Autor: Pingali, K. - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Applications of a hyper-graph grammar system in adaptive finite-element computations
Autorzy:: Gurgul, P.
Jopek, K.
Pingali, K.
Paszyńska, A.
Tematy:: adaptive finite element method
hypergraph grammar
mesh-based computations
metoda elementów skończonych
gramatyka hipergrafu
siatka obliczeniowa; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Powiązania:: https://bibliotekanauki.pl/articles/331397.pdf Link otwiera się w nowym oknie
Opis:: This paper describes application of a hyper-graph grammar system for modeling a three-dimensional adaptive finite element method. The hyper-graph grammar approach allows obtaining a linear computational cost of adaptive mesh transformations and computations performed over refined meshes. The computations are done by a hyper-graph grammar driven algorithm applicable to three-dimensional problems. For the case of typical refinements performed towards a point or an edge, the algorithm yields linear computational cost with respect to the mesh nodes for its sequential execution and logarithmic cost for its parallel execution. Such hyper-graph grammar productions are the mathematical formalism used to describe the computational algorithm implementing the finite element method. Each production indicates the smallest atomic task that can be executed concurrently. The mesh transformations and computations by using the hyper-graph grammar-based approach have been tested in the GALOIS environment. We conclude the paper with some numerical results performed on a shared-memory Linux cluster node, for the case of three-dimensional computational meshes refined towards a point, an edge and a face.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Quasi-optimal elimination trees for 2D grids with singularities
Autorzy:: Calo, V. M.
Paszyński, Maciej
Pingali, K.
Woźniak, M.
Gurgul, P.
Nguyen, D.
Jopek, K.
Lenharth, A.
AbouEisha, H.
Paszyńska, Anna
Moshkov, M.
Goik, D.
Opis:: We construct quasi-optimal elimination trees for 2D finite element meshes with singularities. These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal. We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O(N_{e} log(N_{e})), where N_{e} is the number of elements in the mesh. We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

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