Mark S. Shephard

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This thesisinvestigatesthe mappingproblem: assignthe tasksof a parallel program to the processorsof a parallel computer suchthat the execution time is minimized. First, a taxonomy of objective functions and heuristics usedto solvethe mapping problem is presented. Next, we develop a highly parallel heuristic mapping algorithm, called Cyclic Pairwise Exchange(More)
In this paper, we present a new point of view for e ciently managing general mesh representations. After reviewing some mesh representation basics, we introduce the new Algorithm Oriented Mesh Database (AOMD). Some hypotheses are taken in order to be able to manage any set of adjacencies. Then, we present the design of the AOMD in terms of classes and(More)
An object-oriented framework for general numerical simulations has been developed that is designed to enable the rapid development of new analysis techniques. The framework is currently being used to implement finite element and partition of unity solution techniques. This paper discusses the overall design of the framework and gives details of how finite(More)
Implicit methods for partial differential equations using unstructured meshes allow for an efficient solution strategy for many real-world problems (e.g., simulation-based virtual surgical planning). Scalable solvers employing these methods not only enable solution of extremely-large practical problems but also lead to dramatic compression in(More)
Consideration is given to the techniques required to support adaptive analysis of automatically generated unstructured meshes on distributed memory MIMD parallel computers. The key areas of new development are focused on the support of effective parallel computations when the structure of the numerical discretization, the mesh, is evolving, and in fact(More)
order accurate discontinuous discontinuous nite element solution of the 2D Euler equations, A massively parallel adaptive nite element method with dynamic load balancing, SAND 93-0936C (1993). 21. K. Eriksson and C. Johnson, Adaptive nite element methods for parabolic problems I: A linear model problem, SIAM J. Adaptive nite element methods for parabolic(More)
A stabilized mixed finite element method for finite elasticity is presented. The method circumvents the fulfillment of the Ladyzenskaya-Babuska-Brezzi condition by adding mesh-dependent terms, which are functions of the residuals of the Euler-Lagrange equations, to the usual Galerkin method. The weak form and the linearized weak form are presented in terms(More)