O. Zone

Catholic University of Louvain, Walloon Region, Belgium

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Publications (7)2.63 Total impact

  • O. Zone, R. Keunings, D. Roose
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    ABSTRACT: This work constitutes the first phase of a long-term project, namely the efficient implementation of direct solution methods for complex finite element problems on distributed memory parallel computers. Although for the most part limited to the one-dimensional case, our results demonstrate the potential of parallel computing for this class of problems. It is found that the efficiency of the proposed algorithms increases as the problem size increases. We have shown that a performance model can be developed and used for predicting with good accuracy the behavior of the proposed algorithms. Finally, our preliminary results for the two-dimensional case are encouraging. Work is underway to further generalize the present approach to complex multi-dimensional problems.
    04/2006: pages 294-303;
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    ABSTRACT: Parallel finite element algorithms are proposed for the solution of physical problems described by means of non-linear partial differential or integro-differential equations of mixed type, using unstructured computational meshes. Typical applications include the flow of viscoelastic fluids and of fiber-reinforced polymer melts. A generic parallel approach to the assembly and solution of the finite element equation sets is described, together with the associated load balancing and mesh partitioning tools. Finally, the proposed algorithms are evaluated in the simulation of viscoelastic flows, performed on various distributed memory MIMD parallel computers such as the INTEL iPSC/860 hypercube, the CONVEX Meta Series, and a heterogeneous network of workstations.
    04/2006: pages 254-260;
  • Source
    Massively Parallel Processing Applications and Develompent, Proceedings of the 1994 EUROSIM Conference on Massively Parallel Processing Applications and Develompent, 21-23 June 1994, Delft, The Netherlands; 01/1994
  • 01/1993
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    ABSTRACT: We propose a new approach to determine the element ordering that minimises the frontwidth in finite element computations. The optimisation problem is formulated using graph theoretic concepts. We develop a divide-and-conquer strategy which defines a series of graph partitioning subproblems. The latter are tackled by means of three different heuristics, namely the Kernighan-Lin deterministic technique, and the non-deterministic Simulated Annealing and Stochastic Evolution algorithms. Results obtained for various 2D and 3D finite element meshes, whether structured or non-structured, reveal the superiority of the proposed approach relative to the standard Cuthill-McKee greedy algorithms. Relative improvements in frontwidth are in the range 25–50% in most cases. These figures translate into a significant 2–4 speedup of the finite element solver phase relative to the standard Cuthill-McKee ordering. The best results are obtained with the divide-and-conquer variant that uses the Stochastic Evolution partitioning heuristic. Numerical experiments indicate that the two non-deterministic variants of our divide-and-conquer approach are robust with respect to mesh refinement and vary little in solution quality from one run to another.
    Computer Methods in Applied Mechanics and Engineering 02/1992; 111(3-4). · 2.63 Impact Factor
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    ABSTRACT: The present paper gives an overview of the research activities of our group towards the development and implementation of efficient parallel algorithms for solving non-Newtonian flow problems. Much progress has been made over the last few years in the design of accurate and stable numerical techniques for the simulation of viscoelastic, or memory, fluid flow. The behavior of memory fluids, such as polymer solutions or melts, cannot be predicted by the classical Navier-Stokes equations. The constitutive models describing the rheological behavior of viscoelastic fluids, when combined with the classical conservation laws of continuum mechanics, lead to complex non-linear governing equations which have the form of partial-differential- or integro-partial-differential equations. Standard numerical discretization methods, such as Galerkin finite element schemes for linear elasticity or Stikes flow, are simply inappropriate here. The current issues in viscoelastic flow simulations include (1) the proper mathematical description of the bulk rheology of complex fluids, (2) the physical nature of boundary conditions (e.g. the interaction between the flowing polymer and the die wall), (3) the mathematical behavior of the governing equations and their solutions (e.g. change of type, stability, multiplicity), (4) the accuracy and stability of proposed numerical discretization schemes, and (5) the computer resources necessary to perform realistic simulations. The present work addresses the last issue.
    01/1992; -1:1139-1146.
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    ABSTRACT: The objective is to develop a generic approach to parallel finite element calculations on MIMD computers. Target applications are physical problems solved with unstructured computational meshes that lead to general, sparse system matrices. An example is the flow of viscoelastic fluids whose representative matrices are non symmetric and indefinite. We propose a parallel frontal solver that uses a frontal algorithm in the subdomains, and a multilevel direct solver for the solution of the interface system. Because the quality of the decompositions is crucial for the parallel efficiency, we also investigate a two-step procedure for the automatic decomposition of unstructured grids.