniquely allocated to a certain process. The simplest and most intuitive measure for achieving this is to assign a task a time stamp, i.e. a task is assigned to a process at the same time as it is marked so that other processes are no longer assigned the task. However, because the variables of each process are generally independent of each other during parallel operation, the operation tasks are asymmetric, the operation states of each process are different, and information distributed by any process through the variable marking task cannot be immediately transmitted to other processes, an external explicit marking method is needed to be adopted so that all processes can obtain the information once the operation tasks are marked. Therefore, if the operation task in the parallel particles is distributed to the process, the mark file of the operation task is immediately generated; when a process applies for distributing a certain operation task, the process will try to generate a mark file of the operation task, if the mark file exists, the operation task is indicated to be distributed, and the process will automatically apply for distributing the next operation task.
The specific implementation steps for realizing the correct allocation of the operation tasks by utilizing the marker files are as follows:
step A1, a process applies for distributioniAn arithmetic task;
step A2, judgmentiSign file of individual operation taskFiIf the current state does not exist, jumping to the step A8, and if the current state does not exist, jumping to the step A3;
step A3, judging the mark fileFiWhether the lock is locked or not, jumping to the step A8 if the lock is locked, and jumping to the step A4 if the lock is not locked;
step A4, locking the logo fileFi；
Step A5, generating a logo fileFi；
Step A6, marking fileFiUnlocking;
step A7, completing the first stepiCalculating the operation tasks;
step A8, judging whether all the operation tasks in the parallel particles are completed or not, if not, determining whether all the operation tasks in the parallel particles are completedi＝i+1 and returning to step a1, if finished, jumping to step a 9;
all the operation tasks required to be executed by the parallel particles are all distributed to all the processes, and the distribution of the parallel particles is finished; it returns to executing all the computational tasks that the other parallel grains need to perform to distribute their respective execution.
Further, the basic computing unit includes two types: the first kind of basic calculation unit is used for calculating the field generated by the current in the simple polygon of the integrated circuit in any simple polygon on other layers of the integrated circuit by utilizing a dyadic Green function, and the second kind of basic calculation unit is used for calculating the grid unit in the single-layer two-dimensional finite element calculation of the integrated circuit; the calculation of the grid unit in the integrated circuit single-layer two-dimensional finite element calculation comprises the following steps: calculating the area of the grid unit, calculating the shape function of the grid unit, calculating the finite element rigidity matrix of the grid unit, and calculating the field intensity and the current density of any point in the grid unit.
Further, as shown in fig. 2, the first-class basic computing unit specifically operates as follows:
first, as shown in fig. 4, calculating an electric field generated by a point current source at a field point, where an electric field expression generated by the point current source at the field point is a special analytical expression formed according to a special structure of an integrated circuit layer, and a specific expression of the analytical expression is as follows: aiming at the frequency domain electromagnetic field of the multilayer integrated circuit layout, the electric field intensity generated by a point source at any layer field point is calculated by adopting a dyadic Green function, and the electric field intensity of nine azimuths of any point at any layer of the multilayer integrated circuit layout can be solved through the following formula to represent the electric field intensity.
