JP2000048006A - High speed simultaneous linear equations solving system, its initial value generation device, simultaneous linear equations solving method, and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To shorten simulation time by generating an initial vector capable of reducing iteration frequency required up to the solution of simultaneous linear equations. SOLUTION: A connection contact weight information processing part 1 finds out the weight of each contact from contact connection information stored in a contact connection information storing part and contact coordinates stored in a contact coordinate storing part by using a weight calculation part and stores the weight in a connection contact weight information storing part. An interpolation calculation part stores an interpolation result in each component based on time stored in a time storing part, a vector stored in a vector storing part and time inputted to a time input part in the vector storing part. A weight addition part stores a correcting calculation result based on the vectors stored in the vector storing part, the weight set of contacts stored in the connection contact weight information storing part, an acceleration coefficient stored in an acceleration coefficient storing part 4, and contact connection information stored in the contact connection information storing part 12 in the vector storing part. An iteration method calculation part 9 finds out a solution by using a coefficient matrix inputted to a coefficient matrix input part 7, a right side vector inputted to a right side vector input part 8 and an initial vector stored in the vector storing part.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system for performing simultaneous calculation of simultaneous linear equations at high speed, and more particularly to a high-speed simultaneous linear equation solving system suitable for numerical simulation of structural analysis and fluid analysis, and its initial value generation. The present invention relates to an apparatus, a method for solving simultaneous linear equations, and a medium.

[0002]

2. Description of the Related Art In general, in simulation of structural analysis or fluid analysis by a difference method, a finite component method, or the like,
First, an area for which a solution is to be obtained is divided into small areas such as triangles.
A set of the divided small regions is called a lattice. Next, a partial differential equation, which is a governing equation, is discretized on the lattice, and a system of linear equations is generated. A solution of the simultaneous linear equation is obtained, and the solution is set as an approximate solution of the differential equation. In particular, in the case of transient analysis, the partial differential equation includes a variable indicating time, and the variable is also discretized. The discretized times are sequentially referred to as t1, t2, t3,..., Tn.

A coefficient matrix of a system of linear equations generated by discretizing a partial differential equation has a feature that many zero components are present. In general, a matrix containing many zero components is called a sparse matrix. As a method of solving a system of linear equations having a sparse coefficient matrix, an iterative method as described in "Common sense of numerical calculation, 1985, Kyoritsu Shuppan Co., Ltd., pp. 130-133" is widely used. The iterative method is a method of obtaining a solution of a simultaneous linear equation by giving an initial vector of a solution and repeatedly applying a predetermined operation until an error becomes sufficiently small. In general, the shorter the distance between the initial vector of the solution given to the iterative method and the solution of the simultaneous linear equation to be obtained, the smaller the number of iterations and the shorter the calculation time until the solution. In general, when solving an unsteady partial differential equation, the time is set to t1, t2, t
Each time t1, t2, t
It is necessary to find the solution of the simultaneous equations every 3,..., Tn.

FIG. 14 shows an example of a conventional solution solving system for finding a solution of this type of simultaneous linear equation. The simultaneous linear equation solving system of FIG. 14 includes an initial value generation unit 30 that generates an initial vector based on a time input from the time input unit 11.
Is composed of a past result vector storage unit 31, a control unit 32, and an initial value calculation unit 33. The coefficient matrix is input by the coefficient matrix input unit 7 and the right side vector is input by the right side vector input unit 8. The initial vector, the coefficient matrix, and the right-hand side vector are provided to the iterative method calculation unit 9, the calculation is performed by the above-described iterative method, and the result is output to the solution vector output unit 10.

In this case, in the initial value generation unit 30,
The solution vectors of the iterative method at times t1, t2, t3,..., Tn are stored in the past result vector storage unit 31, and the control unit 32 performs control. The value at time tn + 1 is calculated by extrapolation,
It was output as the initial vector of the solution (Japanese Patent Application
-310132).

Normally, a simulation in which the state changes with time is performed. Therefore, in the conventional system, in the processing of the time step, the previous time step, that is, the immediately preceding time,
, And the distance between the solution vector of the simultaneous linear equation to be solved at the time, that is, the time step of the time, becomes long. As a result, the number of iterations in the iterative method increases, and the time required for the iterative calculation increases.

Examples of techniques applied to an iterative calculation unit 9 for obtaining an approximate solution by iterative calculation based on a coefficient matrix and vector data are described in, for example, JP-A-1-219951 and JP-A-4-77961. JP-A-4-2161
No. 68 and JP-A-7-64962.

Japanese Patent Application Laid-Open No. 1-219951 discloses a coefficient matrix decomposing circuit for decomposing a coefficient matrix into an approximate matrix, an iterative calculation circuit, and an inversion matrix of the approximate matrix generated by the coefficient matrix decomposer from an iterative calculation circuit. A forward / backward substitution circuit that multiplies the input vector data and outputs the result to an iterative calculation circuit,
An equation analyzer that outputs an approximate solution of a system of linear equations is shown. In particular, in the equation analyzer, the coefficient matrix decomposing circuit decomposes the coefficient matrix into a plurality of lower triangular matrices and upper triangular matrices corresponding to individual independent variables of the partial differential equation, and forms a symmetric product thereof. It is characterized in that the approximate forward / backward substitution circuit performs inversion of the approximate matrix by performing forward / backward substitution using the lower triangular matrix and the upper triangular matrix on the vector data input from the iterative calculation circuit.

Japanese Patent Application Laid-Open No. 4-77961 discloses a coefficient matrix decomposition circuit for decomposing a coefficient matrix into an approximate matrix, an iterative calculation circuit, and an inverse matrix of the approximate matrix generated by the coefficient matrix decomposition circuit. A forward / backward substitution circuit that multiplies the input vector data and outputs the result to an iterative calculation circuit, and takes as input data a coefficient matrix and a coefficient vector of a system of linear equations obtained by discrete approximation of a partial differential equation in a rectangular parallelepiped lattice, and An equation analyzer that outputs an approximate solution of a linear equation is shown. In particular, in the equation analyzer, the coefficient matrix decomposing circuit divides the rectangular parallelepiped into small rectangular parallelepipeds, decomposes the coefficient matrix into a lower triangular matrix and an upper triangular matrix corresponding to each of the rectangular parallelepipeds, and obtains a symmetric product thereof. And the forward / backward substitution circuit inverts the approximation matrix by performing forward / backward substitution on the vector data input from the iterative calculation circuit using the lower triangular matrix and the upper triangular matrix.

