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Novel Graph-based Adaptive Triangular Mesh Refinement for Finite-volume Discretizations

Sanderson L. Gonzaga de Oliveira1, Mauricio Kischinhevsky2, João Manuel R. S. Tavares3
Departamento de Ciência da Computação, Universidade Federal de Lavras, Lavras, MG, Brazil. Email: sanderson@dcc.ufla.br
Instituto de Computação, Universidade Federal Fluminense, Niterói, RJ, Brazil.
Email: kisch@ic.uff.br
Instituto de Engenharia Mecânica e Gestão Industrial, Departamento de Engenharia Mecânica, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal. Email: tavares@fe.up.pt

Computer Modeling in Engineering & Sciences 2013, 95(2), 119-141. https://doi.org/10.3970/cmes.2013.095.119

Abstract

A novel graph-based adaptive mesh refinement technique for triangular finite-volume discretizations in order to solve second-order partial differential equations is described. Adaptive refined meshes are built in order to solve timedependent problems aiming low computational costs. In the approach proposed, flexibility to link and traverse nodes among neighbors in different levels of refinement is admitted; and volumes are refined using an approach that allows straightforward and strictly local update of the data structure. In addition, linear equation system solvers based on the minimization of functionals can be easily used; specifically, the Conjugate Gradient Method. Numerical and analytical tests were carried out in order to study the required execution time and the data storage cost. These tests confirmed the advantages of the approach proposed in elliptic and parabolic problems.

Keywords

Adaptive mesh refinement, mesh generation, Sierpi´nski Curve, elliptic and parabolic problems, non-conformal mesh.

Cite This Article

L., S., Kischinhevsky, M., Manuel, J. (2013). Novel Graph-based Adaptive Triangular Mesh Refinement for Finite-volume Discretizations. CMES-Computer Modeling in Engineering & Sciences, 95(2), 119–141.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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