Calculation of domain integrals of two dimensional boundary element method |
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| Affiliation: | 1. Department of Engineering, Bushehr Branch, Islamic Azad University, Bushehr, Iran;2. Department of Applied Mathematics, Amirkabir University of Technology, Tehran, Iran;1. Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, United States;2. KTH Mathematics, Linné Flow Centre/Swedish e-Science Research Center, 100 44 Stockholm, Sweden;1. Instituto de Ciencias Matemáticas, 28049, Madrid, Spain;2. Department of Mathematics, University of Manitoba, Winnipeg, Canada;1. Lund University, Box 118, SE-221 00 Lund, Sweden;2. Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom;1. Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden;2. Electrical and Information Technology, Lund University, Box 118, 221 00 Lund, Sweden;1. Information Technology Laboratory, National Institute of Standards and Technology, Boulder, CO 80305, USA;2. Department of Mathematics Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA;3. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA;4. Beijing Computational Science Research Center, Beijing 100193, China |
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| Abstract: | In this paper, a new method is applied to deal with domain integrals of boundary element method (BEM). In fact we focus to convert the domain integrals into boundary integrals for non-homogenous Laplace, Helmholtz and advection diffusion equations in two dimensional BEM. The transformation presented in this paper is based on divergence theorem. In addition, we prove the efficiency of method mathematically when the domain integrals are weakly singular. Numerical results are presented to verify the validity of this method for different geometries. Numerical implementation is done for the constant BEM, which can be implemented easily. To verify the new scheme, some test problems have been designed at end of the paper. The numerical results generally show that the new scheme has good accuracy with regards to other popular schemes. |
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