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PaMPA ("Parallel Mesh Partitioning and Adaptation") is a middleware for the parallel remeshing and the redistribution of distributed unstructured meshes. PaMPA is meant to serve as a basis for the development of numerical solvers implementing compact schemes. PaMPA represents meshes as a set of interconnected entities (elements, faces, edges, nodes, etc.). Since the underlying structure is a graph, elements can be of any kind, and several types of elements can be used within the same mesh. Typed values (scalars, vectors, structured types) can be associated with entities. Value exchange routines allow users to copy values across neighboring processors, and to specify the width of the overlap across processors. Accessors and iterators allow developers of numerical solvers to write their numerical schemes without having to take into account mesh and value distributions. Parallel mesh partitioning and redistribution is now available, partly based on PT-Scotch. Parallel remeshing will soon be available. It will be handled by calling in parallel a user-provided sequential remesher on non-overlapping pieces of the mesh. A full-featured tetrahedron example will be provided before the end of this year, based on the MMG3D sequential remeshing software also developed at Inria.
Jocelyne Erhel: Hybrid static/dynamic scheduling for already optimized dense matrix factorizationSolving linear systems arising from flow simulations in 3D Discrete Fracture Networks
Underground water is naturally channelled in fractured media, where interconnections can be very intricate. Discrete Fracture Networks are based on a geometrical model, where fractures are 2D domains, for example ellipses, which form a 3D network. We have developed an original numerical model in order to simulate flow in a randomly generated DFN. The spatial discretization leads to a symmetric positive definite linear system, with a
large sparse matrix. We have investigated the efficiency of several linear solvers on parallel and distributed computers. Since the network can be easily partitioned into subdomains (the fractures), we have developed a hybrid solver based on domain decomposition. This approach decouples in some sense the flow at the fracture scale from the interactions at the network scale. The Schur complement, which gathers the unknowns at the intersections of the network, is solved with a preconditioned conjugate gradient. We combine Neumann Neumann, defined at the fracture scale, with a global preconditioner, defined at the network scale, based on a deflation formulation. The numerical model and the solver are implemented in the software MPFRAC, which is embedded into the scientific platform H2OLab. Our numerical experiments highlight the efficiency of this Schur solver.
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