Method of and apparatus for preconditioning of a coefficient mat

Details Method of and apparatus for preconditioning of a coefficient mat Method of and apparatus for preconditioning of a coefficient mat

1992-09-21

1997-02-18

Bowler, Alyssa H.

Boots, shoes, and leggings

364578, G06F 15347

Patent

active

056049110

ABSTRACT:
To analyze a physical phenomenon by a computer having a plurality of vector processors and a parallel computer, there is generated submatrices in a preconditioning for obtaining solutions of simultaneous linear equations. Nonzero elements of the coefficient matrix are stored with column number indices assigned thereto such that the elements of the coefficient matrix and the data of right-side vector are scaled according to a sum of absolute values of nondiagonal elements of the coefficient matrix and a diagonal element related thereto. The nonzero elements are sorted depending on magnitude of their absolute values to subdivide the nondiagonal nonzero elements into m submatrices E1, E2, . . . , Em each having substantially a comparable order. Using products developed between differences between a unit matrix and these submatrices in the iterative calculations for a large-sized numerical simulation, there is obtained quite a satisfactory characteristic of convergence of solutions and hence the processing speed is remarkably increased.

REFERENCES:
patent: 4697247 (1987-09-01), Grinberg et al.
patent: 4787057 (1988-11-01), Hammond
patent: 5301342 (1994-04-01), Scott
Chen et al., "Parallel LU Factorization for Circuit Simulation on a MIMD Computer," International Conference on Computer Design, pp. 129-132. May 1988.
Bratkovic, "Improved Numerical Stability of Sparse Matrix Reduction Method," IEEE International Symposium on Circuits and Systems, pp. 631-634. Aug. 1988.
Gustafsson, "A Class of First Order Factorization Methods," BIT 18 (1978), pp. 142-156.
Van Der Vorst, "ICCG and Related Methods for 3D Problems on Vector Computers," Comp. Phys. Communications, 53 (1989), pp. 223-235.
Van Der Vorst, "B1-CGSTAB: A First and Smoothly Converging Variant of BI-CG for the Solution of Nonsymmetric Linear Systems," pp. 1-16 - Could Not Be Considered Due to Lack of Publishing Date.
Ma et al., "2 Iterative Methods . . . 3 Vectorization and Parallelization," vol. 4, Winter 1990, pp. 12-24.

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