GPU acceleration of preconditioned solvers for ill-conditioned linear systems

In this work we study the implementations of deflation and preconditioning techniques for solving ill-conditioned linear systems using iterative methods. Solving such systems can be a time-consuming process because of the jumps in the coefficients due to large difference in material properties. We have developed implementations of the iterative...

Efficient Iterative Solution of Large Linear Systems on Heterogeneous Computing Systems

This dissertation deals mainly with the design, implementation, and analysis of efficient iterative solution methods for large sparse linear systems on distributed and heterogeneous computing systems as found in Grid computing. First, a case study is performed on iteratively solving large symmetric linear systems on both a multi–cluster and a...

GPU implementation of deflated preconditioned conjugate gradient

Deflated ICCG Method solving the Singular and Discontinuous Diffusion Equation derived from 3-D Multi-Phase Flows

Simulating bubbly flows is a very popular topic in CFD. These bubbly flows are governed by the Navier-Stokes equations. In many popular operator splitting formulations for these equations, solving the linear system coming from the discontinuous diffusion equation takes the most computational time, despite of its elliptic origins. Sometimes these...

New variants of deflation techniques for bubbly flow problems

For various applications, it is well-known that deflated ICCG is an efficient method for solving linear systems with invertible and singular co-efficient matrix. This deflated ICCG with subdomain deflation vectors is used by us to solve linear systems with singular coefficient matrix, arising from a discretization of the Poisson equation with...

Parallel deflated CG methods applied to linear systems from moving boundary problems

In this report we give a short overview of aspects on parallel deflated conjugate gradient method which is applied on large, sparse, symmetric and semi-positive definite linear systems obtained from moving boundary problems. Moreover, we present some results of small numerical experiments. After introducing the Navier-Stokes equations for...

Some results on the eigenvalue analysis of a SIMPLER preconditioned matrix

In this paper, some theoretical results on the eigenvalue analysis of the SIMPLER preconditioning for incompressible now is presented. Some formulations have been derived to characterize the spectrum of the preconditioned matrix. These results could be helpful for the practical use of the SIMPLER preconditioning. Some numerical tests are reported.

Eigenvalue analysis of the SIMPLE preconditioning for incompressible flow

In this paper, an eigenvalue analysis of the SIMPLE preconditioning for incompressible flow is presented. Some formulations have been set up to characterize the spectrum of the preconditioned matrix. This leads to a generalized eigenvalue problem. The generalized eigenvalue problem is investigated. Some eigenvalue bounds and the estimation for...

Deflation in preconditioned conjugate gradient methods for Finite Element Problems

We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods applied to a Finite Element discretization for an elliptic equation. Our set-up is a Poisson problem in two dimensions with continuous or discontinuous coefficients that vary in several orders of...

The influence of deflation vectors at interfaces on the deflated conjugate gradient method

We investigate the influence of the value of deflation vectors at interfaces on the rate of convergence of preconditioned conjugate gradient methods. Our set-up is a Laplace problem in two dimensions with continuous or discontinuous coeffcients that vary in several orders of magnitude. In the continuous case we are interested in the convergence...

Asymptotic seismic inversion