Japanese Patent Application Laid-Open No. Hei 4-216168 discloses a coefficient for decomposing a coefficient matrix into an approximate matrix by using a coefficient matrix and a coefficient vector of a simultaneous linear equation obtained by differential approximation of a partial differential equation on a general coordinate grid as inputs. A matrix decomposing circuit, an iterative calculation circuit, and a forward / backward substitution circuit that multiplies a vector output from the iterative calculation circuit by an inverse matrix of the approximate matrix and outputs the result to the iterative calculation circuit, and outputs an approximate solution of the simultaneous linear equation An analyzer is shown. In particular, the equation analysis apparatus uses a coefficient matrix decomposition circuit to convert only a portion corresponding to a nonzero element of a matrix obtained by differential discretization in a rectangular coordinate system among nonzero elements of a coefficient matrix into a product of an approximate matrix. It is characterized by decomposition. Alternatively, in particular, in the equation analyzer, the iterative circuit extrapolates a coefficient vector value of a lattice point of the Neumann lattice condition from an approximate solution vector value adjacent to the lattice point, and calculates an average value of the approximate solution vector as an approximate solution vector. It is characterized by performing processing to subtract from each element.

Japanese Unexamined Patent Publication No. 7-64962 discloses a method for solving a simultaneous linear equation having positive symmetric values at a high speed. In the method for solving the positive symmetric simultaneous linear equation, the input unit inputs the coefficient matrix and the right-hand side constant vector of the positive symmetric simultaneous linear equation, and the coefficient matrix decomposition unit converts the coefficient matrix input by the input unit into a lower triangular matrix. Decompose it into its transpose. At that time, the decomposition processing is performed at high speed using the matrix / vector product function provided by the compiler. The solving unit obtains a solution vector from the obtained lower triangular matrix, its transposed matrix, and the right-hand side constant vector.

[0012]

In the above-mentioned conventional system, the method of performing extrapolation calculation of each component at each time and generating an initial value is based on the solution at the previous time step for each time used before. Compared to the method using a vector as an initial vector, the number of iterations is further reduced. As a result, the solution of the simultaneous linear equations could be obtained in a shorter time. However, in the unsteady analysis, the physical state at the previous time step is necessarily different from the physical state at the next time step, so we try to calculate the solution vector at the previous time step and this time. The distance between the time step and the solution vector becomes long, and a long time calculation is required.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned circumstances, and it is an object of the present invention to generate an initial vector that requires a smaller number of iterations to solve a system of linear equations than in the past, thereby shortening the simulation time. High-speed simultaneous equation solving system that enables
An object of the present invention is to provide a method and a medium for solving simultaneous linear equations.

[0014]

According to a first aspect of the present invention, there is provided a high-speed simultaneous linear equation solving system according to a first aspect of the present invention. An initial vector for calculating an initial vector by calculating a weight and predicting a value of a required time from a temporal change for each component of the vector, and correcting the predicted value using a weight of the obtained adjacent node. It has a value generating means.

A high-speed simultaneous linear equation solving system according to a second aspect of the present invention includes an initial value generating means, an iterative method calculating means, a coefficient matrix input means, a right side vector input means,
A solution vector output unit, wherein the initial value generation means comprises:
Time input means, connection node weight information processing means, lattice information storage means, past result vector storage means, acceleration coefficient storage means, initial value calculation means, and control means, and the connection node weight information processing means Means and connection node weight information storage means, the grid information storage means has node connection information storage means and node coordinate storage means, and the past result vector storage means has a plurality of time storage means and a plurality of time storage means. A vector storage unit, and the initial value calculation unit is configured to include an interpolation calculation unit, a vector storage unit, and a weight addition unit, and when the time is 0, the connection node weight information processing unit The node connection information is read from the node connection information storage means, the node coordinates are read from the node coordinate storage means, weights of the respective nodes are calculated by weight calculation means, and the result is referred to as the connection node. After completion of the processing when the time is not 0 and when the time is 0, the interpolation calculating means stores the time from the time storing means and the time from the vector storing means. , The time input from the time input means is read, the interpolation calculation is performed for each component, the result is stored in the vector storage means, and the weight addition means is stored in the vector storage means. From the connection node weight information storage means, a set of node weights, the acceleration coefficient from the acceleration coefficient storage means, read the node connection information from the node connection information storage means, respectively, perform a correction calculation, the result Is stored in the vector storage means, and the iterative method calculation means calculates a coefficient matrix from the coefficient matrix input means, An edge vector,
Each of the initial vectors is read from the vector storage unit, a solution of a simultaneous linear equation is performed, and the result is output to the solution vector output unit.The control unit outputs the time and the solution vector input from the time input unit. By controlling the vector output to the output means in the time storage means and the corresponding vector storage means, a solution of a simultaneous linear equation is obtained.

[0016] The weight adding means includes: I-th component = acceleration coefficient × I-th component of the uncorrected vector + (1-acceleration coefficient) × ((weight of adjacent node × adjacent to the I-th component of the uncorrected vector) The correction calculation of the sum of the components (corresponding to the corresponding node numbers) may be performed on all the nodes.

An initial value generating apparatus according to a third aspect of the present invention comprises: means for obtaining weights of adjacent nodes based on connection information of nodes of a grid and node coordinates; Means for predicting the value of the required time from the change, and means for generating an initial vector by correcting the predicted value using the weight of the adjacent node.

