Abstract. This paper describes a quadrilateral mesh generation algorithm ideally suited for transition subdomain meshes in the context of any domain decomposition meshing strategy. The algorithm is based on an automatic hierarchical region decomposition in which, in the last level, it is possible to generate quadrilateral elements with a conventional mapping strategy. In two dimensions, a subdo...

This note summarizes the results in [1, 3, 2] on the construction of parallel local multigrid methods. In addition, we present an extended formalization of the adaptive data structure in order to describe precisely the requirements for adaptive multigrid methods with local smoothing for general finite element discretizations. Based on this formalization algorithms can be defined, developed, and...

In this paper, we introduce a new type of splines—polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects. PHT-splines are a generalization of B-splines over hierarchical T-meshes. We present the detailed construction process of spline basis functions over T-meshes which have the same important properties as B-splines do, such as nonnegativity, local suppor...

This paper describes a quadrilateral mesh generation algorithm ideally suited for transition subdomain meshes in the context of any domain decomposition meshing strategy. The algorithm is based on an automatic hierarchical region decomposition in which, in the last level, it is possible to generate quadrilateral elements with a conventional mapping strategy. In two dimensions, a subdomain is us...

Current Level of Detail (LoD) approaches for triangle meshes use variably triangulated mesh patches, in order to approximate the original mesh surface. The approximation is synthesized from some of these patches, which must cover the whole surface and must not intersect each other. The patches are chosen according to the necessary view dependent triangulation. This paper addresses the creation ...

We analyze the space Sr m,m (T ) of bivariate functions that are piecewise polynomial of bi-degree 6 (m,m) and of smoothness r along the interior edges of a planar T-mesh T . We give new combinatorial lower and upper bounds for the dimension of this space by exploiting homological techniques. We relate this dimension to the weight of the maximal interior segments of the T-mesh, defined for an o...

We propose a multigrid method for solving large-scale sparse linear systems arising from discretizations of partial differential equations, such as those from finite element and generalized finite difference (GFD) methods. Our proposed method has the following two characteristics. First, we introduce a hybrid geometric+algebraic multigrid method, or HyGA, to leverage the rigor, accuracy and eff...