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The design and implementation of parallel finite element methods (FEMs) is a complex and error-prone task that can benefit significantly by simulating models of them first. However, such simulations are useful only if they accurately predict the performance of the parallel system being modeled. The purpose of this contribution is to present a new, practical methodology for validation of a promising modeling and simulation approach for parallel 3-D FEMs. To meet this goal, a parallel 3-D unstructured mesh refinement model is developed and implemented based on a detailed software prototype and parallel system architecture parameters in order to simulate the functionality and runtime behavior of the algorithm. Estimates for key performance measures are derived from these simulations and are validated with benchmark problem computations obtained using the actual parallel system. The results illustrate the potential benefits of the new methodology for designing high performance parallel FEM algorithms. Index Terms--Finite element methods, mesh generation, parallel processing, petri nets.

The potential benefits of employing optimal discretization-based (ODB) refinement criteria for vector tetrahedra to achieve load balancing in three-dimensional parallel adaptive finite-element electromagnetic analysis are considered. Specifically, the ability of this class of adaption refinement criteria to resolve effective domain decompositions based on initial discretizations with only relatively few tetrahedra is examined for generalized vector Helmholtz systems. The effectiveness of the new load balancing method is demonstrated with adaptively refined finite-element meshes for benchmark systems. Index Terms--Adaptive systems, electromagnetic analysis, finite-element methods, parallel processing.

In this paper, a novel graphics-processing unit (GPU) implementation of the recently proposed correction function method (CFM) is presented, for the finite-difference solution of Poisson problems with surface-charge distributions. The CFM is a robust and versatile method most notable for its immersed treatment of interface problems of any geometry, to an arbitrary order of accuracy. Given the well-known interface jump conditions associated with the electric scalar potential, the CFM is here shown to be immediately applicable to the computation of electrostatic fields, in the presence of curved surface-charge distributions. Moreover, an in-depth analysis of the CFM algorithm is presented, in which performance bottlenecks are investigated and significant potential for parallelizability is identified. The resulting parallel CFM algorithm is then implemented using NVIDIA’s compute unified device architecture GPU language, yielding a significant increase in performance. [ABSTRACT FROM AUTHOR]

A novel use of graphics processing units (GPUs) is presented in the execution of the dispersive finite-element time-domain (FETD) method, based upon the Möbius (bilinear) z -transform technique. By utilizing the immense computational power of modern GPUs via NVIDIA’s compute unified device architecture (CUDA) language, a narrowing of the performance gap, which currently exists between dispersive FETD methods and their non-dispersive counterparts, can be achieved, thus facilitating the study of a wider range of physical phenomena. An analysis of the z -transform dispersive FETD algorithm is presented in order to both identify dispersive overhead bottlenecks and determine its suitability to parallelization. Numerical studies are then undertaken to measure the performance increase as a function of simulation parameters, such as number of variables, the amount of dispersive material present, and floating point precision. [ABSTRACT FROM AUTHOR]

The design and implementation of parallel finite element methods (FEMs) is a complex and error-prone task that can benefit significantly by simulating models of them first. However, such simulations are useful only if they accurately predict the performance of the parallel system being modeled. The purpose of this contribution is to present a new, practical methodology for validation of a promising modeling and simulation approach for parallel 3-D FEMs. To meet this goal, a parallel 3-D unstructured mesh refinement model is developed and implemented based on a detailed software prototype and parallel system architecture parameters in order to simulate the functionality and runtime behavior of the algorithm. Estimates for key performance measures are derived from these simulations and are validated with benchmark problem computations obtained using the actual parallel system. The results illustrate the potential benefits of the new methodology for designing high performance parallel FEM algorithms. [ABSTRACT FROM AUTHOR]

A new, efficient pipelined communication strategy that significantly reduces latency for parallel 3-D finite element mesh refinement with tetrahedra is proposed. A Petri Nets-based model is developed in order to simulate the interprocessor communication costs for both the target mesh refinement algorithm and parallel architecture. Benchmark results show that the new pipelined design yields improved communication performance and overall parallel speedup for a range of refinement problem sizes, using different numbers of processors. [ABSTRACT FROM AUTHOR]

Communication strategies in parallel finite element methods can greatly affect system performance. The communication cost for a proposed parallel 3-D mesh refinement method with tetrahedra is analyzed. A Petri Nets-based model is developed for a target mesh refinement algorithm and parallel computing system architecture, which simulates the inter-processor communication. Subsequently, estimates for performance measures are derived from discrete event simulations. The potential benefits of this approach for developing high performance parallel mesh refinement algorithms are demonstrated by optimizing the system communication costs for varying problem size and numbers of processors. [ABSTRACT FROM AUTHOR]

We develop a simulation-based approach for the computational analysis and design of dynamic load balancing algorithms in parallel three-dimensional unstructured mesh refinement with tetrahedra. A Petri Nets model is implemented based on a random polling algorithm and the target multiprocessor architecture, which simulates the behavior of the parallel mesh refinement. Subsequently, estimates for performance measures are derived from discrete event simulations. The benefits of this new approach for developing high-performance parallel mesh refinement algorithms are demonstrated with results for an example geometric mesh refinement model. [ABSTRACT FROM AUTHOR]