We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence....

A dynamic model of multiple-stage planetary gear train composed of a two-stage planetary gear train and a one-stage parallel axis gear is proposed to be used in wind driven generator to analyze the influence of revolution speed and mesh error on dynamic load sharing characteristic based on the lumped parameter theory. Dynamic equation of the model is solved using numerical method to analyze the...

The insatiable demand to optimize and engineer new functionalities in electromagnetic devices has risen their geometrical complexity unprecedented levels. This usually results computationally multiscale problems with some tiny components of great importance the overall behavior these devices. Block meshing is a powerful technique for treating such problems. usage variable mesh size adaptable ad...

In Part I of this work, we analyzed superconvergence for piecewise linear finite element approximations on triangular meshes satisfying an O(h2) approximate parallelogram property. In this work, we consider superconvergence for general unstructured but shape regular meshes. We develop a postprocessing gradient recovery scheme for the finite element solution uh, inspired in part by the smoothing...

In an effort to improve the robustness and efficiency of mesh adaptation, this work proposes an adaptive re-meshing method that can be used for variety of problems in CFD. It should be noted that this method is feature driven adaptivity and that it does not use strategies such as edge split, edge collapse, edge swap, etc as were employed in mesh modifications [2]. Instead, it defines the ”holes...

A very wide range of finite element analyses required to design carbodies calls for quadrilateral meshes with austere quality needs. Quadrilaterals being varying strain and non-planar, element quality, in body-in-white analyses, is virtually impossible to measure with a single parameter. Auto-designers mostly prefer heuristic element quality metrices that catapult the need for predominantly ort...

This paper presents a method to construct an auxiliary planar domain of triangulation for tessellating trimmed parametric surface patches. By minimizing a mapping error function, an approximate locally isometric mapping between a given trimmed parametric surface patch and its triangulation domain is constructed. In this way the shape of triangular elements on the triangulation domain is approxi...

Precise quality control for hierarchical lighting simulations is still a hard problem, due in part to the difficulty of analysing the source of error and to the close interactions between different components of the algorithm. In this paper we attempt to address this issue by examining two of the most central components of these algorithms: visibility computation and the mesh. We first present ...