A wide span of steady-state and transient edge plasma processes simulation problems require accurate discretization techniques and can then be treated with Finite Element (FE) and Finite Volume (FV) methods. The software used here to meet these meshing requirements is a 2D finite element grid generator. It allows to produce adaptive unstructured grids taking into consideration the flux surface ...

This paper discusses the problem of subdividing meshes containing tetrahedra, pyramids, prisms or hexahedra into a consistent set of tetrahedra. This problem occurs in computer graphics where meshes with pyramids, prisms or hexahedra must be subdivided into tetrahedra to use efficient algorithms for volume rendering, iso-contouring and particle advection. Another application is for the use of s...

Abstract This paper applies a complete parametric set for approximating the geometry of a quadrilateral element. The approximation basis used is a complete Pascal polynomial of second order with six free parameters. The interpolation procedure is a natural interpolation scheme. The six free parameters are determined using the natural coordinates of the four nodal points (vertices) of the quadri...

The isoperimetric inequality says that the area of any region in the plane bounded by a curve of a fixed length can never exceed the area of a circle whose boundary has that length. Moreover, if some region has the same length and area as some circle, then it must be the circle. There are dozens of proofs. We give several arguments which depend on more primitive geometric and analytic inequalit...

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted r...

A fully automatic mesher has been developed which is capable of generating both quadrilateral and triangular elements in 2-D and on surfaces using the advancing front algorithm. This allows the formation of meshes which range from being all-quad or nearly all-quad down to all-triangular. In mixed-element meshes, the number of tri elements present is dictated by the maximum allowable level of qu...

Automatic finite element mesh generation techniques have become commonly used tools for the analysis of complex, real-world models. All of these methods can, however, create distorted and even unusable elements. Fortunately, several techniques exist which can take an existing mesh and improve its quality. Smoothing (also referred to as mesh relaxation) is one such method, which repositions noda...

for the nonlinear analysis of structures using the well known newton-raphson method, the tangent stiffness matrices of the elements must be constructed in each iteration. due to the high expense required to find the exact tangent stiffness matrices, researchers have developed novel innovations into the newton-raphson method to reduce the cost and time required by the analysis. in this paper, a ...

a pseudo-complement of a quadrilateral d of order n, n, > 3, is a non-trivial (n+l)- regular linear space with n - 3n + 3 points and n + n - 3 lines. we prove that if n > 18 and d has at least one line of size n - 1, or if n > 25 , then the set of lines of d consists of three lines of size n -1, 6(n - 2) lines of size n - 2, and n - 5n + 6 lines of size n - 3. furthermore, if n > 21 and d has a...