1 September 1995 Domain decomposition, boundary integrals, and wavelets
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Abstract
We present a domain decomposition procedure for solving the Dirichlet problem for the Laplace equation in the union of two intersecting discs in R2. Each subdomain problem is solved using the boundary integral technique, at each iteration integrating the product of the prior solution multiplied by the normal derivative of the Green's function. The subdomain problems are solved in parallel, in a Jacobi fashion. Numerically, they correspond to multiplying dense matrices by vectors of boundary values. We use DAUB4 wavelets to replace the dense matrices by their sparse approximations, thus reducing the computational complexity. The procedure iterates in `wavelet space', on the wavelet transform of the solution at `internal' boundary points, i.e. at subdomain boundary points not part of the full domain boundary. When the convergence criterion is met, an inverse wavelet transform is applied, and each subdomain problem is solved in full to yield the complete solution. Numerical results are presented.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Sergio E. Zarantonello, Sergio E. Zarantonello, Bracy Elton, Bracy Elton, } "Domain decomposition, boundary integrals, and wavelets", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); doi: 10.1117/12.217641; https://doi.org/10.1117/12.217641
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