Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Integral Equations of Helmholtz Equation

CHENG Pan; HUANG Jin; WANG Zhu

doi:10.3879/j.issn.1000-0887.2011.12.002

Volume 32 Issue 12

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CHENG Pan, HUANG Jin, WANG Zhu. Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Integral Equations of Helmholtz Equation[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1405-1414. doi: 10.3879/j.issn.1000-0887.2011.12.002

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Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Boundary Integral Equations of Helmholtz Equation

doi: 10.3879/j.issn.1000-0887.2011.12.002

School of Science, Chongqing Jiaotong University, Chongqing 400074, P. R. China;
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, P. R. China;
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, U. S. A

Received Date: 2010-11-18
Rev Recd Date: 2011-11-02
Publish Date: 2011-12-15

Abstract

Abstract

Mechanical quadrature methods(MQMs) for solving nonlinear boundary integral equations of Helmholtz equation, which possessed high accuracy order O (h³) and low computing complexities, were presented. Moreover, the mechanical quadrature methods were simple without computing any singular integration. A nonlinear system was constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system were proved based on asymptotical compact theory and Stepleman theorem. Using the h³-Richardson extrapolation algorithms (EAs), the accuracy order to O (h⁵) was improved. For solving the nonlinear system, Newton iteration was discussed extensively by Ostrowski fixed point theorem. The efficiency of the algorithms was illustrated by numerical examples.
- Helmholtz equation,
- mechanical quadrature method,
- Newton iteration,
- nonlinear boundary condition

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References(22)

References

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