Generalized boundary element method for galerkin boundary integrals |
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| Affiliation: | 1. Departamento de Engenharia Mecânica, Universidade Federal de Santa Catarina, Florianópolis, SC 88010-970, Brazil;2. IPUC, Pontifícia Universidade Católica de Minas Gerais, Belo Horizonte, MG, CEP 30535-610, Brazil;3. Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada;1. Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran;2. Centre for Infrastructure Engineering, Western Sydney University, Penrith, NSW 2751, Australia;3. Department of Civil Engineering, Isfahan University of Technology, Isfahan, Iran;1. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13560-970, São Carlos, SP, Brazil;2. Department of Mathematics, Rutgers University, Piscataway, NJ, United States of America;1. Università IUAV di Venezia, Italy;2. Department of Engineering; University of Ferrara, Italy |
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| Abstract: | A meshless approach to the Boundary Element Method in which only a scattered set of points is used to approximate the solution is presented. Moving Least Square approximations are used to build a Partition of Unity on the boundary and then used to construct, at low cost, trial and test functions for Galerkin approximations. A particular case in which the Partition of Unity is described by linear boundary element meshes, as in the Generalized Finite Element Method, is then presented. This approximation technique is then applied to Galerkin boundary element formulations. Finally, some numerical accuracy and convergence solutions for potential problems are presented for the singular, hypersingular and symmetric approaches. |
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