Ondřej Jakl

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.

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.

Parallel schwarz methods: algebraic construction of coarse problems, implementation and testing

The paper describes domain decomposition methods of the Schwarz type with coarse problems constructed algebraically by aggregation of unknowns. The description includes a new method with no overlap of subdomains and interfaces on the coarse grid. Implementation issues are discussed for all the methods and their comparison is made on a model elasticity problem. Special attention is given to nonsymmetric hybrid preconditioners. A parallel implementation of the additive Schwarz method is tested on a 3D elasticity problem, employing a Beowulf cluster.

Iterative Solution of Singular Systems with Applications

This paper deals with efficient solution of singular symmetric positive semidefinite problems. Our motivation arises from the need to solve special problems of geotechnics, e.g. to perform upscaling analysis of geocomposites. In that and other applications we have to solve boundary problems with pure Neumann boundary conditions. We show that the stabilized PCG method with various preconditioners is a good choice for systems resulting from the numerical solution of Neumann problems, or more generally problems with a known small dimensional null space.

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.

Optimization methods for calibration of heat conduction models

The paper provides a summary of techniques, which are suitable for calibration of models like both stationary and nonstationary heat conduction. We assume that the PDE based models are discretized by finite elements and PDE coefficients are piecewise constant on apriori given macroelements (subdomains). A special attention is given to Gauss-Newton methods, evaluation of the derivatives and application of these methods to a heat evolution problem, which arose in geoengineering.

Parallel thermo-mechanical modelling for nuclear waste deposition

The context of the paper is finite element solution of transient thermo-elasticity problems, motivated by the global need to simulate the operation of nuclear waste repositories. In this context, the paper deals with large-scale parallel processing of nonstationary heat equations, when the linear systems arising in each time step are solved by the overlapping domain decomposition method. The numerical experiments are performed on a large thermo-elasticity model simulating the behaviour of spent nuclear fuel stored using the Swedish KBS-3 method. The developed parallel codes are based on the OpenMP and MPI standards and their performance is investigated.

Parallel Schwarz methods for T-M modelling

The paper deals with a finite element solution of transient thermo-elasticity problems. In this context, it is especially devoted to the parallel computing of nonstationary heat equations, when the linear systems arising in each time step are solved by the overlapping domain decomposition method. The numerical tests are performed by OpenMP and/or MPI solvers on a large benchmark problem derived from geoenvironmental model KBS.

Parallel simulation of t-m processes in underground repository of spent nuclear fuel

In the background of our interest in the modelling of thermo-mechanical phenomena is its relevancy to the assessment of underground repositories of nuclear waste – a highly urgent topic worldwide, with great impact on the future of nuclear power utilization. In this context, one of the most internationally recognised project is the Aspo Prototype Repository in Sweden, which is a full-scale experimental realisation of the KBS-3 concept of spent nuclear fuel repository [3], where modelling of phenomena such as heat transfer, moisture migration, solute transport and stress/strain development can be verified.

Space Decomposition Solvers and Their Performance in PC-Based Parallel Computing Environments

The paper summarizes progress we have made since PPAM 2001 [1] in the parallel solution of large-scale FE systems arising from mathematical modelling in geomechanics. It tracks both the development of the mathematical methods implemented in the solvers, where the overlapping domain decomposition is contraposed to the displacement decomposition covered in [1], and also the performance advantage provided by a self-made Beowulf cluster for practical parallel computing.