The electric field generated by the point current source at the field point is expressed as:
Figure 343094DEST_PATH_IMAGE157
Figure 39654DEST_PATH_IMAGE158
Figure 887656DEST_PATH_IMAGE159
Figure 720483DEST_PATH_IMAGE160
Figure 143374DEST_PATH_IMAGE161
Figure 45339DEST_PATH_IMAGE162
Figure 211879DEST_PATH_IMAGE163
Figure 164791DEST_PATH_IMAGE164
wherein the content of the first and second substances,
Figure 243737DEST_PATH_IMAGE165
Figure 649310DEST_PATH_IMAGE167
Figure 353961DEST_PATH_IMAGE169
Figure 147998DEST_PATH_IMAGE170
Figure 912692DEST_PATH_IMAGE171
Figure 805561DEST_PATH_IMAGE172
iis the unit of an imaginary number,i 2=-1；
Figure 799056DEST_PATH_IMAGE173
representing a Bessel function of order 0;
Figure 726561DEST_PATH_IMAGE174
representing a Bessel function of order 1;
Figure 662156DEST_PATH_IMAGE175
expressed as a function of the Bessel integral coefficient,
Figure 760431DEST_PATH_IMAGE176
；x, y, zthe coordinates of the field points are represented,
Figure 72464DEST_PATH_IMAGE177
,
Figure 854475DEST_PATH_IMAGE178
,
Figure 446124DEST_PATH_IMAGE179
representing source point coordinates; angular frequency
Figure 48007DEST_PATH_IMAGE180
，
Figure 898151DEST_PATH_IMAGE181
Represents a frequency;
Figure 52445DEST_PATH_IMAGE182
indicating that the site is at the second
Figure 329843DEST_PATH_IMAGE182
A layer of a material selected from the group consisting of,
Figure 700913DEST_PATH_IMAGE183
is as follows
Figure 354748DEST_PATH_IMAGE182
At layer boundarieszCoordinates;
Figure 360619DEST_PATH_IMAGE184
,
Figure 808918DEST_PATH_IMAGE185
respectively represent
Figure 667283DEST_PATH_IMAGE182
The number of complex waves in the horizontal and vertical directions of the layer;
Figure 124810DEST_PATH_IMAGE051
respectively represent
Figure 851764DEST_PATH_IMAGE182
A layer horizontal dielectric constant, a vertical dielectric constant;
Figure 579286DEST_PATH_IMAGE052
,
Figure 908637DEST_PATH_IMAGE053
respectively representlHorizontal magnetic conductivity and vertical magnetic conductivity of the layer;
Figure 920586DEST_PATH_IMAGE186
is shown aslThe anisotropy coefficient of the layer;
Figure 651782DEST_PATH_IMAGE187
,
Figure 959660DEST_PATH_IMAGE188
respectively representlIntegral coefficients of complex wave numbers of the horizontal and vertical layers;
Figure 510727DEST_PATH_IMAGE189
respectively representlThe undetermined coefficient of a layer,A l , B l the following linear equation is solved:
Figure 60788DEST_PATH_IMAGE058
T1is 2n×2nThe complex number matrix of (a) is,
Figure 380911DEST_PATH_IMAGE059
is of length 2nA complex vector of (a);
Figure 341914DEST_PATH_IMAGE190
Figure 363965DEST_PATH_IMAGE062
Figure 701406DEST_PATH_IMAGE191
Figure 876035DEST_PATH_IMAGE192
Figure 24251DEST_PATH_IMAGE066
the following linear equation is solved:
Figure 549910DEST_PATH_IMAGE067
T2is 2n×2nThe complex number matrix of (a) is,
Figure 943238DEST_PATH_IMAGE068
is of length 2nA complex vector of (a);
Figure 972374DEST_PATH_IMAGE193
Figure 540759DEST_PATH_IMAGE072
Figure 38868DEST_PATH_IMAGE074
Figure 983690DEST_PATH_IMAGE075
the following linear equation is solved:
Figure 382179DEST_PATH_IMAGE076
T3is 2n×2nThe complex number matrix of (a) is,
Figure 121465DEST_PATH_IMAGE077
is of length 2nA complex vector of (a);
Figure 356137DEST_PATH_IMAGE078
Figure 855383DEST_PATH_IMAGE080
Figure 859111DEST_PATH_IMAGE082
Figure 21495DEST_PATH_IMAGE194
Figure 743464DEST_PATH_IMAGE085
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 764509DEST_PATH_IMAGE086
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 639055DEST_PATH_IMAGE087
to representxOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzA component;
Figure 720144DEST_PATH_IMAGE088
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 178676DEST_PATH_IMAGE089
to representyOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 3412DEST_PATH_IMAGE090
to representyOriented electric dipole in the second placelSaid field point generation of a layerOf said electric fieldzA component;
Figure 981733DEST_PATH_IMAGE091
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerxA component;
Figure 718876DEST_PATH_IMAGE092
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layeryA component;
Figure 149857DEST_PATH_IMAGE093
to representzOriented electric dipole in the second placelOf said electric field generated by said field points of the layerzAnd (4) components.
The current sources of the multi-layer integrated circuit are distributed in a layered manner, namely the current density distributed on each metal layer of the integrated circuit layout with a complex shape is only equal to that of the current sourcexAndythe axial direction is related tozAxial direction independence, current density distribution of onlyx，yAs a function of (c).
