Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# 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

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

* All users must log in before leaving a comment
Views 0