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Symbolic integration with respect to the Haar measure on the unitary groups

Puchała Z., Miszczak J. A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 1

21--27

We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of special cases which can be used to optimize the calculation speed for some classes of integrals. We also provide some examples of usage of the presented package.

Całkowanie numeryczne i analityczne na przykładzie metody elementów brzegowych Galerkina

Łukasik E., Pańczyk B., Sikora J.

Metody Informatyki Stosowanej

2011

nr 3

91-103

The traditional Boundary Element Method (BEM) is a numerical technique for solving some partial differential equations. The classical BEM produces fully populated coefficients matrix. With Galerkin Boundary Element Method (GBEM) is possible to produce the symmetric coefficients matrix. Generally the Galerkin boundary integral equations lead to the algebraic system where coefficients are defined by one or two dimensional integrals. The main problems are related to the integrals evaluation and treatment of the singularities. The article presents the general form of GBEM equations and problems associated with integration.