An initial value generating device according to a fourth aspect of the present invention includes a connection node weight information processing unit, a lattice information storage unit, a past result vector storage unit, an acceleration coefficient storage unit, and an initial value calculation unit. And a control unit, the connection node weight information processing unit further includes a weight calculation unit and a connection node weight information storage unit, and the grid information storage unit includes a node connection information storage unit and a node coordinate storage unit. The past result vector storage unit has a plurality of time storage units and a plurality of vector storage units, and the initial value calculation unit has an interpolation calculation unit, a vector storage unit, and a weight addition unit. When the time is 0, the connection node weight information processing unit reads the node connection information from the node connection information storage unit, and reads the node coordinates from the node coordinate storage unit, and the weight calculation unit Calculate the weight of each node,
After storing the result in the connection node weight information storage unit and ending the processing when the time is not 0 and when the time is 0, the interpolation calculation unit reads the time from the time storage unit, The vector corresponding to the time is read from the vector storage unit, and the input time is read.
Interpolation calculation is performed for each component, and the result is stored in the vector storage unit.The weight addition unit calculates the vector from the vector storage unit, the node weight set from the connection node weight information storage unit, The acceleration coefficient from the coefficient storage unit,
The node connection information is read from the node connection information storage unit, the correction calculation is performed, the result is stored in the vector storage unit, and the result of the correction calculation is provided to the iterative calculation.

The weight addition section calculates the I-th component = acceleration coefficient × the I-th component of the uncorrected vector + (1−the acceleration coefficient) × ((weight of the adjacent node × the node of the I-th component of the uncorrected vector) Means for performing a correction calculation of (sum of components corresponding to the node numbers).

A method of solving a simultaneous linear equation according to a fifth aspect of the present invention obtains weights of adjacent nodes based on connection information of nodes of a lattice and node coordinates, and calculates a temporal change for each component of a vector. , An initial vector is generated by correcting the predicted value by using the obtained weight of the adjacent node, and a simultaneous linear equation is solved using the initial vector.

A method for solving simultaneous linear equations according to a sixth aspect of the present invention includes an initial value generation device, an iterative method calculation unit, a coefficient matrix input unit, a right side vector input unit, and a solution vector output unit. The initial value generation device includes a time input unit, a connection node weight information processing unit, a grid information storage unit, a past result vector storage unit, an acceleration coefficient storage unit, an initial value calculation unit, and a control unit. The node weight information processing unit has a weight calculation unit and a connection node weight information storage unit, the grid information storage unit has a node connection information storage unit and a node coordinate storage unit, and the past result vector storage unit is , A plurality of time storage units and a plurality of vector storage units, and the initial value calculation unit includes an interpolation calculation unit, a vector storage unit, and a weight addition unit. Is 0, the connection node In the weight information processing unit, the node connection information is read from the node connection information storage unit, the node coordinates are read from the node coordinate storage unit, and the weight calculation unit calculates the weight of each node, and the result is used as the connection. After the processing in the case where the time is not 0 and the case where the time is 0 is ended, the interpolation calculation unit
The time is read from the time storage unit, the vector corresponding to the time is read from the vector storage unit, and the time input from the time input unit is read, interpolation calculation is performed for each component, and the result is stored in the vector storage unit. Department,
In the weight addition unit, a vector from the vector storage unit, a weight set of nodes from the connection node weight information storage unit, an acceleration coefficient from the acceleration coefficient storage unit, the node connection information from the node connection information storage unit. The respective reading and correction calculations are performed, and the results are stored in the vector storage unit.The iterative calculation unit calculates a coefficient matrix from the coefficient matrix input unit, a right side vector from the right side vector input unit, the vector Each of the initial vectors is read from the storage unit, a solution of a simultaneous linear equation is performed, and the result is output to the solution vector output unit. By storing the vector output to the unit in the time storage unit and the corresponding vector storage unit, The seek.

In the weight adding section, the I-th component = acceleration coefficient × the I-th component of the uncorrected vector + (1-acceleration coefficient) × ((weight of adjacent node × adjacent to the node of the I-th component of the uncorrected vector) The correction calculation of the sum of the components (corresponding to the corresponding node numbers) may be performed on all the nodes.

A computer-readable recording medium according to a seventh aspect of the present invention is a computer-readable recording medium which determines a weight of each adjacent node based on connection information of a grid node and the node coordinates, and calculates a weight of each component of the vector. A program for functioning as an initial value generating means for generating an initial vector by predicting a value of a required time from a temporal change and using the obtained weight of an adjacent node to correct the predicted value. Have recorded.

A computer-readable recording medium according to an eighth aspect of the present invention comprises: an initial value generating unit, an iterative calculation unit, a coefficient matrix input unit, a right side vector input unit, and a solution vector output unit. The initial value generating means includes time input means, connection node weight information processing means, grid information storage means, past result vector storage means, acceleration coefficient storage means, initial value calculation means, and control means. The connection node weight information processing means has weight calculation means and connection node weight information storage means, and the lattice information storage means has node connection information storage means and node coordinate storage means, and a past result vector storage means Has a plurality of time storage means and a plurality of vector storage means, and the initial value calculation means has an interpolation calculation means, a vector storage means and a weight addition means, and the time is zero. The connection node weight information processing means reads the node connection information from the node connection information storage means and the node coordinates from the node coordinate storage means, and the weight calculation means calculates the weight of each node, After storing the result in the connection node weight information storage means and ending the processing when the time is not 0 and when the time is 0, the interpolation calculation means reads the time from the time storage means, The vector corresponding to the time is read from the vector storage means, the time input from the time input means is read, interpolation calculation is performed for each component, the result is stored in the vector storage means, and the weight addition means A vector from the vector storage means, a weight set of nodes from the connection node weight information storage means, an acceleration coefficient from the acceleration coefficient storage means, The node connection information is read from the information storage means, the correction calculation is performed, the result is stored in the vector storage means, and the iterative method calculation means reads the coefficient matrix from the coefficient matrix input means and the right side vector input means. From the vector storage means, read the initial vector from the vector storage means, solve the system of linear equations, output the result to the solution vector output means, the control unit, the input from the time input means A control for storing a time and a vector output to the solution vector output means in the time storage means and the vector storage means corresponding thereto, whereby the computer functions as the respective means for obtaining a solution of a simultaneous linear equation. Recording the program.

