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On the efficient convolution with the Newton potential
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W. Hackbusch
Published/Copyright:
December 20, 2010
Abstract
The convolution 
, where ƒ is smooth, except for some local singularities, arises for example in electronic structure calculations. An efficient convolution with the Newton potential in d dimensions has been proposed in [Hackbusch, Numer. Math. 110: 449–489, 2008]. The convolution is approximated on a refined grid and additional approximations are introduced for efficient evaluation. This paper studies the performance of the method and a precise error analysis of the method is discussed.
Keywords:: convolution; refined grid; tensor product representation; 2-microlocal spaces; pointwise smoothness
Received: 2009-09-23
Revised: 2010-09-30
Published Online: 2010-12-20
Published in Print: 2010-December
© de Gruyter 2010
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- A polynomial chaos approach to stochastic variational inequalities
- On the efficient convolution with the Newton potential
- Adaptive finite element methods for the Laplace eigenvalue problem
- Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error
Keywords for this article
convolution;
refined grid;
tensor product representation;
2-microlocal spaces;
pointwise smoothness
Articles in the same Issue
- A polynomial chaos approach to stochastic variational inequalities
- On the efficient convolution with the Newton potential
- Adaptive finite element methods for the Laplace eigenvalue problem
- Adaptive finite element solution of eigenvalue problems: Balancing of discretization and iteration error
