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A fast direct solver for nonlocal operators in wavelet coordinates

Harbrecht, Helmut ; Multerer, Michael

In: Journal of computational physics, 2021, vol. 428, p. 15 p

In this article, we consider fast direct solvers for nonlocal operators. The pivotal idea is to combine a wavelet representation of the system matrix, yielding a quasi- sparse matrix, with the nested dissection ordering scheme. The latter drastically reduces the fill-in during the factorization of the system matrix by means of a Cholesky decomposition or an LU decomposition, respectively. This...

A Note on the Construction of L -Fold Sparse Tensor Product Spaces

Griebel, Michael ; Harbrecht, Helmut

In: Constructive Approximation, 2013, vol. 38, no. 2, p. 235-251

Preconditioning of wavelet BEM by the incomplete Cholesky factorization

Harbrecht, Helmut

In: Computing and Visualization in Science, 2012, vol. 15, no. 6, p. 319-329

On analytical derivatives for geometry optimization in the polarizable continuum model

Harbrecht, Helmut

In: Journal of Mathematical Chemistry, 2011, vol. 49, no. 9, p. 1928-1936

Approximation of bi-variate functions: singular value decomposition versus sparse grids

Griebel, Michael ; Harbrecht, Helmut

In: Ima Journal of Numerical Analysis, 2014, vol. 34, no. 1, p. 28-54