Fast variable preconditioned conjugate gradient method using deflation technique

Fast Linear solvers for electromagnetic field analysis on parallel computing environments are discussed. The preconditioned conjugate gradient (PCG) using incomplete Cholesky (IC) decomposition has been used for finite element analysis so far. However, the IC preconditioning is not suited to parallel computing due to forward/backward substitutions. For this reason, a variable preconditioning in which iterative solvers such as CG are used for preconditioner is introduced in this paper. This method is fit for recent computers with multi core CPUs because of high parallelizing efficiency. Moreover a deflation technique which replaces small eigenvalues with zeros in the system matrix is introduced so as to improve the convergence of PCG method. Numerical results show that the proposed method has high parallelizing efficiency as well as good convergence property in comparison with the conventional PCG method.