6 research outputs found
Fully Generalized Two-Dimensional Constrained Delaunay Mesh Refinement
Traditional refinement algorithms insert a Steiner point from a few possible choices at each step. Our algorithm, on the contrary, defines regions from where a Steiner point can be selected and thus inserts a Steiner point among an infinite number of choices. Our algorithm significantly extends existing generalized algorithms by increasing the number and the size of these regions. The lower bound for newly created angles can be arbitrarily close to . Both termination and good grading are guaranteed. It is the first Delaunay refinement algorithm with a angle bound and with grading guarantees. Experimental evaluation of our algorithm corroborates the theory
Parallel generalized Delaunay mesh refinement
The modeling of physical phenomena in computational fracture mechanics, computational fluid dynamics and other fields is based on solving systems of partial differential equations (PDEs). When PDEs are defined over geometrically complex domains, they often do not admit closed form solutions. In such cases, they are solved approximately using discretizations of domains into simple elements like triangles and quadrilaterals in two dimensions (2D), and tetrahedra and hexahedra in three dimensions (3D). These discretizations are called finite element meshes. Many applications, for example, real-time computer assisted surgery, or crack propagation from fracture mechanics, impose time and/or mesh size constraints that cannot be met on a single sequential machine. as a result, the development of parallel mesh generation algorithms is required.;In this dissertation, we describe a complete solution for both sequential and parallel construction of guaranteed quality Delaunay meshes for 2D and 3D geometries. First, we generalize the existing 2D and 3D Delaunay refinement algorithms along with theoretical proofs of mesh quality in terms of element shape and mesh gradation. Existing algorithms are constrained by just one or two specific positions for the insertion of a Steiner point inside a circumscribed disk of a poorly shaped element. We derive an entire 2D or 3D region for the selection of a Steiner point (i.e., infinitely many choices) inside the circumscribed disk. Second, we develop a novel theory which extends both the 2D and the 3D Generalized Delaunay Refinement methods for the concurrent and mathematically guaranteed independent insertion of Steiner points. Previous parallel algorithms are either reactive relying on implementation heuristics to resolve dependencies in parallel mesh generation computations or require the solution of a very difficult geometric optimization problem (the domain decomposition problem) which is still open for general 3D geometries. Our theory solves both of these drawbacks. Third, using our generalization of both the sequential and the parallel algorithms we implemented prototypes of practical and efficient parallel generalized guaranteed quality Delaunay refinement codes for both 2D and 3D geometries using existing state-of-the-art sequential codes for traditional Delaunay refinement methods. On a heterogeneous cluster of more than 100 processors our implementation can generate a uniform mesh with about a billion elements in less than 5 minutes. Even on a workstation with a few cores, we achieve a significant performance improvement over the corresponding state-of-the-art sequential 3D code, for graded meshes
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Galois : a system for parallel execution of irregular algorithms
textA programming model which allows users to program with high productivity and which produces high performance executions has been a goal for decades. This dissertation makes progress towards this elusive goal by describing the design and implementation of the Galois system, a parallel programming model for shared-memory, multicore machines. Central to the design is the idea that scheduling of a program can be decoupled from the core computational operator and data structures. However, efficient programs often require application-specific scheduling to achieve best performance. To bridge this gap, an extensible and abstract scheduling policy language is proposed, which allows programmers to focus on selecting high-level scheduling policies while delegating the tedious task of implementing the policy to a scheduler synthesizer and runtime system. Implementations of deterministic and prioritized scheduling also are described. An evaluation of a well-studied benchmark suite reveals that factoring programs into operators, schedulers and data structures can produce significant performance improvements over unfactored approaches. Comparison of the Galois system with existing programming models for graph analytics shows significant performance improvements, often orders of magnitude more, due to (1) better support for the restrictive programming models of existing systems and (2) better support for more sophisticated algorithms and scheduling, which cannot be expressed in other systems.Computer Science
A Time Efficient Delaunay Refinement Algorithm
In this paper we present a Delaunay refinement algorithm for
generating good aspect ratio and optimal size triangulations.
This is the first algorithm known to have sub-quadratic
running time. The algorithm is based on the extremely
popular Delaunay refinement algorithm of Ruppert. We
know of no prior refinement algorithm with an analyzed subquadratic
time bound. For many natural classes of meshing
problems, our time bounds are comparable to know bounds
for quadtree methods
Abstract A Time Efficient Delaunay Refinement Algorithm ∗
In this paper we present a Delaunay refinement algorithm for generating good aspect ratio and optimal size triangulations. This is the first algorithm known to have sub-quadratic running time. The algorithm is based on the extremely popular Delaunay refinement algorithm of Ruppert. We know of no prior refinement algorithm with an analyzed subquadratic time bound. For many natural classes of meshing problems, our time bounds are comparable to know bounds for quadtree methods.