Abstract : The development of a suitable, efficient and accurate numerical method to solve wave problems is encountered in many academic and industrial applications. The Boundary Integral Equation (BIE) technique, whose discretization is known as the Boundary Element Method (BEM), is an appealing alternative to classical domain method because it allows to handle problems defined on the exterior of bounded domains as easily as those defined in the interior, without the introduction of an artificial boundary to truncate the computational domain. Very recently, an Isogeometric Analysis based Boundary Element Method (IgA-BEM) has been proposed in literature for the numerical solution of frequency-domain (Helmholtz) wave problems on 3D domains admitting a multi-patch representation of the boundary surface. While being powerful and applicable to many situations, this approach shares with standard BEMs a disadvantage which can easily become significant in the 3D setting. Indeed, when the required accuracy is increased, it can soon lead to large dense linear systems, whose numerical solution requires huge memory, resulting also in important computational cost. Recently the development of fast H-matrix based direct and iterative solvers for oscillatory kernels, as the Helmholtz one, has been studied. Here, we investigate the effectiveness of the H-matrix technique, along with a suitable GMRES iterative solver, when used in the context of multi-patch IgA-BEM.

Keywords : Helmholtz equation; isogeometric analysis; boundary element methods; hierarchical matrices