The weight adding means calculates the I-th component = acceleration coefficient × the I-th component of the uncorrected vector + (1—the acceleration coefficient) × ((weight of adjacent node × neighbor of the I-th component of the uncorrected vector) A program for causing a computer to function as a means for performing a correction calculation of (a sum of components) corresponding to the node numbers to be performed) on all the nodes may be recorded.

In the high-speed simultaneous linear equation solving system, the initial value generating apparatus, the simultaneous linear equation solving method and the medium according to the present invention, the initial value generating means includes a past result vector storing a plurality of past solutions of the simultaneous linear equations. Storage means,
A grid information storage unit for storing information on the calculation grid, an acceleration coefficient storage unit, an initial value calculation unit for calculating an initial vector from the information, and a control unit for controlling the entire unit; After performing a basic extrapolation calculation, spatial correction is applied to generate an initial value close to the distribution of the solution of the simultaneous linear equation to be solved, and as a result, the simultaneous linear equation The number of iterations until a solution can be reduced, and the calculation time can be significantly reduced.

[0027]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows a configuration of a high-speed simultaneous linear equation solving system including the initial value generation device according to the first embodiment of the present invention as an initial value generation unit.

The high-speed simultaneous linear equation solving system shown in FIG. 1 includes a connection point weight information processing unit 1, a grid information storage unit 2, a past result vector storage unit 3, an acceleration coefficient storage unit 4, an initial value calculation unit 5, a control unit. It comprises a unit 6, a coefficient matrix input unit 7, a right side vector input unit 8, an iterative method calculation unit 9, a solution vector output unit 10, and a time input unit 11. Connection point weight information processing unit 1, grid information storage unit 2, past result vector storage unit 3,
The portion including the acceleration coefficient storage unit 4, the initial value calculation unit 5, and the control unit 6 constitutes an initial value generation unit 0, which is different from the configuration of the initial value generation unit 30 in FIG.

Therefore, the coefficient matrix input section 7, the right side vector input section 8, the iterative method calculation section 9, the solution vector output section 10
The time input unit 11 and the time input unit 11 have almost the same configuration as that of FIG. 14, and the functions of the past result vector storage unit 3, the initial value calculation unit 5, and the control unit 6 in the initial value generation unit 0 are the results in FIG. Almost corresponds to the vector storage unit 31, the initial value calculation unit 3, and the control unit 32.

The time input unit 11 supplies time information at predetermined time intervals to the initial value generation unit 0. The initial value generation unit 0 includes:
A connection node weight information processing unit 1 controlled by the control unit 6, a grid information storage unit 2, a past result vector storage unit 3,
An acceleration coefficient storage unit 4 and an initial calculation unit 5 are provided.

The iterative method calculation section 9 is based on the initial vector generated by the above-described initial value generation section 0, the coefficient matrix input from the coefficient matrix input section 7, and the right side vector input from the right side vector input section 8. The solution calculated by the iterative method is output to the solution vector output unit 10. The value output to the solution vector output unit 10 is also output to the outside, but is fed back to the control unit 6, and the value is stored in the past result vector storage unit 3. Details of such control by the control unit 6 are shown in FIGS. 6 and 7. Details of the control by the control unit 6 shown in the flowcharts of FIGS. 6 and 7 will be described later.

FIG. 2 shows a detailed configuration of the grid information storage unit 2. The grid information storage unit 2 includes a node connection information storage unit 12 and a node coordinate storage unit 13. The node connection information storage unit 12 stores the node connection information in order. That is, the node connection information storage unit 12 stores the nodes of the node numbers 1, 2,..., V, that is, sets of node numbers adjacent to the nodes 1, 2,. The node coordinate storage unit 13 similarly stores the node coordinates in order. That is, the coordinates of the nodes 1, 2,..., V are stored in the order of the X axis, the Y axis, and the Z axis in the node coordinate storage unit 13, and are stored in the order of the node numbers.

FIG. 3 shows a detailed configuration of the past result vector storage unit 3. The past result vector storage unit 3 includes a plurality of time storage units 14 and a plurality of vector storage units 15, and the time storage unit 14 and the vector storage unit 15 are associated one-to-one. That is, the time storage unit 14 stores the times 1, 2,... T, and the time storage unit 14 of the times 1, 2,.
2. Corresponds to the vector storage unit 15 that stores the result vector in T. The result vectors at times 1, 2,..., T stored in the vector storage unit 15 at times 1, 2,..., T are respectively composed of first, second,. That is, the time corresponding to the T-th time and the result vector at that time are stored in the time storage unit 14 and the vector storage unit 15 in the same (corresponding) row.

FIG. 4 shows a detailed configuration of the connection node weight information processing section 1. The connection node weight information processing unit 1 includes a weight calculation unit 16 and a connection node weight information storage unit 17. The weight calculator 16 calculates the weight of the connection node.
The connection node weight information storage unit 17 stores the weight information of the connection nodes in the order corresponding to the node connection information storage unit 12 shown in FIG. , 2... V, that is, the weights respectively corresponding to the nodes 1, 2,.
FIG. 9 shows details of the weight calculation in the weight calculator 16. Details of the weight calculation by the weight calculation unit 16 shown in the flowchart of FIG. 9 will be described later.

FIG. 5 shows a detailed configuration of the initial calculation section 5. The initial calculation unit 5 includes an interpolation calculation unit 18, a first vector storage unit 19, a weight addition unit 20, and a second vector storage unit 21. For the interpolation calculation by the interpolation calculation unit 18, for example, a method described in Japanese Patent Application No. 9-310132 can be used, and a calculation for temporally interpolating each component is performed. Further, the weight adding unit 20 performs a weight correction calculation by the processing shown in FIG.

FIG. 6 shows the control centered on the control unit 6.
This will be specifically described with reference to the flowchart shown in FIG.

In FIG. 6, the input information includes a coefficient matrix by the coefficient matrix input unit 7, a right side vector by the right side vector input unit 8, node coordinates stored in the node coordinate storage unit 13 of the grid information storage unit 2, and grid information storage. Node connection information and time input unit 11 stored in the node connection information storage unit 12 of the unit 2
Time.

