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].

Keywords:

• Helmholtz equations
• constraint preconditioner
• preconditioned iteration method
• incomplete Cholesky factorization