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2006年本科毕业于大连理工大学数学与应用数学专业，2008年硕士毕业于大连理工大学计算数学专业(导师：于波 教授)，2011年博士毕业于日本名古屋大学计算理工学专攻，获博士(工学)学位(导师：张绍良 教授)。后在筑波大学计算机科学专攻从事博士后研究工作(日本技术振兴机构CREST项目资助，合作导师：Prof. SAKURAI Tetsuya)。2014年回国任职于大连理工大学数学科学学院。主要研究内容包括：大型稀疏线性方程组求解、矩阵特征值计算、高性能科学计算等。

### Is the Burton-Miller formulation really free of fictitious eigenfrequencies?

• 论文类型：期刊论文
• 发表刊物：ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
• 收录刊物：SCIE、EI、Scopus
• 卷号：59
• 页面范围：43-51
• ISSN号：0955-7997
• 关键字：Boundary element method; Fictitious eigenfrequency; Burton-Miller formulation; Coupling parameter; Pulsating sphere; Contour integral method
• 摘要：This paper is concerned with the fictitious eigenfrequency problem of the boundary integral equation methods when solving exterior acoustic problems. A contour integral method is used to convert the nonlinear eigenproblems caused by the boundary element method into ordinary eigenproblems. Since both real and complex eigenvalues can be extracted by using the contour integral method, it enables us to investigate the fictitious eigenfrequency problem in a new way rather than comparing the accuracy of numerical solutions or the condition numbers of boundary element coefficient matrices. The interior and exterior acoustic fields of a sphere with both Dirichlet and Neumann boundary conditions are taken as numerical examples. The pulsating sphere example is studied and all fictitious eigenfrequencies corresponding to the related interior problem are observed. The reasons are given for the usual absence of many fictitious eigenfrequencies in the literature. Fictitious eigenfrequency phenomena of the Kirchhoff-Helmholtz boundary integral equation, its normal derivative formulation and the Burton-Miller formulation are investigated through the eigenvalue analysis. The actual effect of the Burton-Miller formulation on fictitious eigenfrequencies is revealed and the optimal choice of the coupling parameter is confirmed. (C) 2015 Elsevier Ltd. All rights reserved.
• 发表时间：2015-10-01