First, it is determined whether or not the time is 0 (step S1). If the time is 0, the connection node weight information processing section 1 stores the node connection information storage section of the grid information storage section 2. The node connection information is read from node information 12 and the node coordinates are read from the node coordinate storage unit 13 of the grid information storage unit 2. Based on these pieces of information, the connection node weight information processing unit 1
The weight calculation unit 16 calculates the weight of each node according to the method of FIG. 9 described later, and stores the result in the connection node weight information storage unit 17 of the connection node weight information processing unit 1 (step S2). .

In step S1, if the time is not 0, or if the above-described processing in the case where the time is 0 is completed, the interpolation calculation unit 18 of the initial calculation unit 5 stores the past time in the result vector storage unit 3. The time is read from the storage unit 14, the vector corresponding to the time is read from the vector storage unit 15 of the past result vector storage unit 3, and the time input from the time input unit 11 is read. Based on this information,
The interpolation calculation unit 18 calculates, for each component, Japanese Patent Application No. 09-310.
Interpolation calculation according to the method described in No. 132 is performed, and the result is stored in the first vector storage unit 19 (step S3). Thereafter, the process proceeds to FIG.

In FIG. 7, the weight adding section 20 of the initial calculating section 5 receives the vector from the first vector storing section 19 of the initial calculating section 5 and the vector from the connecting node weight information storing section 17 of the connecting node weight information processing section 1. The weight set of the nodes is read from the acceleration coefficient storage unit 4 for the acceleration coefficient, and the node connection information is read from the node connection information storage unit 12 of the grid information storage unit 2.
Based on this information, the weight addition unit 20 performs a correction calculation according to the processing shown in FIG. 8, and stores the result in the second vector storage unit 21 of the initial value calculation unit 5 (step S4). Next, the iterative method calculation unit 9 outputs the coefficient matrix input unit 7
, The right side vector from the right side vector input unit 8, and the second vector storage unit 2 of the initial value calculation unit 5.
1 to read an initial vector, perform a solution process of simultaneous linear equations based on the information, and output the result to the solution vector output unit 10 (step S).
5). The control unit 6 stores the time input from the time input unit 11 and the vector output to the solution vector output unit 10 in the time storage unit 14 of the past result vector storage unit 3 and the corresponding vector storage unit 15 respectively. (Step S6).

The correction calculation by the weight addition unit 20 of the initial calculation unit 5 will be described with reference to the flowchart shown in FIG. The acceleration coefficient stored in the acceleration coefficient storage unit 4, the connection node weight set stored in the connection node weight information storage unit 17, the uncorrected vector stored in the first vector storage unit 19, and the node connection information storage unit 12 Are supplied to the weight adder 20. The weight adding unit 20 performs the following calculation for all nodes for each component. That is, the weight addition unit 20 sets the variable I to 1 (step S11), and performs the following calculation while determining whether or not the variable I has reached the number of components N (step S12) (step S13).

The I-th component of the second vector storage unit 21 = acceleration coefficient × the I-th component of the uncorrected vector + (1-acceleration coefficient)
× (the sum of (weight of adjacent node × component corresponding to the node number adjacent to the node of the I-th component of the uncorrected vector)) The weight adding unit 20 calculates the variable I
Is incremented by 1 (step S14), the process returns to step S12, and the calculation in step S13 is repeated until the variable I reaches the number of components N. Then, calculation is performed for all nodes for all components, and when the variable I reaches the number N of components, the weight addition unit 20 ends the correction calculation.

Weight calculation unit 1 of connection node weight information processing unit 1
6 will be described with reference to the flowchart shown in FIG. The weight calculation unit 16 includes a set of adjacent node numbers stored in the node connection information storage unit 12 of the grid information storage unit 2 and the node coordinate storage unit 1 of the grid information storage unit 2.
3 are supplied with the coordinates of the nodes. Weight calculator 1
6 performs the following calculation for each node I. That is, the weight calculator 16 sets the variable I to 1 (step S21), and performs the next calculation while determining whether or not the variable I has reached the total number of nodes V (step S22).

The weight calculator 16 calculates the distance between the I-th node and each of the nodes belonging to the set of node numbers adjacent to the I-node using the node coordinates, and calculates the reciprocal thereof as the connection node weight information storage. The 17th node is sequentially stored in a weight set of nodes adjacent to the I-th node (step S23). Further, the weight calculation unit 16 calculates the sum of the weights of the connection node weight information storage unit 17, divides each element belonging to the set of weights of the nodes adjacent to the I-th node by the total, and again calculates the connection node weight. The information is stored in the weight set of the node adjacent to the I-th node in the information storage unit 17 (step S24).

After the calculation in step S24, the weight calculator 16 increments the variable I by "1" (step S24).
25) Return to step S22, and repeat the calculations in steps S23 and S24 until the variable I reaches the number of nodes V.
Then, the calculation is performed for all the nodes, and when the variable I reaches the number of nodes V, the weight calculation unit 16 stores the connection node weight information in the connection node weight information storage unit 17 and ends the correction calculation.

In the numerical calculation, the finite element method is used for simulation. In the finite element method, an unstructured grid is generally used as a calculation grid.
The system shown in FIG. 1 is a system that can be used for such a simulation by the finite element method. FIG. 1 shows a high-speed computing device for this purpose. However, techniques such as the difference method are widely used for simulation,
They often use structured grids. Furthermore, in addition to being a structured grid, a grid having the grid intervals equally spaced is also used. In that case, the set of weights of the nodes adjacent to each node stored in the connection node weight information storage unit 17 all have the same value. Therefore, when a technique such as the difference method is used, the grid information storage unit 2 shown in FIG. 1 becomes unnecessary.

