An efficient matrix-free preconditioned conjugate gradient based multigrid method for phase field modeling of fracture in heterogeneous materials from 3D images

The Multigrid Preconditioned Conjugate Gradient Method

multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wave length components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an e cient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition...

Comparison of the Deflated Preconditioned Conjugate Gradient Method and Algebraic Multigrid for Composite Materials

Many applications in computational science and engineering concern composite materials, which are characterized by large discontinuities in the material properties. Such applications require fine-scale finite-element (FE) meshes, which lead to large linear systems that are challenging to solve with current direct and iterative solutions algorithms. In this paper, we consider the simulation of a...

Multigrid Preconditioned Conjugate Gradient Method in the Mechanical Analysis of Heterogeneous Solids

A fast solver method called the multigrid preconditioned conjugate gradient method is proposed for the mechanical analysis of heterogenous materials on the mesoscale. Even small samples of a heterogeneous material such as concrete show a complex geometry of different phases. These materials can be modeled by projection onto a uniform, orthogonal grid of elements. As one major problem the possib...

Preconditioned Conjugate Gradient Method for Boundary Artifact-Free Image Deblurring

Several methods have been proposed to reduce boundary artifacts in image deblurring. Some of those methods impose certain assumptions on image pixels outside the field-of-view; the most important of these assume reflective or anti-reflective boundary conditions. Boundary condition methods, including reflective and anti-reflective ones, however, often fail to reduce boundary artifacts, and, in s...

Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU