A Schwarz alternating algorithm for a three-dimensional exterior harmonic problem with prolate spheroid boundary

Authors:
Xuqiong Luo;Qikui Du;Hongying Huang;Tianshu He
Affiliations:
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu, 210023, China;Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, Jiangsu, 210023, China;School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, China;School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, China
Venue:
Computers & Mathematics with Applications
Year:
2013

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Abstract

In this paper, we investigate a Schwarz alternating algorithm for a three-dimensional exterior harmonic problem with prolate spheroid boundary. Based on natural boundary reduction, the algorithm is constructed and its convergence is discussed. The finite element method and the natural boundary element method are alternatively applied to solve the problem in a bounded subdomain and a typical unbounded subdomain. The convergence rate is analyzed in detail for a typical domain. Two numerical examples are presented to demonstrate the effectiveness and accuracy of the proposed method.