1. An Adaptive Wavelet Method for Solving High-Dimensional Elliptic PDEs
- Author
-
Christoph Schwab, Rob Stevenson, Tammo Jan Dijkema, and Analysis (KDV, FNWI)
- Subjects
Mathematics(all) ,General Mathematics ,Numerical analysis ,Mathematical analysis ,Sparse grid ,High dimensional ,Poisson distribution ,Computational Mathematics ,symbols.namesake ,Tensor product ,Wavelet ,Norm (mathematics) ,symbols ,Anisotropy ,Analysis ,Mathematics - 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.
- Published
- 2009