And secondly, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the method comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure DEST_PATH_IMAGE195
；
wherein the content of the first and second substances,E(x,y,z) At any point in space for the current source in the two-dimensional plane Sx,y,z) The field that is generated is,
Figure 573359DEST_PATH_IMAGE196
is the twoAny position in the dimension S: (u,v) At any point in space (x,y,z) The expression of the dyadic green function of the generated field,
Figure 406186DEST_PATH_IMAGE096
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure 829077DEST_PATH_IMAGE097
is the weight factor corresponding to the gaussian integral point;
and thirdly, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields.
Further, the integrated circuit layer-layer computation unit includes: combining the first type of basic calculation units, and calculating fields generated by currents distributed on the complex integrated circuit layout filled by the simple polygons on the complex layouts of other layers of the integrated circuit based on the field linear superposition principle; the electromagnetic field and current distribution calculating unit of each layer of the integrated circuit comprises: and combining the second type of basic computing units, taking the influence of other layers on the source layer to be computed as an additional source item, and computing the electromagnetic field and current distribution of the source layer to be computed by adopting a two-dimensional finite element method.
Further, the specific method for calculating the two-dimensional finite element comprises the following steps:
for the direct current electric field model, the three-dimensional model of the multilayer integrated circuit refers to the conductivity in the direct current electric field model
Figure 498087DEST_PATH_IMAGE098
Potential of the electrodeuAll the distributions of (A) and (B) are three-dimensional space coordinatesx,y,z) I.e.:
Figure DEST_PATH_IMAGE197
，
Figure 195784DEST_PATH_IMAGE198
the function of the three-dimensional model satisfies the following equation (1):
Figure DEST_PATH_IMAGE199
in the equation (1),
and boundary condition (2):
Figure 929123DEST_PATH_IMAGE200
in the formula
Figure 522915DEST_PATH_IMAGE103
Is a boundary of the first type and is,nis normal to the boundary of the second type,
Figure 679221DEST_PATH_IMAGE104
represents a potentialuAt the first kind boundary
Figure 383872DEST_PATH_IMAGE103
Value of above, using
Figure 925712DEST_PATH_IMAGE105
It is shown that,
Figure 942603DEST_PATH_IMAGE106
bulk current density for external circuits;
the dimension of an actual PCB or a chip packaged board in the multilayer super large scale integrated circuit is far larger than the thickness of the metal layer, so that the three-dimensional direct current field problem of the multilayer integrated circuit is simplified into a two-dimensional direct current field problem;
the field solving equation set established by the finite element method for the two-dimensional model is an equation set (3):
Figure 835472DEST_PATH_IMAGE202
in the formula (I), theI(u) In order to be a functional function,tis the thickness of the metal layer or layers,
Figure 78235DEST_PATH_IMAGE108
as a grid celleThe electrical conductivity of (a) a (b),
Figure 490893DEST_PATH_IMAGE109
as a grid celleThe potential of (a) is set to be,
Figure 426488DEST_PATH_IMAGE110
as a grid celleThe area of (a) is,
Figure 541074DEST_PATH_IMAGE111
as the density of the surface current, the current density,
Figure 102375DEST_PATH_IMAGE112
representing grid cellseThe edge of (1);
for the alternating electromagnetic field model, the three-dimensional model of the multilayer integrated circuit refers to the dielectric constant in the three-dimensional model of the electromagnetic response characteristic in the frequency domain simulation of the multilayer VLSI
Figure 353227DEST_PATH_IMAGE204
Magnetic permeability of
Figure 459724DEST_PATH_IMAGE114
Electric field intensityEMagnetic field intensityHAll the distributions of (A) and (B) are three-dimensional space coordinatesx,y,z) I.e.:
