Seminar: Developing a Parallel Adaptive Method for Pseudo-Arclength Continuation

There will be a seminar in the “research programming in practice” series by Dhavide Aruliah University of Ontario Institute of Technology (Oshawa, ON, Canada) on Weds 28th August at 2pm in Drayton B06.

Pseudo-arclength continuation is a well-established framework for generating a curve of numerical solutions of nonlinear equations. In my talk, I will review the basic ideas underlying adaptive predictor-corrector schemes for pseudo-arclength continuation emphasising where the bottle-neck arises in computation of rejected corrector steps. We have been developed a parallel code using standard C and MPI for adapting the step-length in pseudo-arclength continuation. Our method employs several predictor-corrector sequences run concurrently on distinct processors with differing step-lengths. Our parallel framework permits intermediate results of unconverged correction sequences to seed new predictor-corrector sequences with longer step-lengths; the goal is to amortise the cost of corrector steps to make further progress along the underlying numerical curve. I shall describe the essence of the parallel code and some of the issues that arose in its implementation. The goal is to have a straightforward interface to an MPI library into which researchers can plug in their serial C continuation codes to achieve modest improvements with widely available multicore desktop machines. This is joint work with Alexander Dubitski (Amadeus R & D, Toronto) and Lennaert van Veen (UOIT).