Chaire d'Analyse Appliquée

 Overview of Parameter Continuation Research

General Research Description

The group's work in this area is focussed on the development and use of visualization techniques to interactively steer multi-parameter continuation computations on various parallel architectures (both work-station clusters and remote massively parallel machines). There is an existing one-parameter continuation code called VBM (which was the subject of a talk at the 1998 International Congress of Mathematicians) which is written in C++/Python/TK/OpenGL to run on a variety of UNIX operating systems using sockets, PVM or MPI for communications, and driving a variety of computation engines (the Fortan code AUTO being one of the most heavily used in the lab).  Current research involves extending this code to multi-parameter continuation, with the primary questions of interest being
  1. how to visualize higher dimension continuation computations,

  3. how to make efficient use of many processors for a multi-level parallelism involving a coarse grain parallelization of computations at different parameter values, and a fine grain parallelization of the computation at a given set of parameters, and

  5. various data reduction strategies.
Some more details regarding these points are described in a conference presentation 3rd SOS Workshop

The main target application is currently models of equilibrium configurations of DNA (which involves the solution of elliptic boundary value problems for differential equations and integro-differential equations). Our models of self-contact are computationally quite intensive and require parallel computation.

The group's work in the development of analytical, numerical and visualization techniques for steered parameter continuation computations is organized around the development of several software packages.

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