PMIRKDC: a parallel mono-implicit Runge--Kutta code with defect control for boundary value ODEs

  • Authors:

  • P. H. Muir;R. N. Pancer;K. R. Jackson

  • Affiliations:

  • Department of Mathematics and Computing Science, Saint Mary's University, Halifax, Nova Scotia, Canada B3H 3C3;Division of Physical Sciences, University of Toronto at Scarborough, Scarborough, Ont., Canada M1C 1A4;Department of Computer Science, University of Toronto, Toronto, Ont., Canada M5S 3G4

  • Venue:
  • Parallel Computing
  • Year:
  • 2003

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Abstract

We describe parallel software, PMIRKDC, for solving boundary value ordinary differential equations (BVODEs). This software is based on the package, MIRKDC, which employs mono-implicit Runge-Kutta schemes within a defect control algorithm. The primary computational costs involve the treatment of large, almost block diagonal (ABD) linear systems. The most significant feature of PMIRKDC is the replacement of sequential ABD software, COLROW, with new parallel ABD software, RSCALE, based on a parallel block eigenvalue rescaling algorithm. Other modifications involve parallelization of the setup of the ABD systems and solution interpolants, and defect estimation. Numerical results show almost linear speedups.