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A dual-primal variant of the FETI-H domain decomposition method is designed for the fast, parallel, iterative solution of large-scale systems of complex equations arising from the discretization of acoustic scattering problems formulated in bounded computational domains. The convergence of this iterative solution method, named here FETI-DPH, is shown to scale with the problem size, the number of subdomains, and the wave number. Its solution time is also shown to scale with the problem size. CPU performance results obtained for the acoustic signature analysis in the mid-frequency regime of mockup submarines reveal that the proposed FETI-DPH solver is significantly faster than the previous generation FETI-H solution algorithm.

The main aim of this paper is to propose a new boundary element algorithm for describing thermomechanical interactions in anisotropic soft tissues. The governing equations are studied based on the dual-phase lag bioheat transfer and Biot’s theory. Due to the advantages of convolution quadrature boundary element method (CQBEM), such as low CPU usage, low memory usage and suitability for treatment of soft tissues that have complex shapes, it is a versatile and powerful method for modeling of bioheat distribution in anisotropic soft tissues and the related deformation. The resulting linear systems for bioheat and mechanical equations are solved by Transpose-free quasi-minimal residual (TFQMR) solver with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner that reduces the iterations number and total CPU time. Numerical results demonstrate the validity, efficiency and accuracy of the proposed algorithm and technique.

The implicit frequency dependence of linear systems arising from the acoustic boundary element method necessitates an efficient treatment for problems in a frequency range. Instead of solving the linear systems independently at each frequency point, this paper is concerned with solving them simultaneously at multiple frequency points within a single iteration scheme. The proposed concept is based on truncation of the frequency range solution and is incorporated into two well-known iterative solvers - BiCGstab and GMRes. The proposed method is applied to two acoustic interior problems as well as to an exterior problem in order to assess the underlying approximations and to study the convergence behavior. While this paper provides the proof of concept, its application to large-scale acoustic problems necessitates efficient preconditioning for multi-frequency systems, which are yet to be developed.

Common multi-frequency solution strategies for acoustic systems are either associated with high computational costs or resort to model reduction strategies, which potentially induce considerable approximation errors. In that context, this work proposes a fast multi-frequency solver for acoustic Boundary Element Method (BEM) analyses that combines conventional preconditioners with an accelerated recycling strategy, achieving in that way a fast and accurate iterative solution. Specifically, by approximating both the system and the related preconditioner by individual affine expressions, an upfront Galerkin projection on a global deflation basis is facilitated, therefore enabling the deployment of the accelerated recycling scheme. The latter acts by accelerating the construction of the related deflation projectors, therefore leading to a significantly faster recycling procedure. Finally, the efficiency of the global deflation basis is guaranteed through an Automatic Krylov subspaces Recycling for Deflation (AKR-D) [D. Panagiotopoulos, W. Desmet and E. Deckers, An accelerated subspaces recycling strategy for the deflation of parametric linear systems based on model order reduction, Comput. Methods Appl. Mech. Eng. 403 (2023) 115765] algorithm and thus, the cumulative number of iterations required by an iterative solver within a frequency sweep is drastically decreased. The proposed multi-frequency solver is tested on two industrially relevant examples of an interior and an exterior scattering problem, benchmarked against the traditional solution strategies.