An ACA accelerated isogeometric boundary element analysis of potential problems with non-uniform boundary conditions

This paper presents an Adaptive Cross Approximation (ACA) accelerated Isogeometric Boundary Element Method (IGBEM) using Non-Uniform Rational B-Splines (NURBS) as shape and interpolation functions. Provided that NURBS are used in CAD programs to describe geometry, mesh generation in the IGBEM is no longer necessary. For large and complex models the traditional BEM quickly becomes very time and memory consuming. In order to overcome this problem, the use of ACA is considered in this paper. As the NURBS control points are typically located outside the boundary, non-uniform boundary conditions cannot be applied at control points. So, a transformation matrix is used to allow the application of boundary conditions at control points without losing accuracy and, with a special approach, preserving the time and memory advantages of hierarchical matrices provided by the ACA. Two and tree dimensional numerical examples are presented in order to assess the accuracy and feasibility of the method.