Publications (9)2.96 Total impact
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ABSTRACT: Parallel finite element algorithms are proposed for the solution of physical problems described by means of nonlinear partial differential or integrodifferential equations of mixed type, using unstructured computational meshes. Typical applications include the flow of viscoelastic fluids and of fiberreinforced 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.  [Show abstract] [Hide abstract]
ABSTRACT: This work constitutes the first phase of a longterm 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 onedimensional 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 twodimensional case are encouraging. Work is underway to further generalize the present approach to complex multidimensional problems. 

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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 divideandconquer strategy which defines a series of graph partitioning subproblems. The latter are tackled by means of three different heuristics, namely the KernighanLin deterministic technique, and the nondeterministic Simulated Annealing and Stochastic Evolution algorithms. Results obtained for various 2D and 3D finite element meshes, whether structured or nonstructured, reveal the superiority of the proposed approach relative to the standard CuthillMcKee 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 CuthillMcKee ordering. The best results are obtained with the divideandconquer variant that uses the Stochastic Evolution partitioning heuristic. Numerical experiments indicate that the two nondeterministic variants of our divideandconquer approach are robust with respect to mesh refinement and vary little in solution quality from one run to another.  [Show abstract] [Hide abstract]
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 nonNewtonian 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 NavierStokes equations. The constitutive models describing the rheological behavior of viscoelastic fluids, when combined with the classical conservation laws of continuum mechanics, lead to complex nonlinear governing equations which have the form of partialdifferential or integropartialdifferential 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. 


Publication Stats
55  Citations  
2.96  Total Impact Points  
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Institutions

1992

Catholic University of Louvain
 Center for Operations Research and Econometrics
Walloon Region, Belgium
