A Grid-based integral approach for quasilinear problems |
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Authors: | Jian Ding Wenjing Ye |
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Affiliation: | (1) George W.Woodruff School of Mechanical Engineering, Georgia Institute of Technology, 771 Ferst Dr. MRDC II, Room 316, Atlanta, GA 30332-0405, USA |
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Abstract: | For non-homogeneous and nonlinear problems, a major difficulty in applying the Boundary Element Method is the treatment of
the volume integrals that arise. A recent proposed method, the grid-based integration method (GIM), uses a 3-D uniform grid
to reduce the complexity of volume discretization, i.e., the discretization of the whole domain is avoided. The same grid
is also used to accelerate both surface and volume integration. The efficiency of the GIM has been demonstrated on 3-D Poisson
problems. In this paper, we report our work on the extension of this technique to quasilinear problems. Numerical results
of a 3-D Helmholtz problem and a quasilinear Laplace problem on a multiply-connected domain with Dirichlet boundary conditions
are presented. These results are compared with analytic solutions. The performance of the GIM is measured by plotting the
L2-norm error as a function of the overall CPU time and is compared with the auxiliary domain method in the Helmholtz problem. |
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Keywords: | Quasilinear equation BEM Volume integral Fast algorithm Grid-based integration method |
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