JPH1011421A - Simultaneous linear equation solution for parallel arithmetic processing - Google Patents

Abstract

PROBLEM TO BE SOLVED: To perform an analysis of a large scale in a short calculation time by calculating every area via each relevant processor based on the coefficient matrix concerning every area and the connection boundary information on divided areas and calculating a solution of an entire analysis area. SOLUTION: A solver part 5 inputs the coefficient matrices A14 to A16 and the right side vectors b17 to b19 which are produced from the areas 1 to 3 managed by processors 1 to 3 respectively in response to the area division. The part 5 also inputs the connection boundary information 13 on the areas 1 to 3 of processors 1 to 3 which are produced when an area is divided. Then the processors 1 to 3 solve the simultaneous linear equations of their areas 1 to 3 respectively and perform the communication 20 of data with other processor 1 to 3 having the nodes of a connection boundary 12 against the value concerning these nodes. Furthermore, the part 5 carries out the communication shared by all processors against the value which is necessary for convergence of the matrix calculation. In such a processing procedure, the processors 1 to 3 output the answers x22 to x24 of their relevant area 1 to 3 respectively.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for solving simultaneous linear equations in a numerical analysis for calculating an entire analysis area using a mesh, and more particularly, to a method for reducing a calculation time by using a parallel computer having a plurality of arithmetic processing units. The present invention relates to a method for solving simultaneous linear equations of parallel arithmetic processing for realizing shortening and large-scale analysis.

[0002]

2. Description of the Related Art Conventional simultaneous linear equation solving methods using parallel arithmetic processing are described in, for example, "Introduction to Parallel Computing Design and Analysis of Algorithm", Chapter 11 (published by Benjamin / Coming Publishing Company, 1994). In general, a matrix composed of simultaneous linear equations created from the entire analysis domain is calculated by dividing the matrix by a simultaneous linear equation solver (hereinafter referred to as a solver). It did not correspond.

[0003]

In the above technique, when the matrix is divided, the solver section divides the matrix created from the entire analysis area, and does not consider the division of the analysis area. Therefore, it has been difficult to apply the method to the distributed processing by region division, which is one of the effective methods of the numerical solution by the parallel operation processing. Further, it takes time to divide the matrix in the solver unit and to create a shared list of the divided elements for each processor. Further, when a single processor has a matrix created from the entire analysis area, there is a problem that the calculation scale is greatly limited by the amount of memory of the processor.

A first object of the present invention is to realize, using a parallel computer, a simultaneous linear equation solution method by parallel arithmetic processing corresponding to a processing distribution method by area division.

[0005] A second object of the present invention is to realize a simultaneous linear equation solution method of a parallel operation process that can perform a large-scale analysis in a short time by using a parallel computer.

[0006]

SUMMARY OF THE INVENTION A first and second object of the present invention is to provide a numerical analysis method for calculating an analysis area using a mesh, wherein the analysis area is divided into a plurality of areas, and a processor is provided for each area. It has the function of communicating data between processors in charge of each area with respect to the value of the shared node on the boundary of the allocation and division area, and the data necessary for convergence of matrix calculation obtained from the calculation value in each area On the other hand, by having a function of sharing data among all processors, each processor calculates a responsible area from the coefficient matrix for each area and the connection boundary information of the divided areas, and obtains a solution for the entire analysis area. Is achieved by

A second object of the present invention is to manage a data communication function between processors for a value relating to a shared node and a data sharing function between all processors for data required for convergence of matrix calculation, and to analyze each data. This is achieved by providing a separate processor for collecting and distributing data to the processor in charge of the area.

