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Enforce the Dirichlet boundary condition by volume constraint in Point Integral method

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arxiv 1506.02343 v1 pith:AIPDZSFY submitted 2015-06-08 math.NA cs.NA

Zuoqiang Shi This is my paper · ORCID
classification math.NAcs.NA
keywords boundarydirichletpointintegralmethodconditionconstraintproposed
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Recently, Shi and Sun proposed Point Integral method (PIM) to discretize Laplace-Beltrami operator on point cloud. In PIM, Neumann boundary is nature, but Dirichlet boundary needs some special treatment. In our previous work, we use Robin boundary to approximate Dirichlet boundary. In this paper, we introduce another approach to deal with the Dirichlet boundary condition in point integral method using the volume constraint proposed by Du et.al.

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    Tensor neural network approximation reduces high-dimensional nonlocal diffusion integrals to low-dimensional ones via separability, with L2 error estimates for Dirichlet and Neumann conditions and tests up to dimension 20.

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