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Parallel solvers for spline collocation equations
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DOI：10.1016/0965-9978(96)00019-1.png)
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Abstract
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A variety of solvers for the spline collocation equations arising from the discretisation of elliptic partial differential equations (PDEs) are considered. The convergence properties of semi-iterative and Krylov subspace acceleration methods applied to the system of spline collocation equations are studied. 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. The parallelisation of some of the above iterative methods is studied and their advantages and disadvantages discussed. 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 PDEs are presented. Copyright (C) 1996 Civil-Comp Limited and Elsevier Science Limited
Keywords:
elliptic partial differential equations
iterative methods
domain decomposition
distributed memory machines
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