By combining element-by-element estimates for the field of values of a preconditioned matrix with GMRES-convergence estimates it is possible to derive an easily computable upper bound on the GMRES-residual norm. This method can be applied to general finite element systems, but the preconditioner has to be Hermitian and positive definite. The resulting upper bound for the GMRES-residual norm can...

In this paper, the efficiency of a parallelizable preconditioner for Domain Decomposition Methods in the context of the solution of non-symmetric linear equations arising from the discretization of the conservation laws in hydrology (e.g., the coupled surface and sub-surface flow over a freatic acuifer) is investigated. The Interface Strip Preconditioner (IS) proposed is based on solving a prob...

Immersed finite element methods generally suffer from conditioning problems when cut elements intersect the physical domain only on a small fraction of their volume. De Prenter et al. [Computer Methods in Applied Mechanics and Engineering, 316 (2017) pp. 297–327] present an analysis for symmetric positive definite (SPD) immersed problems, and for this class of problems an algebraic precondition...

We discuss techniques for accelerating the self-consistent field iteration for solving the Kohn–Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied by the total potential. They can be viewed as preconditioners for a fixed point iteration. We point out different requirements for constructing prec...

A parallel preconditioner is presented for the solution of general sparse linear systems of equations. A sparse approximate inverse is computed explicitly and then applied as a preconditioner to an iterative method. The computation of the preconditioner is inherently parallel, and its application only requires a matrix-vector product. The sparsity pattern of the approximate inverse is not impos...

We introduce a preconditioner for the solution of the Bidomain system governing the propagation of action potentials in the myocardial tissue. The Bidomain model is a degenerate parabolic set of nonlinear reaction-diffusion equations. The nonlinear term describes the ion flux at the cellular level. The degenerate nature of the problem results in a severe ill conditioning of its discretization. ...

We investigate and compare a few parallel preconditioning techniques in the iterative solution of large sparse linear systems arising from solid Earth simulation with and without using contact information in the domain partitioning process. Previous studies are focused on using static or matrix pattern based incomplete LU (ILU) preconditioners in a localized preconditioner implementation. Our c...

A Newton–Krylov method is developed for the solution of the steady compressible Navier– Stokes equations using a discontinuous Galerkin (DG) discretization on unstructured meshes. Steady-state solutions are obtained using a Newton–Krylov approach where the linear system at each iteration is solved using a restarted GMRES algorithm. Several different preconditioners are examined to achieve fast ...

The classical optimal (in the Frobenius sense) diagonal preconditioner for large sparse linear systems Ax = b is generalized and improved. The new proposed approximate inverse preconditioner N is based on the minimization of the Frobenius norm of the residual matrix AM − I, where M runs over a certain linear subspace of n × n real matrices, defined by a prescribed sparsity pattern. The number o...