Open Collections

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

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: University of Saskatchewan

2019-03-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69225

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/