Sequential decision-making approach for quadrangular mesh generation

Abstract

A new indirect quadrangular mesh generation algorithm which relies on sequential decision-making techniques to search for optimal triangle recombinations is presented. In contrast to the state-of-art Blossom-quad algorithm, this new algorithm is a good candidate for addressing the 3D problem of recombining tetrahedra into hexahedra.

Two-dimensional mesh generator and quality analysis of elements on the curvilinear coordinates system

“…It is known that in a lower quality element the resolution of differential equations, which describe any phenomenon, can produce unsatisfactory results, such as numerical instability and inadequacy to reality (PARK; SHONTZ, 2010). It can be stated that the greater regularity of the element's geometry, this implies a better quality of the mesh that contains it (BOROUCHAKI;FREY, 1998;JOHNEN;ERNST;GEUZAINE, 2015). Since the elements belonging to the meshes in generalized coordinates are quadrilateral, it is important that the geometry of the element approaches a square.…”

“…the ratios between the size of each side of the element with the others (BOROUCHAKI; FREY, 1998;JOHNEN;ERNST;GEUZAINE, 2015), the internal angles (COELHO; LOURENCO et al, 2001) and the compactness of the element (GOSE; JOHNSONBAUGH; JOST, 1996;GONZALEZ;WOODS, 2011). All criteria verify the similarity of the elements of the computational mesh to a square, the element considered ideal, thus identifying those elements considered to be of low quality.…”