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1

Hypergraph grammar based multi-thread multi-frontal direct solver with Galois scheduler

Jopek Konrad, Paszyński Maciej, Paszyńska Anna, Hassan Muhammad Amber, Pingali Keshav

Computer Science

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2019

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Vol. 20 (1)

27--55

EN

In this paper, we analyze two-dimensional grids with point and edge singularities in order to develop an eficient parallel hypergraph grammar-based multi- frontal direct solver algorithm. We express these grids by a hypergraph. For these meshes, we define a sequence of hypergraph grammar productions expressing the construction of frontal matrices, eliminating fully assembled nodes, merging the resulting Schur complements, and repeating the process of elimination and merging until a single frontal matrix remains. The dependency relationship between hypergraph grammar productions is analyzed, and a dependency graph is plotted (which is equivalent to the elimination tree of a multi- frontal solver algorithm). We utilize a classical multi-frontal solver algorithm; the hypergraph grammar productions allow us to construct an eficient elimination tree based on the graph representation of the computational mesh (not the global matrix itself). The hypergraph grammar productions are assigned to nodes on a dependency graph, and they are implemented as tasks in the GALOIS parallel environment and scheduled according to the developed dependency graph over the shared memory parallel machine. We show that our hypergraph grammar-based solver outperforms the parallel MUMPS solver.

2

Projection-based interpolation algorithm over two-dimensional grids with triangular elements

Ryzner Jakub, Paszyńska Anna

Computer Methods in Materials Science

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2019

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Vol. 19, No. 1

29--39

EN

In this paper, we employ the projection-based interpolation algorithm for approximation of two-dimensional bitmaps resulting from photographs of multi-phase material samples. The algorithm uses h-adaptive two-dimensional finite element grid with triangular elements. It results in a continuous approximation of material data with Lagrange polynomial, which makes them more suitable for finite element method computations.

PL

Artykuł przedstawia zastosowanie algorytmu interpolacji bazującej na projekcji do aproksymacji dwuwymiarowych bitmap reprezentujących zdjęcia struktury wielo-fazowych materiałów. Algorytm ten używa h-adaptacyjnej dwuwymiarowej metody elementów skończonych z elementami trójkątnymi. W wyniku jego zastosowania dostajemy ciągłą aproksymację materiału z wykorzystaniem wielomianów Lagrange'a rozpiętych na siatce obliczeniowej, na której można następnie przeprowadzić obliczenia metodą elementów skończonych.

3

Using the Hypergraph Grammar for generation of quasi optimal element partition trees in two dimensions

Ryzner Jakub, Paszyński Maciej, Paszyńska Anna

Computer Methods in Materials Science

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2018

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Vol. 18, No. 1

29--40

EN

The paper presents the graph grammar model of Finite Element Method allowing for speeding up performed numerical simulations. In the presented approach, the finite element mesh operations are performed together with operations generating so-called element partition tree. The element partition tree sets the ordering of matrix operations performed by solver in order to solve the computational problem. The quality of element partition tree influences the computational time of the solver. Our method allows for generation good quality element partition trees for h-adaptive Finite Element Method. The paper is concluded with numerical results confirming the quality of generated element partition trees.

4

Decision making in building maintenance using a graph-based knowledge representation

Palacz Wojciech, Ślusarczyk Grażyna, Łachwa Andrzej, Strug Barbara, Paszyńska Anna, Grabska Ewa

Annals of Computer Science and Information Systems

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2017

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Vol. 13

17--25

EN

This paper is an attempt to support effective decision making in building management by assisting maintenance processes. Knowledge about buildings is stored in a graph with many hierarchies. This representation allows us to express different types of hierarchical dependencies between building parts, like geometrical and functional ones, in one structure. Moreover, such a structure is useful to extract subgraphs containing information necessary for a given computational task, such as locating a desired place and the shortest path leading to it. As maintanance processes often require dynamic path target selection, modified indoor navigation methods are proposed. The paper presents the capability of the described knowledge model to cope with complex queries referring to different types of information. The considered examples show that the proposed approach can be used for various facility maintenance management applications.