In a numerical analysis method for calculating an analysis area using a mesh, the analysis area is divided into a plurality of areas, a processor is assigned to each area, and each area is assigned a value relating to a shared node on the boundary of the divided area. Has the function of communicating data between processors in charge of each area, and the function of sharing data among all processors for data necessary for convergence of matrix calculation obtained from calculation values in each area. From the coefficient matrix relating to the region and the connection boundary information of the divided region, the simultaneous linear equation solution for each region can be calculated in parallel by matrix division corresponding to the divided region. A processing distribution method applied to region division, which is one of the effective methods, becomes possible. Further, since the division method of the area division can be used as it is for the division method of the matrix, and the connection boundary list at the time of division can be used as it is, the processing of the matrix division in the solver unit and the creation of a shared list of the elements of the divided matrix The processing is eliminated, and the calculation time and the required memory can be reduced.

Further, by separately providing a processor for collecting and distributing data with respect to the value relating to the shared node and the value required for the convergence of the matrix calculation, the operation of the collected data, the synchronization of each processor, and the efficiency of the processor are improved. Data communication processing becomes possible.

[0010]

DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below with reference to the drawings.

The simultaneous linear equation solving method described here is defined as A
A vector x is obtained by inputting a matrix A and a vector b of an equation given by x = b.

FIG. 1 shows a processing flow of the simultaneous linear equation solving unit when the calculation of the whole analysis area 1 is performed using a single processor. The solver unit inputs a coefficient matrix A2 and a right side vector b4 created from the entire analysis area. When the number of nodes in the entire analysis area is N, the coefficient matrix A2 is an N × N-order square matrix, and the right side b4 is an N-order vector. The simultaneous linear equation solution is calculated from these input data, and the answer x6 is output. The vector x6 here is an N-order vector.

FIG. 2 shows the processing flow of the solver unit when the input matrix is divided and the simultaneous linear equation solution is calculated in parallel using a plurality of processors, together with its configuration. This is the method for solving simultaneous linear equations in general parallel arithmetic processing. The solver section includes a coefficient matrix A2 created from the entire analysis area and a right side vector b4.
Enter When the number of nodes in the entire analysis area is N, the coefficient matrix A2 is an N × N-order square matrix, and the right side b4 is an N-order vector. Next, processing 7 for dividing the input coefficient matrix A2 and the right-hand side vector b4 into a plurality of parts is performed in order to distribute and calculate by a plurality of processors. Further, a shared list 8 of the overlapping part of the matrix elements is created and prepared by the process 7 for each processor. From the matrix divided for each of these parts and the shared list, communication is performed between the processors as necessary to execute the calculation, and the entire answer x6 is output. The vector x6 here is an N-order vector.

FIG. 3 shows the flow of the processing of the solver unit in the simultaneous linear equation solution method of the parallel operation processing according to the present invention. Here, a case will be described as an example where the entire analysis area 1 is divided into three areas 9-11 and calculation is performed using three processors. In this method, the solver unit inputs a coefficient matrix A14-16 and a right-hand side vector b17-19 created from an area assigned to each processor in accordance with the area division.
The number of nodes of the entire analysis region is N, and the region 9-
Assuming that the number of nodes of the eleventh node is n1, n2, and n3, the coefficient matrix A14 input to the processor 1 is n1 ×
This is an n1 order square matrix, and the right side b17 is an n1 order vector. Similarly, processor 2, processor 3
, The matrices are of order n2 and n3, respectively. Further, the matrix solver unit inputs the connection boundary information 13 created for each region at the time of region division and owned by each processor. Each processor solves a system of linear equations in a region in which it is in charge, and performs data communication 20 with other processors sharing the node with respect to a value related to the node of the connection boundary 12. In addition, communication 21 is performed in which all processors share a value for a value required for convergence of matrix calculation, which is obtained from a value obtained by calculation of each area. Through the above processing, each processor outputs the answer x22-24 of the assigned area. Here, x is processor 1, processor 2,
The vectors are n1, n2, and n3 order vectors corresponding to the processor 3, respectively.

