<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

Applications of A Hyper–Graph Grammar System in Adaptive Finite–Element Computations

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

This paper describes application of a hyper-graph grammar system for modeling a three-dimensional adaptive finite element method. The hyper-graph grammar...

Applications of A Hyper–Graph Grammar System in Adaptive Finite–Element Computations

Online veröffentlicht: 03. Okt. 2018

Seitenbereich: 569 - 582

Eingereicht: 13. Juni 2017

Akzeptiert: 19. Apr. 2018

DOI: https://doi.org/10.2478/amcs-2018-0044

Schlüsselwörter
adaptive finite element method, hyper-graph grammars, mesh-based computations

© 2018 Piotr Gurgul, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Applications of A Hyper–Graph Grammar System in Adaptive Finite–Element Computations

Online veröffentlicht: 03. Okt. 2018

Seitenbereich: 569 - 582

Eingereicht: 13. Juni 2017

Akzeptiert: 19. Apr. 2018

DOI: https://doi.org/10.2478/amcs-2018-0044

Schlüsselwörteradaptive finite element method, hyper-graph grammars, mesh-based computations

© 2018 Piotr Gurgul, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schlüsselwörter
adaptive finite element method, hyper-graph grammars, mesh-based computations