3D adaptive mesh refinement

Abstract

SUMMARYAn adaptive ®nite element (FE) method for the solution of three-dimensional elasto-static problems is described. The computational domain is represented by an assembly of tetrahedral elements and the mesh adaptation is achieved by a 3D bisection method using an error estimator procedure coupled with an automatic 3D mesh generator. The performance of the method is demonstrated using a number of examples.

Spacetime meshing with adaptive refinement and coarsening

“…Finally, we would like to extend all the current results to higher dimensions, specifically to 3D×time. For the actual mesh refinement, we can directly use the generalization of newest-vertex bisection to three dimensions by Bänsch [3] and others [2,5,13,14,16,17]. Again, the main theoretical hurdle in higher dimensions is deriving minimal progress constraints that guarantee that the front can always advance.…”

Adaptive refinement of all-hexahedral elements for three-dimensional metal forming analysis

“…Unlike automatic meshing of tetrahedral element mesh, the research works with automatic remeshing of hexahedral element mesh are not so widely conducted as tetrahedral automatic mesh generator [13][14][15][16]. However, hexahedral meshes are preferred over tetrahedral meshes for the analysis of metal forming process experiencing grossly "large" deformation.…”

Meshing methods and adaptive algorithms in two and three dimensions for solving closed electromagnetic problems by means of the finite element method

“…Dentro del refinamiento tipo h conforme, se pueden desarrollar técnicas de inserción de nodos internos que, como se puede apreciar en la figura 5.31, producen elementos muy irregulares, lo que se traduce en un aumento del error asociado al elemento. Es también posible implementar técnicas similares a las descritas en el caso bidimensional, como la división por la arista más larga [Jon97], [Mer98] o la regular, que garanticen unas cotas mínimas de regularidad, como muestran las figuras 5.32. Sin embargo, el mantenimiento de estas premisas en el caso volumétrico presenta una enorme casuística que hace muy complejo este tipo de refinamiento y aconseja la utilización de métodos generales de inserción de nodos y reestructuración de la malla como el método de Delaunay-Voronoï…”