Discontinuities Handled with Events in Assimulo

Often integrating ordinary differential equations or differential algebraic equations (DAE) do not constitute the problem alone. A common complement is finding the root of an algebraic function (an event function) that depends on the states of the problem. This formulation of a model enables the possibility of including discontinuities, an important part of the Functional Mock-up Interface standard which allows hybrid models of differential algebraic equations. The problem of root-finding during integration is however difficult. Both in a theoretical aspect and as a software problem. An implementation of software for root-finding is done in Assimulo, a Python/Cython wrapper for integrators. The implementation takes the Functional Mock-up Interface standard into consideration. The implementation is made usable for a wide variety of integration algorithms and is also verified and benchmarked with advanced industrial models, showing good indications of being robust and scaling well for large systems.