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Parallelization of Preconditioned MRTR Method With Eisenstat’s Technique by Means of Algebraic Multicolor Ordering

The performance of preconditioned Minimized Residual method based on the Three-term Recurrence formula of the conjugate gradient CG-type (MRTR) method has been demonstrated on various symmetric linear systems based on 3-D FEM. The symmetric Gauss-Seidel-preconditioned MRTR method with Eisenstat's technique (MESGS-MRTR) has higher validity for reducing the elapsed time when a conventional PC is used. However, MESGS-MRTR cannot be parallelized, when a block preconditioner is adopted. Therefore, we propose a parallelized MESGS-MRTR method supported by algebraic multicolor ordering in the 3-D low-frequency electromagnetic problems. We present a performance comparison of the proposed method with block preconditioner using reverse Cuthill-McKee ordering.