FIG. 4 shows the flow of the processing of the solver unit in the simultaneous linear equation solving method of the parallel operation processing according to another embodiment of the present invention, together with its configuration. Here, similar to the above embodiment,
An example in which the entire analysis area is divided into three areas and calculation is performed using four processors will be described. Here, the processor 1 collects 25, processes, and distributes the boundary node data 2
6, collection of values obtained by calculation of each area 27, processing,
Provided for performing distribution 28. The solver unit corresponds to the area division, and the coefficient matrix A14-16 created from the area in charge of each processor and the right side vector b
Enter 17-19. The number of nodes in the entire analysis region is N, and the number of nodes in the region 9-11 divided into three is n1,
Assuming that n2 and n3, the coefficient matrix A14 input to the processor 2 is an n1 × n1 order square matrix, and the right side b17 is an n1 order vector. Similarly, the processors 3 and 4 have the n2 order and the n3 order, respectively. In addition, the solver unit inputs connection boundary information 13 created for each region and divided by each processor and for each region. Each processor solves a system of linear equations in its area,
Regarding the value related to the node on the connection boundary, for example, when the contact point of the connection boundary of the area in charge of the processor 2 and the contact point of the connection boundary of the area in charge of the processor 4 are shared, the processor 2 and the processor 4 are connected. The data relating to the boundary node is transferred to the processor 1. The processor 1 performs processing as soon as the data is collected 25, and returns 26 the processed data to the processors 2 and 4. Further, with respect to the values required for the convergence of the matrix calculation, which are obtained from the values obtained by the calculation of the areas, data is collected from all processors in charge of each area.
7. After that, data processing is performed, and the processed data is returned 28 to all processors. By the calculation using the data communication described above, each processor obtains the answer x22-24 of the responsible area.
Is output. Here, x is n1, n2, n corresponding to the processor 2, the processor 3, and the processor 4, respectively.
It becomes a tertiary vector.

[0016]

According to the simultaneous linear equation solution method of the present invention, a large-scale problem can be solved in a short time by load distribution by parallel processing. Can be calculated.

Further, it becomes possible to divide a matrix corresponding to the division of the analysis region, and it is possible to solve simultaneous linear equations by a parallel operation process from the matrix of each region and the connection boundary information of the region division. Accordingly, there is no need to perform a process of dividing the matrix of the entire analysis region by the matrix solver unit and create a matrix division list for each processor, so that it is possible to reduce the memory and time required for calculation.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram of a process of a solver unit when calculating an entire analysis area using a single processor.

FIG. 2 is an explanatory diagram of a process of a solver unit of a simultaneous linear equation solution method of general parallel operation processing using a parallel computer.

FIG. 3 is an explanatory diagram of a process of a solver unit of the simultaneous linear equation solution method of the parallel operation processing according to the embodiment of the present invention.

FIG. 4 is an explanatory diagram of a process of a solver unit of a simultaneous linear equation solution method of parallel operation processing according to another embodiment of the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Analysis area, 2 ... N * N order coefficient matrix, 3 ... Solution vector to be searched, 4 ... Right side vector, 5 ... Solver part, 6
... solution of the whole analysis area, 7 ... matrix division processing and element sharing list creation, 8 ... element sharing list, 9, 10, 1
1 ... area, 12 ... connection boundary, 13 ... connection boundary information, 14
... N1 × n1 order coefficient matrix, 15 ... n2 × n2 order coefficient matrix, 20 ... value communication related to boundary nodes, 2
1. Sharing processing of values obtained in each area, 22, 23, 24
… Solution of the domain.

 ──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Masayuki Kaiho 502, Kandachicho, Tsuchiura-shi, Ibaraki Pref.

Claims (1)

[Claims] In a numerical analysis method for calculating an analysis area using a mesh, an analysis area is divided into a plurality of areas, a processor is assigned to each area, and a value relating to a shared node on a boundary of the divided area is determined. By having a function to communicate data between processors in charge of each area, and a function to share data among all processors for data necessary for convergence of matrix calculation obtained from calculated values in each area A simultaneous linear equation solving method for parallel arithmetic processing, wherein each processor calculates a responsible area from a coefficient matrix relating to an individual area and connection boundary information of a divided area to obtain a solution for the entire analysis area.