MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Tensor Structured Evaluation of Singular Volume Integrals

Jonas Ballani and Peter Meszmer


In this article, we introduce a new method for the accurate and fast computation of singular integrals over cuboids in three-dimensional space. Using a straightforward geometric parametrisation of the domain of integration, we interpret the integral as a smooth function on a high-dimensional parameter space. A standard interpolation scheme then leads to a high-dimensional tensor to which an approximation in the data-sparse hierarchical tensor format is applied. Once this approximation is available, the evaluation of an integral value becomes an easy task which does no longer require the treatment of singular terms. Numerical experiments illustrate the potential of the proposed approach for typical examples.

singular integrals, tensor approximation, Hierarchical Tensor Format, Hierarchical Quadrature

Related publications

2012 Repository Open Access
Peter Meszmer and Jonas Ballani

Tensor structured evaluation of singular volume integrals

In: Computing and visualization in science, 15 (2012) 2, pp. 75-86