Generalization of High-Performance Solver for Asymmetric EFG-Type Saddle-Point Problem

Abstract

An application of the eXtended Element-Free Galerkin method to a boundary-value problem reduces to an asymmetric EFG-type Saddle-Point (EFG-SP) problem. How-ever, saddle-point problems are difficult to solve even with iterative methods. For the pur-pose of resolving the difficulties, four types of high-performance solvers were developed for asymmetric EFG-SP problems in the previous study. In the four solvers, after elimi-nating Lagrange multipliers from the problems, the resulting linear systems are solved with Krylov subspace methods. In the present study, the Lagrange-multiplier-elimination method is generalized. As a result, an infinite number of solvers can be derived in principle. Three categories of solvers are introduced and their performance is investigated numerically. Con-sequently, it is found that the resulting solvers are effective especially for large-scale asym-metric EFG-SP problems.