Incremental spectral preconditioners for sequences of linear systems
Applied Numerical Mathematics
ACM Transactions on Mathematical Software (TOMS)
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Flexible GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
Iterative Near-Field Preconditioner for the Multilevel Fast Multipole Algorithm
SIAM Journal on Scientific Computing
The BiCOR and CORS Iterative Algorithms for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Combining analytic preconditioner and Fast Multipole Method for the 3-D Helmholtz equation
Journal of Computational Physics
Coupled BEM-FEM for the convected Helmholtz equation with non-uniform flow in a bounded domain
Journal of Computational Physics
Hi-index | 0.01 |
The boundary element method has become a popular tool for the solution of Maxwell's equations in electromagnetism. From a linear algebra point of view, this leads to the solution of large dense complex linear systems, where the unknowns are associated with the edges of the mesh defined on the surface of the illuminated object. In this paper, we address the iterative solution of these linear systems via preconditioned Krylov solvers. Our primary focus is on the design of an efficient parallelizable preconditioner. In that respect, we consider an approximate inverse method based on the Frobenius-norm minimization. The preconditioner is constructed from a sparse approximation of the dense coefficient matrix, and the patterns both for the preconditioner and for the coefficient matrix are computed a priori using geometric information from the mesh. We describe how such a preconditioner can be naturally implemented in a parallel code that implements the multipole technique for the matrix-vector product calculation. We investigate the numerical scalability of our preconditioner on realistic industrial test problems and show that it exhibits some limitations on very large problems of size close to one million unknowns. To improve its robustness on those large problems we propose an embedded iterative scheme that combines nested GMRES solvers with different fast multipole computations. We show through extensive numerical experiments that this new scheme is extremely robust at affordable memory and CPU costs for the solution of very large and challenging problems.