TED-AJ03-104 A PARALLEL DOMAIN DECOMPOSITION APPROACH FOR SOLVING DIFFUSSION EQUATIONS USING THE METHOD OF FUNDAMENTAL SOLUTIONS

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概要

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• The analysis of transient heat conduction problems in large, complex computational domains is a problem of interest in many technological applications including electronic cooling, encapsulation using functionally-graded composite materials, and cryogenics. In many of these applications, the domains may be multiply connected and contain moving boundaries making it desirable to consider meshless methods of analysis. The method of fundamental solutions along with a parallel domain decomposition method is developed for the solution of three-dimensional parabolic differential equations. In the current approach, time is discretized using the generalized trapezoidal rule transforming the original parabolic partial differential equation into a sequence of nonhomogeneous modified Helmholtz equations. An approximate particular solution is derived using thin-plate splines. Interfacial conditions between subdomains are satisfied using a Schwarz Neumann-Neumann iteration scheme. Outside of the first time step where zero initial flux is assumed, the initial estimate for the interfacial flux is given from the converged solution obtained during the previous time step. This significantly reduces the number of iterations required to meet the convergence criterion. The accuracy of the method of fundamental solutions approach is demonstrated through a benchmark problem. The parallel efficiency of the domain decomposition method is evaluated by considering cases with 8,27,and 64 sub-domains.

• 一般社団法人日本機械学会の論文

著者

• Chen C.

  Department Of Mathematical Sciences University Of Nevada Las Vegas

• Chen C.

  Department Of Electrical Engineering National Central University

• INGBER M.

  Department of Mechanical Engineering, University of New Mexico

• Chen C.

  Department Of Aeronautics And Astronautics National Cheng-kung University

• Ingber M.

  Department Of Mechanical Engineering University Of New Mexico

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