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International Journal of High Performance Computing Applications
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A Parallel Adaptive Mesh Refinement Algorithm for Solving Nonlinear Dynamical Systems

Weicheng Huang

NATIONAL CENTER FOR HIGH PERFORMANCE COMPUTING HSIN-CHU, TAIWAN

Danesh K. Tafti

MECHANICAL ENGINEERING DEPARTMENT, VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY BLACKSBURG, VA 24061, USA

An unstructured adaptive mesh refinement (AMR) method is used in conjunction with the cell-to-cell mapping method for solving nonlinear dynamical systems. The global analysis is initiated with a coarse mesh without any a priori knowledge of the cell state space of the system. The process of investigation of nonlinear systems is improved through an iterative cell refinement and cell lumping process. In this paper, a parallel algorithm for the AMR procedure is developed using a shared memory programming paradigm. In addition, the concept of dynamic computing for better resource management is introduced. The approach compensates for changes in the computing workload by dynamically allocating/deallocating shared memory threads for more efficient computations. Results on the SGI Origin series are presented to exhibit the scalability of the algorithm and the feasibility of dynamic computing for resource management.

Key Words: Parallelism • adaptive mesh refinement • nonlinear dynamical system

International Journal of High Performance Computing Applications, Vol. 18, No. 2, 171-181 (2004)
DOI: 10.1177/1094342004044009
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