This report introduces BACOLIKR, a new event detection software package for the
error controlled numerical solution of systems of one-dimensional time-dependent
partial differential equations (PDEs). A novel feature of this package is that it
allows the user to specify a solution dependent condition, called an event, and
then the software will determine the point in time at which the specified event
occurs. This feature is a generalization of the well-known event detection capability
commonly available in state-of-the-art software for the numerical solution of initial
value ordinary differential equations.
BACOLIKR employs adaptive B-spline Gaussian collocation for the spatial discretization
of the PDE system within a spatial error control algorithm. The event detection
capability in BACOLIKR is based on its use of a modified version of the time
integrator, DASKR, which implements time-dependent event detection within a temporal
error control algorithm. BACOLIKR was developed through modifications of an earlier
error control PDE solver, BACOLI.
This report first provides an overview of the BACOLI and DASKR packages and then
describes the software modifications required in order to develop BACOLIKR. The rest
of the report demonstrates the use of BACOLIKR for the solution of a number of
PDE-based event detection problems including solution layer-boundary intersection
detection and solution layer merge detection in fluid mechanics models, critical
tumor mass detection in a brain tumor model, steady state detection in the
Cahn-Allen equation and the Gierer-Meinhardt model, and boundary event detection in
a discontinuous heat flow model.