An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs |
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Authors: | Tammo Jan Dijkema Christoph Schwab Rob Stevenson |
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Institution: | 1. Department of Mathematics, Utrecht University, P.O. Box 80.010, 3508 TA, Utrecht, The Netherlands 2. Seminar for Applied Mathematics, ETHZ HG G58.1, ETH Zürich, 8092, Zürich, Switzerland 3. Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV, Amsterdam, The Netherlands
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Abstract: | Adaptive tensor product wavelet methods are applied for solving Poisson’s equation, as well as anisotropic generalizations, in high space dimensions. It will be demonstrated that the resulting approximations converge in energy norm with the same rate as the best approximations from the span of the best N tensor product wavelets, where moreover the constant factor that we may lose is independent of the space dimension n. The cost of producing these approximations will be proportional to their length with a constant factor that may grow with n, but only linearly. |
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