Deflated iterative methods

In Vui99SM the Deflated ICCG method is presented to solve problems with large jumps in the coefficients on layered domains. The idea of deflation combined with an iterative solver is also presented in papers of Nicolaides and Mansfield. It appears that the convergence of DICCG is independent of the size of the jump in the coefficients

The method is generalized to arbitrary domains in Vui01SMW. The deflation vectors used in this paper are denoted as "physical" deflation vectors, because their shape resembles the shape of the eigenvectors. This method is succesfully applied to electromagnetical problems in the paper:

H. De Gersem and K. Hameyer
A deflated iterative solver for magnetostatic finite element models with large differences in permeability
Eur. Phys. J. Appl. Phys., 13, 45-49, 2000

In Fra01V a parallel version of Deflated Krylov subspace methods are given. The deflation vectors are 1 in one subdomain and 0 in all other subdomains. These vectors are called "algebraic" deflation vectors. It appears that the convergence is independent of the number of subdomains. In Vui02SYD a comparison is given of the various choices of the deflation vectors.

For some software see the Deflated Krylov method page.

Other relevant publications are given below.

Contact information:

Kees Vuik


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