Institut für Mathematik


Modul:   MAT870  Zurich Colloquium in Applied and Computational Mathematics

A Fast Isogeometric Boundary Element Method

Vortrag von Prof. Dr. Helmut Harbrecht

Datum: 09.12.20  Zeit: 16.15 - 17.45  Raum: Online ZHACM

This talk is concerned with an interpolation-​based fast multipole method which is tailored to the context of isogeometric analysis. Hence, the surface is described in terms of a piecewise smooth parameterization by four-​sided patches. This surface representation is in contrast to the common approximation of surfaces by flat panels. Nonetheless, parametric surface representations are easily accessible from Computer Aided Design (CAD). Our fast multipole method is based on Galerkin's method with higher-​order ansatz functions such as B-​splines. Due to an element-​based integration scheme, an element-​wise clustering is possible. This results in a balanced cluster tree, leading to a superior performance. By performing the interpolation for the fast multipole method directly on the two-​dimensional reference domain, we reduce the cost complexity in the polynomial degree by one order. This gain is independent of the application of either $\mathcal{H}$- or $\mathcal{H}^2$-​matrices. Numerical examples are provided in order to quantify and qualify the proposed method.