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Using a graph grammar system in the finite element method

Barbara StrugAnna PaszyńskaMaciej PaszyńskiEwa Grabska — 2013

International Journal of Applied Mathematics and Computer Science

The paper presents a system of Composite Graph Grammars (CGGs) modelling adaptive two dimensional hp Finite Element Method (hp-FEM) algorithms with rectangular finite elements. A computational mesh is represented by a composite graph. The operations performed over the mesh are defined by the graph grammar rules. The CGG system contains different graph grammars defining different kinds of rules of mesh transformations. These grammars allow one to generate the initial mesh, assign values to element...

An agent-oriented hierarchic strategy for solving inverse problems

Maciej SmołkaRobert SchaeferMaciej PaszyńskiDavid PardoJulen Álvarez-Aramberri — 2015

International Journal of Applied Mathematics and Computer Science

The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically...

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