We consider nonlinear algebraic systems resulting from numerical discretizations of nonlinear partial differential equations of diffusion type. To solve these systems, some iterative nonlinear solver and, on each step of this solver, some iterative linear solver are used. We derive adaptive stopping criteria for both iterative solvers. Our criteria are based on an a posteriori error estimate wh...

This article is the second in a series of two papers concerning mathematical study boundary integral equation kind that describes interaction N dielectric spherical particles undergoing mutual polarisation. The first presented numerical analysis Galerkin method used to solve this and derived -independent convergence rates for induced surface charges total electrostatic energy. current will focu...

We describe the iterative solution of dense linear systems arising from a surface integral equation of electromagnetic scattering. The complex symmetric version of QMR has been used as an iterative solver together with a sparse approximate inverse preconditioner. The preconditioner is computed using the topological information from the computational mesh. The matrix-vector products are computed...

Large CFD problems are often solved using iterative methods. Preconditioning is mandatory to accelerate the convergence of iterative methods. This paper presents new results using several preconditioning techniques. These preconditoners are non-standard in the CFD community. Several numerical tests were carried out for solving three-dimensional incompressible, compressible and magneto-hydrodyna...

Three-dimensional device simulations of sidewall trench-isolated MOSFETs involve Linear systems of equations that are extremely ill-conditioned if the geometric channel length exceeds 2pm. Since conventional preconditioned iterative methods tend to fail in such cases we have implemented a robust iterative linear solver using a hierarchy of incomplete factorizations of the coefficient matrix.

We consider algorithms for solving narrow-banded diagonally dominant linear systems which are suitable for multiprocessors. We describe a direct solver similar to that in [12] for tridiagonal systems, and in [9] for solving a banded system on a linearly connected set of processors. We will also provide and analyze a parallel implementation of the partitioning algorithm and the matrix decomposit...

In this project, parallel general-purpose software for two classes of mathematical problems has been developed. PVODE is a portable solver for ordinary di erential equation systems, based on robust mathematical algorithms, and targeted at large systems on parallel machines. It is the parallel extension of the earlier sequential solver CVODE. A related solver called KINSOL has been developed for...

2 Sparse Matrices ……………………………………………………………………………… 4 2.1 The direct solution of sparse unsymmetric linear sets of equations (I.S. Duff and J.K. Reid) …………………………………………………………………………… 4 2.2 The design and use of algorithms for permuting large entries to the diagonal 2.6 Element resequencing for use with a multiple front solver (J. A. Scott) ………… 10 2.7 Exploiting zeros on the diagonal in the direct s...