A constraint preconditioner for solving symmetric positive definite systems and application to the helmholtz equations and poisson equations
Abstract
In this paper, first, by using the diagonally compensated reduction and incomplete Cholesky factorization methods, we construct a constraint preconditioner for solving symmetric positive definite linear systems and then we apply the preconditioner to solve the Helmholtz equations and Poisson equations. Second, according to theoretical analysis, we prove that the preconditioned iteration method is convergent. Third, in numerical experiments, we plot the distribution of the spectrum of the preconditioned matrix M−1A and give the solution time and number of iterations comparing to the results of [5, 19].
First published online: 09 Jun 2011
Keywords:
Helmholtz equations, constraint preconditioner, preconditioned iteration method, incomplete Cholesky factorizationHow to Cite
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Copyright (c) 2010 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2010 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.