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• W3130672287 abstract "Linear equation solvers require considerable computational time in many computer simulation methods, such as the stress analysis using the finite element method (FEM), or the fluid dynamics using an implicit time integration scheme. Because of their favorable nature to modern supercomputers, Krylov-type linear equation solvers have become dominant. Krylov-type solvers are usually used with preconditioners, which accelerate the convergence of Krylov solvers, and therefore developing robust preconditioners draws attention from researchers. The basic idea of preconditioning is to transform the original system to a system which can be solved more easily by using a matrix which resembles the original system but the associated linear system can be solved without any difficulties. In this study, we propose a new methodology of constructing such a matrix by updating the matrix using the information obtained through the Krylov solver computation. More precisely, we employ the limited memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) Hessian matrix update scheme. The proposed scheme is combined with the orthogonal minimum (ORTHOMIN) residual method, which accepts a variable preconditioner. As a result of performance tests, in the best case scenario, (1) with the Matrix Market matrices, our new method combined with Algebraic Multigrid (AMG) shows the successful convergence in 12 cases out of 13 problems, whilst the conventional AMG converged only in four cases and (2) with FEM problems, we obtained [Formula: see text] acceleration in the rate of converge and [Formula: see text] in computational time over the AMG preconditioned conjugate gradient (CG) solver. With those results, our newly developed algorithm provides robustness to the conventional preconditioning, whilst the computational speed is superior to conventional ones." @default.
• W3130672287 created "2021-03-01" @default.
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• W3130672287 date "2021-04-12" @default.
• W3130672287 modified "2023-10-03" @default.
• W3130672287 title "Iterative Approximation of Preconditioning Matrices Through Krylov-Type Solver Iterations" @default.
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• W3130672287 doi "https://doi.org/10.1142/s0219876221500274" @default.
• W3130672287 hasPublicationYear "2021" @default.
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