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We investigate the use of sparse approximate inverse preconditioners for the iterative solution of linear systems with dense complex coefficient matrices arising in industrial electromagnetic problems. An approximate inverse is computed via a Frobenius norm approach with a prescribed nonzero pattern. Some strategies for determining the nonzero pattern of an(More)
When solving the linear system Ax = b with a Krylov method, the smallest eigenvalues of the matrix A often slow down the convergence. This is usually still the case even after the system has been preconditioned. Consequently if the smallest eigenvalues of A could be somehow “removed” the convergence would be improved. Several techniques have been proposed(More)
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(More)
In this article we describe our implementations of the GMRES algorithm for both real and complex, single and double precision arithmetics suitable for serial, shared memory and distributed memory computers. For the sake of portability, simplicity, flexibility and efficiency the GMRES solvers have been implemented in Fortran 77 using the reverse(More)
The solution of elliptic problems is challenging on parallel distributed memory computers as their Green's functions are global. To address this issue, we present a set of preconditioners for the Schur complement domain decomposition method. They implement a global coupling mechanism, through coarse space components, similar to the one proposed in 3]. The(More)
The advent of extreme scale machines will require the use of parallel resources at an unprecedented scale, probably leading to a high rate of hardware faults. High Performance Computing (HPC) applications that aim at exploiting all these resources will thus need to be resilient, i.e., be able to compute a correct solution in presence of faults. In this(More)
When solving the Symmetric Positive Definite (SPD) linear system Ax = b with the conjugate gradient method, the smallest eigenvalues in the matrix A often slow down the convergence. Consequently if the smallest eigenvalues in A could be somehow “removed”, the convergence may be improved. This observation is of importance even when a preconditioner is used,(More)
Multigrid methods are among the fastest techniques to solve linear systems arising from the discretization of partial differential equations. The core of the multigrid algorithms is a two-grid procedure that is applied recursively. A two-grid method can be fully defined by the smoother that is applied on the fine grid, the coarse grid and the grid transfer(More)