Figure DEST_PATH_IMAGE205
,
Figure 874656DEST_PATH_IMAGE206
,
Figure DEST_PATH_IMAGE207
，
Figure 508156DEST_PATH_IMAGE118
the function of the three-dimensional model satisfies the following equation:
Figure 144673DEST_PATH_IMAGE119
in the formulaJFor the purpose of the applied current density distribution,
Figure 156492DEST_PATH_IMAGE120
for the angular frequency simulated for the integrated circuit,
Figure 261982DEST_PATH_IMAGE121
indicating the strength of the magnetic fieldHThe degree of rotation of the screw is reduced,
Figure 650238DEST_PATH_IMAGE122
indicates the electric field intensityEThe degree of rotation of the screw is reduced,jis the unit of an imaginary number,j 2=-1；
the board size of the actual PCB or chip package in the multilayer VLSI is far larger than the metal layer spacing, the three-dimensional model of the electromagnetic response characteristics in the frequency domain simulation of the multilayer VLSI is simplified into a two-dimensional model, and the dielectric constant in the model is at the moment
Figure 875683DEST_PATH_IMAGE113
Magnetic permeability of
Figure 838829DEST_PATH_IMAGE114
Electric field intensityEMagnetic field intensityHAll the distributions are two-dimensional plane coordinates (x,y) I.e.:
Figure 415304DEST_PATH_IMAGE208
，
Figure DEST_PATH_IMAGE209
，
Figure 889141DEST_PATH_IMAGE210
，
Figure DEST_PATH_IMAGE211
distribution thereof andzindependent of and potential in the fielduAnd surface current densityJ sSatisfies the following conditions:
Figure 31410DEST_PATH_IMAGE212
in the formula (I), the compound is shown in the specification,
Figure 902807DEST_PATH_IMAGE128
respectively representx, y, zThe unit vector of the direction is,E zof electric field strengthzThe direction component of the light beam is,H xandH yrespectively of magnetic field strengthxAndythe direction component of the light beam is,his the metal layer spacing;
through the simplification from the three-dimensional model to the two-dimensional model, the two-dimensional finite element functional extreme value formula corresponding to the two-dimensional model is obtained as follows:
Figure DEST_PATH_IMAGE213
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE215
in order to be a functional function,
Figure 45207DEST_PATH_IMAGE132
it is shown that the extreme value is taken for the functional,
Figure 40844DEST_PATH_IMAGE216
as a grid celliThe surface admittance of the first and second electrodes,
Figure 240882DEST_PATH_IMAGE134
is a boundary
Figure 280251DEST_PATH_IMAGE135
The boundary condition of the opening of (a),u kis a boundary
Figure 831318DEST_PATH_IMAGE136
The distribution of the electric potential on the upper side,
Figure 381379DEST_PATH_IMAGE137
indicating a position to the right of the boundary and infinitely close to the boundary,
Figure 701502DEST_PATH_IMAGE138
indicating a position to the left of the boundary and infinitely close to the boundary,
Figure 928084DEST_PATH_IMAGE139
representing grid cellsiThe area of (a) is,
Figure 206925DEST_PATH_IMAGE140
as a grid celliThe current density of (a) is,
Figure 809945DEST_PATH_IMAGE141
as a grid celliThe surface resistance of the glass substrate is higher than the surface resistance of the glass substrate,
Figure 532045DEST_PATH_IMAGE142
as a grid celliThe potential of (a) is set to be,kis referred to askAnd (4) a boundary.
The device can realize different particle parallels in the coupled iterative computation among the layers of the multilayer very large scale integrated circuit, greatly reduces the communication among the processes and the waiting time generated by synchronization, simultaneously, adopts a random dynamic allocation method of computation tasks, ensures that computation models with unequal complexity are randomly and uniformly distributed on each computation node, and avoids the bottleneck of hard disk read-write caused by virtual memory access due to overhigh peak memory.
The above description is only for the specific embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.

