A massively parallel adaptive finite element method with dynamic load balancing

• Published in: Proceedings of the 1993 ACM/IEEE conference on Supercomputing pp. 2 - 11
• Main Authors: Devine, K. D., Flaherty, J. E., Wheat, S. R., Maccabe, A. B.
• Format: Conference Proceeding
• Language: English
• Published: New York, NY, USA ACM 01.12.1993; IEEE
• Series: ACM Conferences
• Subjects: Boundary conditions; Computer science; Computer systems organization > Architectures > Distributed architectures > Grid computing; Computer systems organization > Architectures > Parallel architectures; Computer systems organization > Architectures > Parallel architectures > Multicore architectures; Computer systems organization > Architectures > Serial architectures > Superscalar architectures; Computing methodologies > Modeling and simulation > Simulation types and techniques > Massively parallel and high-performance simulations; Concurrent computing; Finite element methods; Hypercubes; Laboratories; Load management; Mathematics of computing > Mathematical analysis > Functional analysis > Approximation; Mathematics of computing > Mathematical analysis > Numerical analysis > Computations in finite fields; Mathematics of computing > Mathematical analysis > Numerical analysis > Computations on polynomials; Moment methods; Parallel processing; Polynomials; Software and its engineering > Software organization and properties > Software system structures > Distributed systems organizing principles > Grid computing
• ISBN: 0818643404; 9780818643408
• ISSN: 1063-9535
• DOI: 10.1145/169627.169638

The authors construct massively parallel adaptive finite element methods for the solution of hyperbolic conservation laws. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. The authors demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. They present results using adaptive p-refinement to reduce the computational cost of the method, and tiling, a dynamic, element-based data migration system that maintains global load balance of the adaptive method by overlapping neighborhoods of processors that each perform local balancing.