A significant portion of the time required for simulating full three-dimensional (3D) charge transport in semiconductor devices using particle-based methods is spent solving the necessary field equations. Two highly effective, iterative techniques available for solving largesparse systems of equations are the conjugate gradient (CG) method and the multigrid (MG) method. In this work, variants o...

We develop a basic mathematical framework for specifying and formally designing highperformance constraint solving algorithms. The framework is based on concepts from abstract interpretation which generalizes earlier work on a Galois Connection-based model of Global Search algorithms. The main focus is on how to use the framework to automate the calculations necessary to construct a correct, hi...

In this white paper we describe work done on the development of an efficient iterative solver for lattice QCD based on the Algebraic Multi-Grid approach (AMG) within the tmLQCD software suite. This development is aimed at modern computer architectures that will be relevant for the Exa-scale regime, namely multicore processors together with the Intel Xeon Phi coprocessor. Because of the complexi...

.. ................................................................................................................... ix Chapter 1. Introduction ..................................................................................................1 Chapter 2. Background ..................................................................................................6 2.1. Matrix Compu...

An iterative method is described that solves the constrained min-imisation of a convex function, when the constraints g j (x 1 ; ::; x n) 0 are function of only a few variables and can be partitioned in some way. A proof of convergence is given which is based on the fact that the function values that are generated decrease. The relation to the non-linear equation solver TanGS VKL93] is shown, t...

In this paper, we present a parallel software for solving linear flow equations in two kinds of subsurface media, a 2D highly heterogeneous porous medium and a 3D fracture network. Parallel computing allows us to solve very large linear systems improving the realism of simulations. For these two applications, we perform a scalability analysis of two parallel solvers : HYPRE and PSPASES. HYPRE i...

A parallel implementation of the preconditioned conjugate residual (PCR) method is described. The method is used to solve the discretized generalised Stokes problem derived from the simulation of complex 2D axisymetrical hot metal forming process. We numerically show that the use of a simple diagonal block (BDS) preconditioner results in a high level of parallelism. Nevertheless in 2D, the iter...

Investigating the fractal behavior of iteration methods on special polynomials can help to find iterative with global convergence for finding matrix functions. By employing such a methodology, we propose new solver sign an invertible square matrix. The presented method achieves fourth rate by using as few products possible. Its attraction basin shows larger radii, in contrast its Padé-type same...

Background: Photon attenuation as an inevitable physical phenomenon influences on the diagnostic information of SPECT images and results to errors in accuracy of quantitative measurements. This can be corrected via different physical or mathematical approaches. As the correction equation in mathematical approaches is nonlinear, in this study a new method of linearization called ‘Piece ...