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An improvement strategy of a convergence property of a communication-avoiding Krylov subspace method is numerically investigated, and the method is adopted for a linear system obtained from the Element-Free Galerkin (EFG) method. Although a communicationavoiding Krylov subspace method such as k-skip Conjugate Gradient (k-skip CG) improves parallelization efficiency, a convergence property of the method is degraded. To improve this degradation, we propose two improvement techniques, calculating a true residual vector once in several iterations and adopting weighted average of the a true residual and a numerical residual. As the result, the convergence of k-skip CG becomes more stabilized and faster.

Improvement of Convergence Property of Communication Avoiding Conjugate Gradient Method for Linear System Obtained from Meshless Approaches