Multi-dimensional quadrature of singular and discontinuous functions
2002 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 42, no 3, 644-669 p.Article in journal (Refereed) Published
In many simulations of physical phenomena, discontinuous material coefficients and singular forces pose severe challenges for the numerical methods. The singularity of the problem can be reduced by using a numerical method based on a weak form of the equations. Such a method, combined with an interface tracking method to track the interfaces to which the discontinuities and singularities are confined, will require numerical quadrature with singular or discontinuous integrands. We introduce a class of numerical integration methods based on a regularization of the integrand. The methods can be of arbitrary high order of accuracy. Moment and regularity conditions control the overall accuracy.
Place, publisher, year, edition, pages
2002. Vol. 42, no 3, 644-669 p.
multi-dimensional quadrature, singular integrands, interface tracking, finite element method, discontinuous material coefficients, singular forces, vortex methods, flow
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-21873ISI: 000177846900012OAI: oai:DiVA.org:kth-21873DiVA: diva2:340571
QC 201005252010-08-102010-08-102012-03-08Bibliographically approved