Declarative mesh subdivision using topological rewriting in mgs.

Abstract. Mesh subdivision algorithms are usually specified informally using graphical schemes defining local mesh refinements. These algorithms are then implemented efficiently in an imperative framework. The implementation is cumbersome and implies some tricky indices management

Hypergraph Grammars in hp-adaptive Finite Element Method

AbstractThe paper presents the hypergraph grammar for modelling the hp-adaptive finite element method algorithm with rectangular elements. The finite element mesh is represented by a hypergraph. All mesh transformations are modelled by means of hypergraph grammar rules. These rules allow to generate the initial mesh, to assign values of polynomial order to the element nodes, to generate the matrix for each element, to solve the problem and to perform the hp-adaptation

Arbitrary Nesting of Spatial Computations

International audienceModern programming languages allow the definition and the use of arbitrary nested data structures but this is not generally considered in unconventional programming models. In this paper, we present arbitrary nesting in MGS, a spatial comput- ing language. By considering different classes of neighborhood relationships, MGS can emulate several unconventional computing models from a programming point of view. The use of arbitrary nested spatial structures allows a hierarchical form of coupling between them. We propose an extension of the MGS pattern- matching facilities to handle directly nesting. This makes possible the straightforward emulation of a larger class of unconventional programming models

Declarative mesh subdivision using topological rewriting in MGS

International audienceMesh subdivision algorithms are usually specified informally using graphical schemes defining local mesh refinements. These algorithms are then implemented efficiently in an imperative framework. The implementation is cumbersome and implies some tricky indices management. Smith et al. (2004) asks the question of the declarative programming of such algorithms in an index-free way. In this paper, we positively answer this question by presenting a rewriting framework where mesh refinements are described by simple rules. This framework is based on a notion of topological chain rewriting. Topological chains generalize the notion of labeled graph to higher dimensional objects. This framework has been implemented in the domain specific language MGS. The same generic approach has been used to implement Loop as well as Butterfly, Catmull-Clark and Kobbelt subdivision schemes