The Numerical Solution of a Nonlinear Boundary Integral Equation on Smooth Surfaces
نویسنده
چکیده
We study a boundary integral equation method for solving Laplace s equation u with nonlinear boundary conditions This nonlinear boundary value problem is reformulated as a nonlinear boundary in tegral equation with u on the boundary as the solution being sought The integral equation is solved numerically by using the collocation method with piecewise quadratic functions used as approximations to u Convergence results are given for the cases that the origi nal surface is used and the surface is approximated by piecewise quadratic interpolation In addition we de ne and analyze a two grid iteration method for solving the nonlinear system that arises from the discretization of the boundary integral equation Numerical exam ples are given and the paper concludes with a short discussion of the relative cost of di erent parts of the method This work was supported in part by NSF grant DMS
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