This is the high-speed simultaneous linear equation solving system according to the second embodiment of the present invention shown in FIG. In this case, the connection node weight information processing section 1A
Can be configured with a smaller capacity as compared with the configuration of FIG. 1. As shown in FIG. 11, the configuration can be made only by providing a weight storage unit 22 instead of the connection node weight information storage unit 17. Can be. That is, the connection node weight information processing section 1A
Can be composed of only the weight calculation unit 16 and the weight storage unit 22. Therefore, the value stored in the weight storage unit 22 is 1 / the number of adjacent nodes. As the weight in the correction calculation in FIG. 8, a value stored in the weight storage unit 22 is used instead of a set of weights of nodes adjacent to the node.

The high-speed simultaneous linear equation solving system according to the second embodiment of the present invention is shown in FIGS.
1, 3 and 5, and operates according to FIGS.

The high-speed simultaneous primary solution system shown in FIG. 10 includes a connection node weight information processing section 1A, a past result vector storage section 3, an acceleration coefficient storage section 4, an initial value calculation section 5, a control section 6, and a coefficient matrix input section. 7, a right side vector input unit 8, an iterative method calculation unit 9, and a solution vector output unit 10. The connection node weight information processing unit 1A includes a weight calculation unit 16 and a weight storage unit 22, as shown in FIG. Therefore, the initial value generation unit 0A includes the connection node weight information processing unit 1A, the past result vector storage unit 3, the acceleration coefficient storage unit 4, the initial value calculation unit 5, and the control unit 6. The operation of each unit is almost the same as that of the first embodiment except for the points described above, and therefore, an evaluation example in a specific simulation will be described here.

In the evaluation of this system, the dimension of the vector, that is, the number of components N was set to 157440. An example of the evaluation is three-dimensional, and assuming that the operation of the liquid crystal molecules is simulated, discretization is performed with equal time intervals. In the simulation, an orthogonally-spaced grid is used. That is, the weight storage unit 22 stores a value of 1/6. In addition, a simulation was performed when the voltage was changed (increased) from 0.5 V to 5.0 V at 0.5 V intervals at equal time intervals. The upper limit T of the time shown in FIG. 3 is set to 2, and an interpolation formula based on a linear expression is used as an interpolation method. Specifically, the past two times are set to t1 and t
Assuming that the value of the nth component is Ft1 and Ft2 at that time and the value of the time to be obtained is t, the initial value F is calculated according to the following equation.

F = (Ft1-Ft2) / (t1-t2) *
(T-t1) + Ft1 In the operation simulation of liquid crystal molecules, the calculation of the electric field and the calculation of the liquid crystal are combined and calculated simultaneously.

FIG. 12 shows the result of comparing the performance of the conventional system and the system of the present invention. FIG. 12 shows the number of iterations of the iterative method until a simulation result is obtained. The conventional initial generator required 18509 iterations to complete the simulation.

On the other hand, in the initial value generating section 0A according to the present invention, a change in the number of repetitions caused by variously changing the acceleration coefficient was examined. 15840 times when the acceleration coefficient is 1.3,
When the acceleration coefficient is 1.5, 13241 times, and when the acceleration coefficient is 1.
7,617 times, 956 when the acceleration coefficient is 1.8
Three times, the number of repetitions was 17512 when the acceleration coefficient was 2.0. The computation time by the iterative method is proportional to the number of iterations,
The time required for calculating the initial value is almost the same as the time required for one iterative calculation in the iterative method. Therefore, according to FIG. 12, the system according to the present invention requires about 5 times less time for simulation than the conventional system.
It can be seen that it has been reduced to 2%.

Further, in order to examine the effectiveness of the present invention, evaluation was performed by applying the present invention to other subjects. The system configuration and the like are the same as in the case described above.
The simulation of the operation of the liquid crystal molecules to reduce the change over time, which is a subject to which the conventional method is suitable, was performed. More specifically, FIG. 13 shows the results of a simulation when the voltage was increased from 3.0 V to 4.0 V at equal time intervals at 0.1 V intervals to perform the simulation.

In this case, a simulation was performed with an acceleration coefficient of 1.3. In the conventional method, the number of iterations is 1
In contrast to 3098 times, the method according to the present invention requires only 10854 iterations, and the simulation time is shortened.

In the conventional system, an initial value is generated by tracking a time change at each time step at each node. On the other hand, in the present invention, the initial value of the simultaneous linear equation at the time to be solved is generated by tracking the time change of the solution of the past simultaneous linear equation, adding a spatial correction, and generating the initial value. Has been generated. By doing so, it is possible to generate an initial value in a state physically close to the solution of the simultaneous linear equation to be obtained, and as a result, it is possible to obtain the solution of the simultaneous linear equation with a small number of iterations . Therefore, the total calculation time required for the simulation can be reduced. That is, in the present invention, the same simulation can be executed in a conventional calculation time of, for example, about 52%.

It should be noted that the initial value generating apparatus of the present invention or the high-speed simultaneous linear equation solving system incorporating the initial value generating apparatus can be realized by using an ordinary computer system without configuring as a dedicated system. For example, a medium (floppy disk, CD-RO) storing a program for executing the above-described operation in a computer system.
M, etc.), a system for executing the above processing can be constructed. By the installation, the program is stored in a medium such as a hard disk in the computer system, configures the system, and is provided for execution.

The medium for supplying the program to the computer is not limited to a storage medium in a narrow sense, but may be a communication line,
Like a communication network and a communication system, it may be a storage medium in a broad sense including a communication medium that temporarily and fluidly stores information such as a program.

For example, the program may be registered in an FTP (File Transfer Protocol) server provided on a communication network such as the Internet and distributed to an FTP client via the network, or a bulletin board (BBS: Bulletin) of the communication network may be used. The program may be registered in a board system or the like and distributed via a network. Then start this program and run the OS
The above processing can be achieved by executing under the control of the (Operating System). Furthermore, the above-described processing can also be achieved by starting and executing the program while transferring the program via the communication network.

[0060]

As described above, according to the present invention,
Generating an initial vector based on node information and a solution vector at a past time, and generating an initial vector that requires less iterations to solve a system of linear equations than before, thereby shortening the simulation time. , A system for solving simultaneous linear equations, a method for solving simultaneous linear equations, and a medium can be provided.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a high-speed simultaneous linear equation solving system incorporating an initial value generation device according to a first embodiment of the present invention.

