CMRH method as iterative solver for boundary element acoustic systems

Disceretization of boundary integral equations leads to complex and fully populated linear systems. One inherent drawback of the boundary element method (BEM) is that, the dense linear system has to be constructed and solved for each frequency. For large-scale problems, BEM can be more efficient by improving the construction and solution phases of the linear system. For these problems, the application of common direct solver is inefficient. In this paper, the corresponding linear systems are solved more efficiently than common direct solvers by using the iterative technique called CMRH (Changing Minimal Residual method based on Hessenberg process). In this method, the generation of the basis vectors of the Krylov subspace is based on the Hessenberg process instead of Arnoldi's one that the most known GMRES (Generalized Minimal RESidual) solver uses. Compared to GMRES, the storage requirements are considerably reduced in CMRH.

► In acoustics, CMRH was not used for BEM systems before even its availability in the literature.
► The performance of CMRH when applied to acoustic problems solved by BEM was compared to GMRES.
► The behaviour of CMRH is similar to the one of GMRES with less storage and arithmetical operations.
► However, GMRES still a minimizing residual method and therefore an optimal one compared to CMRH.
► Due to their same behaviour, CMRH constitutes a good alternative of GMRES for large-scale problems.