Parallel tools for the bifurcation analysis of large-scale chemically reactive dynamical systems

In this work we propose a set of tools for the parallel application of pseudo-arclength continuation to a class of systems for which the right hand side can be properly represented by a time numerically calculated evolution operator. For example, the reverse flow reactor and the reactors network with periodically switched inlet and outlet sections belong to this class of system. To conduct a dynamical analysis of these systems when the key parameters are changed, it is necessary to compute the eigenvalues of the Jacobian matrix many times. Since the Jacobian can only be obtained numerically, and this in turn takes away really significant computational power, running this operation in parallel saves real time of computation. Examples, solution lines and performance diagrams for selected systems are presented and discussed.

► A set of tools for the parallel application of pseudo-arclength continuation are proposed.
► These tools have been made available as modification of the robust and popular code AUTO.
► The proposed tools have shown the best performances when applied to systems that require numerically expensive evaluation of the right hand side and for which the Jacobian matrix can only be obtained numerically.
► Parallelization was developed and tested with two different parallel versions of the software, allowing alternatively synchronous and asynchronous regime of computation.