FIG. 2 is a block diagram showing a configuration of a lattice information storage unit in the high-speed simultaneous linear equation solving system of FIG. 1;

FIG. 3 is a block diagram showing a configuration of a past result vector storage unit in the high-speed simultaneous linear equation solution system of FIG. 1;

FIG. 4 is a block diagram illustrating a configuration of a connection node weight information processing unit in the high-speed simultaneous linear equation solving system of FIG. 1;

FIG. 5 is a block diagram illustrating a configuration of an initial value calculation unit in the high-speed simultaneous linear equation solving system of FIG. 1;

FIG. 6 is a first half flowchart for explaining a control operation in the high-speed simultaneous linear equation solving system of FIG. 1;

FIG. 7 is a flowchart of the latter half for explaining a control operation in the high-speed simultaneous linear equation solving system of FIG. 1;

FIG. 8 is a flowchart illustrating a correction calculation process performed by a weight addition unit in the high-speed simultaneous linear equation solving system of FIG. 1;

FIG. 9 is a flowchart illustrating a weight calculation process performed by a weight calculation unit in the high-speed simultaneous linear equation solving system of FIG. 1;

FIG. 10 is a block diagram showing a configuration of a high-speed simultaneous linear equation solving system incorporating an initial value generation device according to a second embodiment of the present invention.

11 is a block diagram illustrating a configuration of a connection node weight information processing unit in the high-speed simultaneous linear equation solving system of FIG. 10;

FIG. 12 is a diagram for explaining an example of evaluation in comparison of the high-speed simultaneous linear equation solving system of the present invention with a conventional system.

FIG. 13 is a diagram for explaining another example of evaluation in comparison of the high-speed simultaneous linear equation solving system of the present invention with a conventional system.

FIG. 14 is a block diagram showing a configuration of a high-speed simultaneous linear equation solving system incorporating a conventional initial value generation device.

[Explanation of symbols]

 0 Initial value generation unit 0A Initial value generation unit 1 Connection node weight information processing unit 1A Connection node weight information processing unit 2 Grid information storage unit 3 Past result vector storage unit 4 Acceleration coefficient storage unit 5 Initial value calculation unit 6 Control unit 7 Coefficient matrix input section 8 right side vector input section 9 iterative method calculation section 10 solution vector output section 11 time input section 12 node connection information storage section 13 node coordinate storage section 14 time storage section 15 vector storage section 16 weight calculation section 17 connection node weight Information storage unit 18 Interpolation calculation unit 19 Vector storage unit 20 Weight addition unit 21 Vector storage unit 22 Weight storage unit

Claims (12)

