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- Tsogtgerel Gantumur, Helmut Harbrecht, Rob P. Stevenson
- Math. Comput.
- 2007

In this paper, an adaptive wavelet method for solving linear operator equations is constructed that is a modification of the method from [Math. Comp, 70 (2001), pp. 27â€“75] by Cohen, Dahmen andâ€¦ (More)

Compression Techniques for Boundary Integral Equations - Asymptotically Optimal Complexity Estimates

- Wolfgang Dahmen, Helmut Harbrecht, Reinhold Schneider
- SIAM J. Numerical Analysis
- 2006

Matrix compression techniques in the context of wavelet Galerkin schemes for boundary integral equations are developed and analyzed that exhibit optimal complexity in the following sense. The fullyâ€¦ (More)

- Helmut Harbrecht, Reinhold Schneider, Christoph Schwab
- Numerische Mathematik
- 2008

We consider the numerical solution of elliptic boundary value problems in domains with random boundary perturbations. Assuming normal perturbations with small amplitude and known mean field andâ€¦ (More)

- Helmut Harbrecht, Rob P. Stevenson
- Math. Comput.
- 2006

We construct wavelets on general n-dimensional domains or man-ifolds via a domain decomposition technique, resulting in so-called composite wavelets. With this construction, wavelets with supportsâ€¦ (More)

The present paper is dedicated to the application of the pivoted Cholesky decomposition to compute low-rank approximations of dense, positive semi-definite matrices. The resulting approximation errorâ€¦ (More)

- Helmut Harbrecht, Reinhold Schneider
- SIAM J. Scientific Computing
- 2006

In this paper we consider the fully discrete wavelet Galerkin scheme for the fast solution of boundary integral equations in three dimensions. It produces approximate solutions within discretizationâ€¦ (More)

Sparse tensor product spaces provide an efficient tool to discretize higher dimensional operator equations. The direct Galerkin method in such ansatz spaces may employ hierarchical bases,â€¦ (More)

- Helmut Harbrecht, Johannes Tausch
- SIAM J. Scientific Computing
- 2013

Abstract. The present paper is concerned with the numerical solution of a shape identification problem for the heat equation. The goal is to determine of the shape of a void or an inclusion of zeroâ€¦ (More)

- Karsten Eppler, Helmut Harbrecht
- Optimization Methods and Software
- 2003

- Karsten Eppler, Helmut Harbrecht
- Comp. Opt. and Appl.
- 2012

The present paper is concerned with the solution of a Bernoulli type free boundary problem by means of shape optimization. Two state functions are introduced, namely one which satisfies the mixedâ€¦ (More)