Load flow computation and contingency analysis is the foundation of power system analysis. Numerical solution to load flow equations are typically computed using Newton-Raphson iteration, and the most time consuming component of the computation is the solution of a sparse linear system needed for the update each iteration. When an appropriate elimination ordering is used, direct solvers are mor...

With respect to the " influence on the development and practice of science and engineering in the 20th century " , Krylov space methods are considered as one of the ten most important classes of numerical methods [1]. Large sparse linear systems of equations or large sparse matrix eigenvalue problems appear in most applications of scientific computing. Sparsity means that most elements of the m...

Given a linear system there are several solvers which can be used to solve it. However, according to the properties of the linear system different solvers may have different convergence speeds, or may even not converge at all. Nevertheless, it can be difficult to verify these properties in practice, mainly due to rounding errors, and there are also some cases where no direct property can be use...

We present the motivation and results of a benchmarking project for linear solvers employed for semiconductor device and circuit simulation. Based on examples coming from current research projects, the performance of a specific set of linear solvers is evaluated. In rare circumstances the results show that it is important to choose the appropriate type of solver for different kind of simulation...

This thesis presents two new linear equation solvers, and investigates their applications in VLSI design automation. Both solvers are derived in the context of a special class of large-scale sparse left-hand-side matrices that are commonly encountered in engineering applications, and techniques are presented that can potentially extend the theory to more general cases. The first is a stochastic...

Quadratic Spline Collocation (QSC) methods of optimal order of convergence have been recently developed for the solution of elliptic Partial Differential Equations (PDEs). In this paper, linear solvers based on Fast Fourier Transforms (FFT) are developed for the solution of the QSC equations. The complexity of the FFT solvers is O(N2 logN), where N is the gridsize in one dimension. These direct...