Boundary Integral Equations for the Laplace-Beltrami Operator

Details Boundary Integral Equations for the Laplace-Beltrami Operator Boundary Integral Equations for the Laplace-Beltrami Operator

2011-11-29

arxiv.org/abs/1111.6962v1

Mathematics and computation, a contemporary view, 21-37, Abel Symp., 3, Springer, Berlin, 2008

Mathematics

Analysis of PDEs

Scientific paper

10.1007/978-3-540-68850-1_2

We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of the unit sphere $\S$ in $\mathbb{R}^3$. We consider a closed curve ${\cal C}$ on ${\cal S}$ which divides ${\cal S}$ into two parts ${\cal S}_1$ and ${\cal S}_2$. In particular, ${\cal C} = \partial {\cal S}_1$ is the boundary curve of ${\cal S}_1$. We are interested in solving a boundary value problem for the Laplace-Beltrami operator in $\S_2$, with boundary data prescribed on $\C$.

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