Roman Kohut

Schwarz methods for discrete elliptic and parabolic problems with an application to nuclear waste repository modelling

The paper is devoted to the numerical solution of both elliptic and parabolic problems by overlapping Schwarz methods. It demonstrates that while the two-level Schwarz method is necessary for the efficient solution of discrete elliptic problems, the one-level Schwarz method can be sufficiently efficient in the parabolic case. The paper includes results from numerical simulations of a large-scale model of the performance of a nuclear waste repository.

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.

Inexact Newton solvers in plasticity: Theory and experiments

Applications of inexact Newton and inexact Newton-like solvers are described and analysed for the solution of non-linear systems arising in the numerical solution of problems of elastoplasticity. Both explicit and return mapping incremental finite element algorithms are considered.

GEM: a platform for advanced mathematical geosimulations

The contribution deals with the development of a 3-D finiteelement package called GEM and its aspirations in demanding mathematical modelling and simulations arising in geosciences. On the background of two complex applications from the presently running projects, formulated as linear elasticity and thermo-elasticity problems, the most important characteristics, especially those of the solvers, are presented. Features related to high performance computing, including parallel processing, are focused on.

Parallel computing of thermoelasticity problems

The paper deals with a finite element solution of transient thermoelasticity problems. For each time step the system of linear algebraic equations is solved using a parallel solver based on the overlapping domain decomposition method. The time steps are chosen adaptively. The results of numerical tests on a large benchmark problem are presented.

Material parameter identification with parallel processing and geo-applications

The paper describes numerical solution of material parameter identification problems, which arise in geo-applications and many other fields. We describe approach based on nonlinear least squares minimization using different optimization techniques (Nelder-Mead, gradient methods, genetic algorithms) as well as experience with OpenMP+MPI parallelization of the solution methods.

Solution of identification problems in computational mechanics --- parallel processing aspects

Problems of identification of material parameters (mostly parameters appearing in constitutive relations) have applications in many fields of engineering including investigation of processes in a rock mass. This paper outlines the structure of parameter identification problems, methods for their solution and describes an identification (calibration) problem from geotechnics, which will serve as a realistic benchmark problem for illustration of the behaviour of selected parameter identification methods.

Composite grid finite element method: Implementation and iterative solution with inexact subproblems

This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits of the described methods. We also discuss the case of inexact subproblems, which can frequently arise in the course of hierarchical modelling.

The Evaluation of the Thermal Behaviour of an Underground Repository of the Spent Nuclear Fuel

The paper concerns the evaluation of the thermal behaviour of an underground repository of the spent nuclear fuel where the canisters are disposed at a vertical position in the horizontal tunnels. The formulation of thermo-elastic problems should regard the basic steps of the construction of the repository. We tested the influence of the distance between the deposition places on the thermo-elastic response of the rock massif. The problems are solved by the in-house GEM-FEM finite element software. One sided coupling allows a separate solution of the temperature evolution and the computation of elastic responses only in predefined time points as a post-processing to the solution of the heat equations. A parallel solution of the arising linear systems by the conjugate gradient method with a preconditioning based on the additive Schwarz methods is used.

MPI and openMP computations for nuclear waste deposition models

In this paper, we introduce one important source of highperformance computations, namely mathematical modelling of deep geological repositories of the spent nuclear fuel, and describe two real concepts of such repositories. Mathematical modelling is practically the only way how to predict the behaviour of such facilities in their long-term existence. We present a simplified mathematical model that considers thermo-mechanical behaviour of the repositories and the corresponding in-house solver. This solver is analyzed as a parallel application with both MPI and OpenMP realizations. On the example of the two repositories and related demanding computations we develop a case study focused on practical comparison of those two paradigms of parallel processing.