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Parallel Computing in Geosciences

UPPMAX project no. P2004009, 2004 - 2006


The project represents multi-disciplinary research involving mathematical modelling of problems arising in geophysics and geo-engineering applications, numerical solution methods with an emphasis on preconditioned iterative techniques and their efficient implementation on parallel computers. The geosciences and geo-engineering nowadays consider a variety of problems, which demand the use of sophisticated large-scale computer modelling. The target problems with this project include modelling of stress field changes due to mining and underground constructions, assessment of underground nuclear waste repository projects as well as elastic and viscoelastic effects of the Earth due to other glacial advance and recession.

The very high complexity of these problems is usually determined by the required models. As an example, the mechanical behaviour of rocks can be described by models ranging from linear elasticity to models involving nonlinear material response, permanent deformation, rheology phenomena or influence of thermal changes and flow in porous media. The large-scale arises when we consider large 3D domains to enable monitoring of the far field effects as well as to be able to specify realistic boundary conditions. Simultaneously, some engineering decisions are based on a detailed analysis of the near field processes.

The solution of the above described problems then requires the use of robust and numerically efficient iterative solution methods and their implementation on modern parallel computer architectures. This project addresses both discretization of the mathematical models by the finite element method and solution of the discretized problems by robust and efficient iterative methods using domain decomposition ideas combined with hierarchical substructuring approaches.

The considered numerical methods include Krylov subspace methods preconditioned by Schwarz-type decomposition methods accelerated by an auxiliary coarse grid problem. Such methods are applied to a hierarchy of problems including elasticity, thermo-elasticity, visco-elasticity and poro-elasticity.

Aims of project

  • To implement the developed methods on various types of computer architectures using different programming paradigms (MPI and OpenMP) and to improve the overall parallel performance of the methods to insure short simulation times.
  • To compare the scalability and performance of the solvers on various computer platforms.

Solved problems

  • DR - development of stresses due to mining.
    Large-scale 3D geotechnical model, Dolni Rozinka, the Czech Republic.
  • KBS - modelling thermo-mechanical phenomena.
    Large-scale 3D geoenvironmental model, Aspo Prototype Repository, Sweden.

Used computers

Reports and presentations
J. Stary: Application of parallel computing to elasticity and thermoelasticity problems ( PDF, 896 kB ), Uppsala, November 23, 2004
G. Bencheva, S. Margenov, J. Stary: Parallel PCG Solver for Nonconforming FEM problems: Overlapping of Communication and Computations. LSSC 2005, Springer, LNCS. Conference Large-Scale Scientific Computations 2005, Sozopol, June 6 - 10, 2005
R. Blaheta, R. Kohut, M. Neytcheva, J. Stary: Schwarz Methods for Discrete Elliptic and Parabolic problems with an Application to Nuclear Waste Repository Modelling. Submitted to Mathematics and Computers in Simulation, IMACS/Elsevier, special issue Modelling 2005. IMACS conference Modelling 2005, Pilsen, July 4 - 8, 2005
Research team
UU - Scientific Computing Group
Department of Information Technology
Uppsala University, Sweden
IGAS - Department of Applied Mathematics and Computer Science
Institute of Geonics AS CR
Ostrava, Czech Republic
IPP - Scientific Computing Department
Institute for Parallel Processing BAS
Sofia, Bulgaria
ARTEC - Research Centre for Advanced Remediation Technologies
Technical University of Liberec, Czech Republic