[Claims] 1. A method for determining weights of adjacent nodes based on connection information of nodes of a lattice and node coordinates, predicting a value of a required time from a temporal change for each component of a vector, and determining the calculated adjacent time. A high-speed simultaneous linear equation characterized by comprising initial value generating means for generating an initial vector by correcting the predicted value using the weight of a node to be used, and solving a simultaneous linear equation using the initial vector. Solution system. 2. An apparatus according to claim 1, further comprising an initial value generating means, an iterative method calculating means, a coefficient matrix input means, a right side vector input means, and a solution vector output section. Node weight information processing means, grid information storage means,
A past result vector storage unit, an acceleration coefficient storage unit, an initial value calculation unit, and a control unit; the connection node weight information processing unit further includes a weight calculation unit and a connection node weight information storage unit; The means has node connection information storage means and node coordinate storage means, the past result vector storage means has a plurality of time storage means and a plurality of vector storage means, and the initial value calculation means has an interpolation. When the time is 0, the connection node weight information processing means stores the node connection information from the node connection information storage means, and stores the node coordinate information. The node coordinates are read from the means, the weight of each node is calculated by the weight calculation means, and the result is stored in the connection node weight information storage means. After finishing the processing in the case of 0, the interpolation calculation means sets the time from the time storage means, the vector corresponding to the time from the vector storage means, and the time input from the time input means. Read, perform an interpolation calculation for each component, and store the result in the vector storage means.The weight addition means stores a vector from the vector storage means and a node weight set from the connection node weight information storage means. The acceleration coefficient is read from the acceleration coefficient storage means, the node connection information is read from the node connection information storage means, correction calculation is performed, and the result is stored in the vector storage means. The coefficient matrix is input from the coefficient matrix input means, the right side vector is input from the right side vector input means, and the initial vector is output from the vector storage means. Each of them reads and solves a system of linear equations, and outputs the result to the solution vector output means. The control unit outputs the time inputted from the time input means and the vector outputted to the solution vector output means. A high-speed simultaneous linear equation solving system, wherein a solution of a simultaneous linear equation is obtained by control of storing the simultaneous linear equations in the time storage means and the corresponding vector storage means. 3. The weight addition means, wherein the I-th component = acceleration coefficient × the I-th component of the uncorrected vector + (1-acceleration coefficient) × ((weight of adjacent node × node of the I-th component of the uncorrected vector) 3. The high-speed simultaneous linear equation solving system according to claim 1, wherein a correction calculation is performed for all the nodes. 4. A means for calculating weights of adjacent nodes based on connection information of the nodes of the lattice and the coordinates of the nodes; a means for predicting a required time value from a temporal change for each component of the vector; Means for generating an initial vector by correcting the predicted value using a weight of an adjacent node. 5. A connection node weight information processing unit, a lattice information storage unit, a past result vector storage unit, an acceleration coefficient storage unit, an initial value calculation unit, and a control unit, further comprising: the connection node The weight information processing unit has a weight calculation unit and a connection node weight information storage unit, the lattice information storage unit has a node connection information storage unit and a node coordinate storage unit, and the past result vector storage unit is It has a plurality of time storage units and a plurality of vector storage units, and the initial value calculation unit includes an interpolation calculation unit, a vector storage unit, and a weight addition unit, and when the time is 0, The connection node weight information processing unit reads the node connection information from the node connection information storage unit, reads the node coordinates from the node coordinate storage unit, and in the weight calculation unit,
After calculating the weight of each node, the result is stored in the connection node weight information storage unit, and when the processing when the time is not 0 and when the time is 0 is completed, the interpolation calculation unit The time is read from the time storage unit, the vector corresponding to the time is read from the vector storage unit, and the input time is read, interpolation calculation is performed for each component, and the result is stored in the vector storage unit. The weight addition unit, the vector from the vector storage unit, a weight set of nodes from the connection node weight information storage unit, the acceleration coefficient from the acceleration coefficient storage unit, the node connection information from the node connection information storage unit. An initial value generation device, wherein the initial value is read, a correction calculation is performed, the result is stored in the vector storage unit, and the result of the correction calculation is subjected to an iterative calculation. 6. The weight adding section, wherein the I-th component = acceleration coefficient × the I-th component of the uncorrected vector + (1—the acceleration coefficient) × ((weight of adjacent node × node of the I-th component of the uncorrected vector) The initial value generation apparatus according to claim 4, further comprising a means for performing a correction calculation on all the nodes). 7. The weight of each adjacent node is determined based on the connection information of the nodes of the lattice and the node coordinates, and the value of the required time is predicted from the temporal change for each component of the vector. A method for solving simultaneous linear equations, comprising: generating an initial vector by correcting the predicted value using the weights of the above; and solving a simultaneous linear equation using the initial vector. 8. An initial value generator, an iterative method calculator, a coefficient matrix input unit, a right side vector input unit, and a solution vector output unit, wherein the initial value generator includes a time input unit, A node weight information processing unit, a lattice information storage unit, a past result vector storage unit, an acceleration coefficient storage unit, an initial value calculation unit, and a control unit; and the connection node weight information processing unit includes a weight calculation unit and a connection node weight. An information storage unit, the grid information storage unit includes a node connection information storage unit and a node coordinate storage unit, and the past result vector storage unit includes a plurality of time storage units and a plurality of vector storage units. The initial value calculation unit includes an interpolation calculation unit, a vector storage unit, and a weight addition unit, and determines the solution of the simultaneous linear equation. When the time is 0, the connection node weight information processing unit In the node connection information storage unit, The node connection information is read out from the node coordinate storage unit to read the node coordinates, the weight calculation unit calculates the weight of each node, and stores the result in the connection node weight information storage unit. After the processing when the time is 0 is completed, the interpolation calculation unit inputs a time from the time storage unit and a vector corresponding to the time from the vector storage unit from the time input unit. The obtained times are read, interpolation calculation is performed for each component, and the result is stored in the vector storage unit. The weight addition unit stores the vector from the vector storage unit in the connection node weight information storage unit. From the acceleration coefficient storage unit, read the node connection information from the node connection information storage unit, perform a correction calculation, and calculate the result as the vector In the iterative calculation unit, a coefficient matrix is read from the coefficient matrix input unit, a right side vector is read from the right side vector input unit, and an initial vector is read from the vector storage unit. The result is output to the solution vector output unit, the control unit, the time input from the time input unit and the vector output to the solution vector output unit, the time storage unit and the A method for solving a simultaneous linear equation, wherein a solution of the simultaneous linear equation is obtained by storing the solution in the corresponding vector storage unit. 9. The method according to claim 1, wherein the I-th component = acceleration coefficient × the I-th component of the uncorrected vector + (1−the acceleration coefficient) × ((weight of adjacent nodes × the I-th component of the uncorrected vector) 9. A method for solving simultaneous linear equations according to claim 7, wherein a correction calculation is performed for all the nodes. 10. A computer calculates a weight of each adjacent node based on connection information of a node of the grid and node coordinates,
And an initial value generation unit that predicts a value of a required time from a temporal change for each component of the vector, and corrects the predicted value using the obtained weight of the adjacent node to generate an initial vector. A computer-readable recording medium recording a program for causing the computer to function. 11. An initial value generation means, an iterative calculation means,
A coefficient matrix input unit, a right side vector input unit, and a solution vector output unit, wherein the initial value generation unit includes a time input unit, a connection node weight information processing unit, a grid information storage unit, a past result vector storage unit , Acceleration coefficient storage means,
An initial value calculating unit and a control unit; the connection node weight information processing unit includes a weight calculation unit and a connection node weight information storage unit; and the grid information storage unit includes a node connection information storage unit and a node coordinate storage unit. Means, the past result vector storage means has a plurality of time storage means and a plurality of vector storage means, and the initial value calculation means has an interpolation calculation means, a vector storage means, and a weight addition means. If the time is 0, the connection node weight information processing means reads the node connection information from the node connection information storage means and the node coordinates from the node coordinate storage means, and the weight calculation means Is calculated, and the result is stored in the connection node weight information storage means. After the processing when the time is not 0 and when the time is 0, the interpolation calculation means A time corresponding to the time is read from the time storage means, a vector corresponding to the time is read from the vector storage means, and a time input from the time input means is read, interpolation calculation is performed for each component, and the result is stored in the vector storage. The weight addition means, the vector from the vector storage means, the weight set of the nodes from the connection node weight information storage means, the acceleration coefficient from the acceleration coefficient storage means, from the node connection information storage means Each of the node connection information is read, a correction calculation is performed, and the result is stored in the vector storage means.The iterative method calculation means calculates a coefficient matrix from the coefficient matrix input means and a right side vector from the right side vector input means. , The initial vectors are respectively read from the vector storage means, and simultaneous linear equations are solved. Output to the solution vector output means, the control unit stores the time input from the time input means and the vector output to the solution vector output means in the time storage means and the corresponding vector storage means A computer-readable recording medium on which a program for causing a computer to function is recorded as the means for obtaining a solution of the simultaneous linear equations by the control performed. 12. The weight adding means, wherein: I-th component = acceleration coefficient × I-th component of uncorrected vector + (1-acceleration coefficient) × ((weight of adjacent node × node of I-th component of uncorrected vector) The computer-readable recording medium according to claim 10, wherein a program for causing a computer to function as a means for performing a correction calculation of (a sum of components corresponding to node numbers adjacent to) on all nodes is recorded.