Arkadiusz Szymczak

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The paper presents the graph grammar based multi-thread multi-frontal parallel direct solver for one and two dimensional Finite Difference Method (FDM). The multi-frontal solver algorithm has been expressed by graph grammar productions. Each production represents an atomic task that internally must be executed in serial. The sequence of graph grammar(More)
The paper presents a grammar for anisotropic two-dimensional mesh adaptation in hp-adaptive Finite Element Method with rectangular elements. It occurs that a straightforward approach to modeling this process via grammar productions leads to potential deadlock in h-adaptation of the mesh. This fact is shown on a Petri net model of an exemplary adaptation.(More)
In this paper we present a graph grammar based direct solver algorithm for hp-adaptive finite element method simulations with point singularities. The solver algorithm is obtained by representing computational mesh as a graph and prescribing the solver algorithm by graph grammar productions. Classical direct solvers deliver O(Np+N) computational cost for(More)
In this paper we present the Petri net setting the optimal order of elimination for direct solver working with hp refined finite finite element meshes. The computational mesh is represented by a graph, with graph vertices corresponding to finite element nodes. The direct solver algorithm is expressed as a sequence of graph grammar productions, attributing(More)
Standard representations of irregular finite element meshes combine vertex data (sample coordinates and node values) and connectivity (tetrahedron–vertex incidence). Connectivity specifies how the samples should be interpolated. It may be encoded as four vertex-references for each tetrahedron, which requires 128m bits where m is the number of tetrahedra in(More)
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