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...

We develop a new formulation of the Control Volume Finite Element Method (CVFEM) with a multidimensional Scharfetter-Gummel (SG) upwinding for the drift-diffusion equations. The formulation uses standard nodal elements for the concentrations and expands the flux in terms of the lowest-order Nedelec H(curl,Ω)-compatible finite element basis. The SG formula is applied to the edges of the elements...

We present a novel approach named T-Base for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element – square – can be virtually divided into a pair of equilateral right triangles by any of its diagonals. When move a node to smooth a quadrilateral, it is optimal to make a pair of triangles divided by a diagonal be equilateral right trian...

The Lagrange-Galerkin spectral element method for the two-dimensional shallow water equations is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the nonlinearities introduced by the advection operator o...

to carry out searching and interpolation efficiently. Brackbill and Ruppert [6] and Westermann [7] have designed A generalized iterative algorithm for searching and locating particles in arbitrary meshes is presented. The algorithm uses Newton schemes to perform searching and bilinear interpolation on method to invert a bijective map of the mesh elements onto a structured meshes composed of non...

We present a high-order spectral element method for solving layered media scattering problems featuring an operator that transparently enforces the far-field boundary condition. The incorporation of this Dirichlet-to-Neumann (DtN) map into the spectral element framework is a novel aspect of this work, and the resulting method can accommodate plane-wave radiation of arbitrary angle of incidence....

This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow. Beyond the previous research works [9, 8, 4], we propose a general strategy to construct the basis functions. Under several specific constraints, the optimal error estimates are obtained, i.e. the first order accuracy of the velocities in H-norm and the pressure ...

This paper proposes a computational method for fully automated quadrilateral meshing. Unlike previous methods, this new scheme can create a quadrilateral mesh whose directionality is precisely controlled. Given as input: (1) a 2D geometric domain, (2) a desired node spacing distribution as a scalar function deened over the domain, and (3) a desired mesh directionality as a vector eld deened ove...

This paper describes an approach to smooth the surface and improve the quality of quadrilateral/hexahedral meshes with feature preserved using geometric flow. For quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by relocating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent ...

In this paper, we build on the mesh improvement methods intended for parallel execution with the paving method [1] and introduce topological changes in an existing quadrilateral-only mesh to improve element shape and nodal valence. This discussion is intended to demonstrate the effectiveness of utilizing mesh cleanup operations as a post-processing step to other mesh generation algorithms. The ...