A node elimination algorithm for cubature of high-dimensional polytopes

نویسندگان

چکیده

Node elimination is a numerical approach for obtaining cubature rules the approximation of multivariate integrals. Beginning with known rule, nodes are selected elimination, and new, more efficient rule constructed by iteratively solving moment equations. This paper introduces new criterion selecting which to eliminate that based on linearization equation. In addition, penalized iterative solver introduced, ensures weights positive inside integration domain. A strategy constructing an initial various polytopes in several space dimensions described. High efficiency presented two, three four dimensional polytopes. The compared obtained combining tensor products one quadrature domain transformations, as well analytically rules.

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ژورنال

عنوان ژورنال: Computers & mathematics with applications

سال: 2023

ISSN: ['0898-1221', '1873-7668']

DOI: https://doi.org/10.1016/j.camwa.2023.06.001