Ondrej Jakl

Large scale parallel FEM computations of far/near stress field changes in rocks

The paper describes an application of large scale finite element analysis for the assessment of stress changes in rocks induced by mining. This application allows us to illustrate efficiency of an approach based mainly on problem decomposition and parallel computing. For the main part of the computations, which is the solution of large linear systems, we use two decomposition techniques (displacement and domain decomposition). Another decomposition technique is exploited for local FE analysis of the near stress field on so called composite grids. The described methods are tested on the solution of two benchmark problems, which originate from the modelling of the effects of mining. The parallel computations are performed on a small Linux cluster.

Space decomposition preconditioners and their application in geomechanics

This paper addresses the use of space decomposition preconditioners for the numerical solution of boundary value problems. As special cases, it deals with the displacement decomposition (DiD) and overlapping domain decomposition (DD) preconditioners. A special attention is also devoted to inexact solution of sub-problems and the use of non-symmetric preconditioners. In these cases, the generalized preconditioned congugate gradient method is shown to be efficient to use. The considered methods are applied to the solution of selected model problems as well as to a large scale problem arising from assessment of stress changes induced by mining activities.

Displacement decomposition and parallelisation of the PCG method for elasticity problems

This paper describes the displacement decomposition for elasticity problems solved by the finite element method. This decomposition can be used for parallel implementation of the conjugate gradient solvers and construction of parallelisable preconditioners. Both the fixed and variable preconditioning can be applied according to the solution of subproblems. Numerical efficiency of the parallel algorithms is demonstrated on an academic benchmark and real-life modelling problem. A comparison with a domain decomposition technique is also provided.

Parallel Displacement Decomposition Solvers for Elasticity Problems

This article describes the displacement decomposition and its benefits for the parallelization of the preconditioned conjugate gradient method for finite element elasticity problems. It deals with both the fixed and variable preconditioning based on this decomposition. Numerical efficiency of the parallel algorithms is demonstrated on an academic benchmark and real-life modelling problem.

Large-Scale FE Modelling in Geomechanics: A Case Study in Parallelization

The paper develops the Displacement Decomposition technique used already in [1] for parallelization of the Preconditioned Conjugate Gradient method. This time, the solution of very large problems is tackled. We present our experience with (PVM-)parallel solution of a huge finite element model arising from geomechanical practice on usual hardware and describe various facets of the optimizing process, leading to a tenfold improvement of the solution time. Special effects of parallelizing I/O-constrained programs are also addressed.

Parallel solvers for numerical upscaling

This contribution deals with numerical upscaling of the elastic material behaviour, namely of geocomposites, from microscale to macroscale through finite element analysis. This computationally demanding task raises many algorithmic and implementation issues related to efficient parallel processing. On the solution of the arising boundary value problem, considered with either Dirichlet or Neumann boundary conditions, we discuss various parallelization strategies, and compare their implementations in the specialized in-house finite element package GEM and through the general numerical solution framework Trilinos.

Displacement decomposition and parallelization of the PCG method for elasticity problems

This article describes the displacement decomposition and its benefits for the parallelization of the preconditioned conjugate gradient method for finite element elasticity problems. It deals with both the fixed and variable preconditioning based on this decomposition. Numerical efficiency of the parallel algorithms is demonstrated on an academic benchmark and real-life modelling problem.

PVM-Implementation of the PCG Method with Displacement Decomposition

The paper describes a parallel solver based on the Preconditioned Conjugate Gradient Method and its testing on 3D finite element tasks of geomechanics. The parallelization makes use of separation of displacement components (Displacement Decomposition). Two preconditioning techniques are considered. The implementation is based on the message passing model and uses the PVM computing environment. Experience from test runs in on an IBM SP multicomputer is evaluated.

High Performance Computing Applications

Abstract High Performance Computing (HPC) is required for many important applications in chemistry, computational fluid dynamics, etc., see, e.g., an overview in [1]. In this paper we shortly describe an application (a multiscale material design problem) that requires HPC for several reasons. The problem of interest is analysis of the fiber-reinforced concrete and we focus on modelling of stiffness through numerical homogenization and computing local material properties by inverse analysis. Both problems require a repeated solution of large-scale finite element problems up to 200 million degrees of freedom and therefore the importance of HPC computing is evident.

Parallel High-Performance Computing in Geomechanics with Inner/Outer Iterative Procedures

In this paper we address the solution of large linear systems arising from the mathematical modelling in geomechanics and show an example of such modelling. The solution of linear systems is based on displacement decomposition or domain decomposition techniques with inexact solution of the arising subproblems by inner iterations. The use of inner iterations requires a generalization of the preconditioned CG method but brings additional benefits for parallel computation, possibility of reduction of the interprocessor communications and an additional tool of load balance.