We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant factor longer than the distance from v to its Euclidean nearest neighbor and (2) the lengths of the longest and shortest edges differ by at most a polynomial factor. A polyhedron is local if all its faces are simplices and its edges form a local geometric graph. We show that any boolean combination of any two local polyhedra in IR d each with n vertices, can be computed in O(n log n) time, using a standard hierarchy of axis-aligned bounding boxes. Using results of de Berg, we also show that any local polyhedron in IR d has a binary space partition tree of size O(n log d-1 n). Finally, we describe efficient algorithms for computing Minkowski sums of local polyhedra in two and three dimensions.

Simulation of solid rocket motors requires coupling physical models and software tools from multiple disciplines, and in turn demands advanced techniques to integrate independently developed physics solvers e ectively. In this paper, we overview some computer science components required for such integration. We package these components into a software framework that provides system support of high-level data management and performance monitoring, as well as computational services such as novel and robust algorithms for tracking Lagrangian surface meshes, parallel mesh optimization, and data transfer between nonmatching meshes. From these reusable framework components we construct domain-speci c building blocks to facilitate integration of parallel, multiphysics simulations from high-level speci cations. Through examples, we demonstrate the exibility of our framework and its components. I.

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1.1 What constitutes multiphysics?................................................................................................................. 5 1.2 Prototype algebraic forms......................................................................................................................... 6

Local Polyhedra and Geometric Graphs 1 1 Introduction Nonconvex polyhedra are ubiquitous in computer graphics, solid modeling, computer aided design and manufacturing, robotics, and other geometric application areas. Unlike nonconvex polygons or convex objects in space, for which many problems can be solved easily, polyhedra are notoriously difficult to handle efficiently, at least in the worst case.