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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 20
Edited by: B.H.V. Topping and M. Papadrakakis
Paper II.1

High Performance Computing of Elliptic Partial Differential Equations with Spline Collocation

C.C. Christara

Department of Computer Science, University of Toronto, Toronto, Ontario, Canada

Full Bibliographic Reference for this paper
C.C. Christara, "High Performance Computing of Elliptic Partial Differential Equations with Spline Collocation", in B.H.V. Topping, M. Papadrakakis, (Editors), "Advances in Parallel and Vector Processing for Structural Mechanics", Civil-Comp Press, Edinburgh, UK, pp 23-34, 1994. doi:10.4203/ccp.20.2.1
We consider a variety of solvers for the spline collocation equations arising from the discretisation of elliptic Partial Differential Equations. We study the convergence properties of semi-iterative and conjugate gradient acceleration methods applied to the system of spline collocation equations. The preconditioners tested include incomplete factorisation and SSOR for both the natural and multicolour orderings, domain decomposition based on Schur complement methods with nonoverlapping subdomains, or Schwarz methods with overlapping subdomains, and multigrid methods.

We study the parallelisation of some of the above iterative methods and discuss their advantages and disadvantages. The communication requirements of the methods are discussed when the methods are implemented on distributed memory machines. Results which show that spline collocation methods are very competitive for the solution of BVPs are presented.

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