Hierarchical matrices for fast multi-patch IgA--BEMs
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Because of the dimensionality reduction they endow, Boundary Element Methods (BEMs) are particularly attractive within the context of Isogeometric Analysis (IgA). Indeed, in such setting the geometry of the domain boundary is exactly specified in (possibly multi-patch generalized) B-spline form and thus generating boundary meshes is much easier than producing volume ones. On the other hand, the matrices associated with both collocation and Galerkin IgA-BEMs are dense and thus accuracy increase becomes soon expensive, in particular in the 3D case. A possibility to reduce the cost of the assembly phase consists of relying on the Adaptive Cross Approximation (ACA) algorithm combined with the hierarchical technique (H-matrices) proposed in which ensures a significant reduction in the number of integrals to be computed and in the required memory storage. The potentialities of H-matrices and of a related implementation of the GMRES iterative solver will be considered and discussed when applied to the IgA-BEM approach for 3D Helmholtz problems introduced in the CAMWA journal by the team Degli Esposti, Falini, Kanduc, Sampoli, Sestini.