Claims (7)

1. A partitioning method for iterative computation parallel particles of integrated circuit interlayer coupling is characterized by comprising the following steps:
s1, dividing the iterative computation of the interlayer coupling of the multilayer ultra-large scale integrated circuit into three types of computation units: a basic calculation unit, a layer-to-layer calculation unit of an integrated circuit, and an electromagnetic field and current distribution calculation unit of each layer of the integrated circuit;
the basic computing unit includes two types: the first kind of basic calculation unit is used for calculating the field generated by the current in the simple polygon of the integrated circuit in any simple polygon on other layers of the integrated circuit by utilizing a dyadic Green function, and the second kind of basic calculation unit is used for calculating the grid unit in the single-layer two-dimensional finite element calculation of the integrated circuit; the calculation of the grid unit in the integrated circuit single-layer two-dimensional finite element calculation comprises the following steps: calculating the area of the grid unit, calculating a shape function of the grid unit, calculating a finite element rigidity matrix of the grid unit, and calculating the field intensity and the current density of any point in the grid unit;
the layer-to-layer computation unit of the integrated circuit comprises: combining the first type of basic calculation units, and calculating fields generated by currents distributed on the complex integrated circuit layout filled by the simple polygons on the complex layouts of other layers of the integrated circuit based on the field linear superposition principle; the electromagnetic field and current distribution calculating unit of each layer of the integrated circuit comprises: combining the second type of basic computing units, taking the influence of other layers on the source layer to be computed as an additional source item, and computing the electromagnetic field and current distribution of the source layer to be computed by adopting a two-dimensional finite element method;
s2, dividing iterative computation of integrated circuit interlayer coupling into non-overlapping computation particles according to the three types of computation cells, wherein the computation particles are one or more computation cells executing all independent operations of the same type;
s3, obtaining the weighted CPU time and the total CPU time of each calculation particle based on one-time complete serial iterative calculation, and combining the calculation particles into different parallel particles according to the proportion of the weighted CPU time;
and S4, classifying the parallel particles, wherein the similar parallel particles are mutually independent, the corresponding calculation task sequences can be randomly disordered, in the process of executing the parallel particles, the sequences of all calculation tasks executed by the similar parallel particles are randomly disordered to form a new calculation task sequence, and the new calculation task sequence is dynamically distributed to different calculation processes to complete the parallel calculation of the calculation tasks.
2. The method of partitioning iterative computation parallel particles of integrated circuit inter-layer coupling according to claim 1, wherein said first class of basic computation elements are specifically operated as:
the method comprises the steps of firstly, calculating an electric field generated by a point current source at a field point, wherein the electric field generated by the point current source at the field point is a special analytical expression formed according to a special layered structure of an integrated circuit, and the current sources of a multilayer integrated circuit are layered, namely the current density distributed on each metal layer of an integrated circuit layout with a complex shape is only equal to that of each metal layerxAndyis related tozIndependently, the current density distribution is onlyx, yA function of (a);
and secondly, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the method comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure DEST_PATH_IMAGE002
；
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE004
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure DEST_PATH_IMAGE006
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure DEST_PATH_IMAGE008
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure DEST_PATH_IMAGE010
is the weight factor corresponding to the gaussian integral point;
and thirdly, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields.
3. The method of partitioning iterative computation parallel granularity of integrated circuit layer-to-layer coupling according to claim 1, wherein said computing a weighted CPU time of the granularity is represented by the formula:
Figure DEST_PATH_IMAGE012
in the formula:
Figure DEST_PATH_IMAGE014
is as followsiThe weighted CPU time of each calculated grain,
Figure DEST_PATH_IMAGE016
is as followsiEach calculation particle has a single calculated CPU time,
Figure DEST_PATH_IMAGE018
is as followsiA counting particleThe number of executions.
4. The method of partitioning iterative computation of parallel particles of integrated circuit layer-to-layer coupling as recited in claim 3, wherein the total CPU time over the entire computation process is calculated by the formula:
Figure DEST_PATH_IMAGE020
wherein, in the step (A),Tfor the total CPU time of the entire calculation process,mthe number of calculation particles divided for the entire calculation program,
Figure 149273DEST_PATH_IMAGE014
is as followsiThe weighted CPU time of the particles is calculated.
5. The method of partitioning iterative computation parallel grains of integrated circuit layer coupling as recited in claim 4, wherein weighted CPU times for each compute grain are sorted in descending order and accumulated sequentially until an accumulated sum exceeds 90% of said total CPU time, each compute grain in said accumulated sum being treated as a parallel grain.
