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...

Several preconditioners based on multigroup diffusion are developed for application to multiplying fixed-source transport problems using the discrete ordinates method. By starting from standard, one-group, diffusion synthetic acceleration (DSA), a multigroup diffusion preconditioner is constructed that shares the same fine mesh as the transport problem. As a cheaper but effective alternative, a...

Boundary value methods (BVMs) for ordinary di erential equations require the solution of nonsymmetric, large and sparse linear systems. In this paper, these systems are solved by using the generalized minimal residual (GMRES) method. A block-circulant preconditioner with circulant blocks (BCCB preconditioner) is proposed to speed up the convergence rate of the GMRES method. The BCCB preconditio...

A special procedure for the numerical solution of two-dimensional obstacle scattering problems is considered. The original exterior problem is approximated by introducing a rectangular artiicial boundary and by imposing an absorbing boundary condition. The scatterer is assumed to have a dielectric coating of variable thickness. Finite element discretization is performed with a structured mesh, ...

In this work, preconditioners for the iterative solution by Krylov methods of the linear systems arising at each Newton iteration are studied. The preconditioner is defined by means of a Broyden-type rank-one update of a given initial preconditioner, at each nonlinear iteration, as described in [5] where convergence properties of the scheme are theoretically proved. This acceleration is employe...