Linear complexity iterative and log-linear complexity direct solvers are developed for the volume integral equation (VIE) based general large-scale electrodynamic analysis. The dense VIE system matrix is first represented by a new clusterbased multilevel low-rank representation. In this representation, all the admissible blocks associated with a single cluster are grouped together and represent...

When powerful machines such as the Cray-2 became available in the late 1980s, a number of researchers investiWe investigate the use of an inexact Newton’s method to solve the potential equations in the transonic regime. As a test case, gated use of exact Newton’s method for solving steady we solve the two-dimensional steady transonic small disturbance state CFD problems. Direct sparse matrix so...

This thesis presents a parallel resolution method for sparse linear systems which combines effectively techniques of direct and iterative solvers using a Schur complement approach. A domain decomposition is built ; the interiors of the subdomains are eliminated by a direct method in order to use an iterative method only on the interface unknowns. The system on the interface (Schur complement) i...

The present paper is devoted to the numerical solution of nonlinear boundary value problems arising in the magnetic eld computation and in solid mechanics. These problems are discretized by using nite elements. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely mult...

In one type the 6,are fed into the machine in such a way as to drive the unknowns Xj to their correct values. In the second type, the xf are not driven by power supplied from the constant inputs but reach an equilibrium situation corresponding to the solution by a process of adjustment. We are concerned in this article with the operating conditions for this last type of machine when the adjusti...

Time plays an important role in medical and neuropsychological diagnosis and research. In the eld of Electro-and MagnetoEncephaloGraphy (EEG/MEG) source localization, a current distribution in the human brain is reconstructed noninvasively by means of measured elds outside the head. High resolution nite element modeling for the eld computation leads to a sparse, large scale, linear equation sys...

The present paper is devoted to the numerical solution of nonlinear boundary value problems arising in the magnetic eld computation and in solid mechanics. These problems are discretized by using nite elements. The nonlinearity is handled by a nested Newton solver, and the linear systems of algebraic equations within each Newton step are solved by means of various iterative solvers, namely mult...