6. The device for partitioning iterative computation parallel particles coupled among integrated circuit layers is characterized by comprising a computing unit partitioning module, a computing particle partitioning module, a parallel particle partitioning module and a parallel particle operation module,
the calculation unit division module is used for dividing the iterative calculation of the interlayer coupling of the multilayer ultra-large scale integrated circuit into three types of calculation units: a basic calculation unit, a layer-to-layer calculation unit of an integrated circuit, and an electromagnetic field and current distribution calculation unit of each layer of the integrated circuit;
the basic computing unit includes two types: the first kind of basic calculation unit is used for calculating the field generated by the current in the simple polygon of the integrated circuit in any simple polygon on other layers of the integrated circuit by utilizing a dyadic Green function, and the second kind of basic calculation unit is used for calculating the grid unit in the single-layer two-dimensional finite element calculation of the integrated circuit; the calculation of the grid unit in the integrated circuit single-layer two-dimensional finite element calculation comprises the following steps: calculating the area of the grid unit, calculating a shape function of the grid unit, calculating a finite element rigidity matrix of the grid unit, and calculating the field intensity and the current density of any point in the grid unit;
the layer-to-layer computation unit of the integrated circuit comprises: combining the first type of basic calculation units, and calculating fields generated by currents distributed on the complex integrated circuit layout filled by the simple polygons on the complex layouts of other layers of the integrated circuit based on the field linear superposition principle; the electromagnetic field and current distribution calculating unit of each layer of the integrated circuit comprises: combining the second type of basic computing units, taking the influence of other layers on the source layer to be computed as an additional source item, and computing the electromagnetic field and current distribution of the source layer to be computed by adopting a two-dimensional finite element method;
the calculation particle dividing module is used for dividing the three types of calculation units into calculation particles which are not overlapped with each other;
the parallel particle division module obtains weighted CPU time of each calculation particle and total CPU time of an iteration method of integral multilayer ultra-large scale integrated circuit interlayer coupling based on one-time complete serial iterative calculation, the calculation particles are combined into different parallel particles according to the ratio of the weighted CPU time to the total CPU time, the similar parallel particles are mutually independent, and corresponding calculation task sequences can be randomly disordered;
the parallel particle operation module is used for randomly disordering the sequences of all the calculation tasks executed by the same type of parallel particles in the process of executing the parallel particles to form a new calculation task sequence, and dynamically distributing the new calculation task sequence to different calculation processes to complete the parallel calculation of the calculation tasks.
7. The apparatus for partitioning parallel particles for iterative computation of coupling between layers of an integrated circuit according to claim 6, wherein said first class of basic computation elements are specifically operated as:
first, calculate the electric field generated by the point current source at the field pointThe electric field expression of the point current source generated at the field point is a special analytical expression formed according to the layered special structure of the integrated circuit, and the current sources of the multilayer integrated circuit are distributed in a layered mode, namely the current density distributed on each metal layer of the integrated circuit layout with a complex shape is only equal to that of the integrated circuit layout with a complex shapexAndyis related tozIndependently, the current density distribution is onlyx, yA function of (a);
and secondly, taking an electric field expression generated by the point current source at the field point as an integrand function of two-dimensional Gaussian integration, and calculating fields generated by the surface current source of the simple-shaped polygon at the same position based on a linear superposition principle of the fields, wherein the method comprises the following steps: the field generated by the current source in the two-dimensional plane S at any point in space can be calculated by the two-dimensional gaussian integral:
Figure 4097DEST_PATH_IMAGE002
；
wherein the content of the first and second substances,
Figure 721517DEST_PATH_IMAGE004
at any point in space for the current source within the two-dimensional plane S (x,y,z) The field that is generated is,
Figure 54409DEST_PATH_IMAGE006
is an arbitrary position within the two-dimensional surface S: (u,v) At any point in space (a)x,y,z) The expression of the field that is generated,
Figure 806465DEST_PATH_IMAGE008
representing a gaussian integration point corresponding to a two-dimensional gaussian integration in the two-dimensional plane S,p,qrespectively representu,vIn the first directionpA first, aqThe number of the Gaussian integration points is equal to the total number of the points,
Figure DEST_PATH_IMAGE021
is the weight factor corresponding to the gaussian integral point;
and thirdly, calculating fields generated by the current on the simple-shaped polygon at different positions of other layers of the integrated circuit, and determining the fields generated by the current on the simple-shaped polygon divided on the layout of other layers of the integrated circuit based on the linear superposition principle of the fields.
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