- An Efficient Approximate Residual Evaluation in the Adaptive Tensor Product Wavelet Method
- Journal of Scientific Computing
- Volume | Issue number
- 57 | 3
- Pages (from-to)
- Document type
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
A wide class of well-posed operator equations can be solved in optimal computational complexity by adaptive wavelet methods. A quantitative bottleneck is the approximate evaluation of the arising residuals that steer the adaptive refinements. In this paper, we consider multi-tree approximations from tensor product wavelet bases for solving linear PDE’s. In this setting, we develop a new efficient approximate residual evaluation. Other than the commonly applied method, that uses the so-called APPLY routine, our approximate residual depends affinely on the current approximation of the solution. Our findings are illustrated by numerical results that show a considerable speed-up.
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