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VRP-GMRES(m) Iteration Algorithm for Fast Multipole Boundary Element Method
Version 1
: Received: 2 December 2016 / Approved: 2 December 2016 / Online: 2 December 2016 (09:01:51 CET)
A peer-reviewed article of this Preprint also exists.
Yu, C.; Ren, C.; Bai, X. VRP-GMRES(m) Iteration Algorithm for Fast Multipole Boundary Element Method. Math. Comput. Appl. 2016, 21, 49. Yu, C.; Ren, C.; Bai, X. VRP-GMRES(m) Iteration Algorithm for Fast Multipole Boundary Element Method. Math. Comput. Appl. 2016, 21, 49.
Abstract
To solve large scale linear equations involved in the Fast Multipole Boundary Element Method (FM-BEM) efficiently, an iterative method named the generalized minimal residual method (GMRES)(m)algorithm with Variable Restart Parameter (VRP-GMRES(m) algorithm) is proposed. By properly changing a variable restart parameter for the GMRES(m) algorithm, the iteration stagnation problem resulting from improper selection of the parameter is resolved efficiently. Based on the framework of the VRP-GMRES(m) algorithm and the relevant properties of generalized inverse matrix, the projection of the error vector rm+1 on rm is deduced. The result proves that the proposed algorithm is not only rapidly convergent but also highly accurate. Numerical experiments further show that the new algorithm can significantly improve the computational efficiency and accuracy. Its superiorities will be much more remarkable when it is used to solve larger scale problems. Therefore, it has extensive prospects in the FM-BEM field and other scientific and engineering computing.
Keywords
FM-BEM; variable restart parameter; GMRES(m); error vector projection; convergence
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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