An accelerated deflation preconditioner for acoustic BEM systems based on subspace recycling

Following a classic Krylov subspace recycling [1] technique in the context of frequency sweep analyses performed with the acoustic BEM [2] might inflict unnecessary overhead costs. To speed up such a procedure, this work employs an accelerated recycling technique that is based on the recently proposed model order reduction framework for BEM systems [3]. Specifically, employing an affine approximation of a BEM system in combination with a Galerkin projection on the deflation basis, the operation of constructing the corresponding deflation based preconditioner is significantly accelerated. The efficiency of the deflation basis for the entire frequency range is guaranteed through an Automatic Krylov subspace Recycling (AKR) [4] algorithm, thus leading to a drastic decrease of the number of iterations required by an iterative solver. The proposed approach is tested on an academic BEM example and achieves significant acceleration of the computed frequency sweep by ensuring fast convergence of the employed iterative solver, avoiding overhead projection costs.