Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models. (English) Zbl 1289.65048

Bai, Zhong-Zhi

Numer. Linear Algebra Appl. 19, No. 6, 914-936 (2012).

The time-harmonic eddy current model is often used to simulate the electromagnetic phenomena concerning alternating currents at low frequencies. This paper studies the solution for the saddle-point systems that arise from the finite element discretizations of the hybrid formulations of the time-harmonic eddy current problems. By sufficiently utilizing the algebraic properties and the sparse structures of the coefficient matrix, they establish a class of block alternating splitting implicit iteration methods and demonstrate its unconditional convergence. Experimental results shown the feasibility and effectiveness of this class of iterative methods when they are employed as preconditioners for Krylov subspace methods such as GMRES and BiCGSTAB.

Reviewer: Guo-Feng Zhang (Lanzhou)

MSC:

65F10	Iterative numerical methods for linear systems
65F08	Preconditioners for iterative methods
65N22	Numerical solution of discretized equations for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78M10	Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65F50	Computational methods for sparse matrices

Keywords:

splitting iteration method; preconditioning; saddle-point problem; time-harmonic eddy current problem; hybrid formulation; finite element approximation; numerical examples; convergence; Krylov subspace methods; GMRES; BiCGSTAB

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