BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

eBACOLI: a time- and space-adaptive multi-scale PDE solver Spiteri, Ray


Multi-scale models are commonly used to mathematically describe the evolution of many interesting and important systems. They attempt to capture dynamics on multiple scales and integrate them into a common framework. One way to do this is via partial differential equations (PDEs) that do not depend on spatial derivatives to represent dynamics on small scales. Upon spatial discretization, these PDEs reduce to sets of ordinary differential equations (ODEs) at each discrete spatial point. eBACOLI is a numerical software package for solving multi-scale models consisting of parabolic PDEs coupled with PDEs that do not depend on spatial derivatives in one spatial dimension. eBACOLI features adaptive error control in the temporal and spatial domains. It uses a B-spline collocation method for the spatial discretization to yield a set of ODEs, which together with the boundary conditions, form a system of differential-algebraic equations (DAEs). These DAEs are then solved using DASSL. We demonstrate this applicability and efficiency of this software package on a number of examples, including the monodomain model of cardiac electrophysiology.

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