Abstract We present a simple yet effective method for constructing 3D self-supporting surfaces with planar quadrilateral (PQ) elements. Starting triangular discretization of surface, we first compute the principal curvatures and directions each face using new discrete differential geometry approach, yielding more accurate results than existing methods. Then, smooth direction field to reduce num...

This paper presents a triangular-to-quadrilateral mesh conversion method that can control the directionality of the output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts th...

The accuracy and eeciency of the solution to numerical systems depends on the quality of the mesh used. Automatic mesh generation and adaptive reenement methods can, however, produce poor quality elements, even invalid elements, for quadrilateral or hexahedral mesh. We present an optimization-based approach for quadrilateral or hexahedral mesh untangling that maximizes the minimum area or volum...

The introduction of the Quadrilateral Area Coordinate (QAC) membrane elements has generated more heat than light on the subject of why distorted membrane elements perform very poorly. The canonical guidelines for construction of robust elements are continuity and completeness. It is known that isoparametric (or parametric) quadrilateral membrane elements satisfy the continuity requirements alwa...

We present a comprehensive assessment of nodal and hybrid modal/nodal discontinuous Galerkin (DG) finite element solutions on a range of unstructured meshes to nonlinear shallow water flow with smooth solutions. The nodal DG methods on triangles and a tensor-product nodal basis on quadrilaterals are considered. The hybrid modal/nodal DG methods utilize two different synergistic polynomial bases...

1Landau Associates, 130 2nd Ave South, Edmonds, WA 98020, U.S.A. 2Civil and Environmental Engineering and National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign, 205 North Mathews Ave Urbana, IL 61801, U.S.A. 3Department of Nuclear, Plasma and Radiological Engineering, University of Illinois at Urbana-Champaign, 216 Talbot Lab, 104 S. Wright St., Urbana, IL ...