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A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION

Electrical propagation in excitable tissue, such as nerve fibers and heart muscle, is described by a nonlinear diffusion-reaction parabolic partial differential equation for the transmembrane voltage $V(x,t)$, known as the cable equation. This equation involves a highly nonlinear source term, representing the total ionic current across the membrane, governed by a Hodgkin-Huxley type ionic model, and requires the solution of a system of ordinary differential equations. Thus, the model consists of a PDE (in 1-, 2- or 3-dimensions) coupled to a system of ODEs, and it is very expensive to solve, especially in 2 and 3 dimensions.
In order to solve this equation numerically, we develop an algorithm, extended from the Parareal Algorithm, to efficiently incorporate space-parallelized solvers into the framework of the Parareal algorithm, to achieve time-and-space parallelization. Numerical results and comparison of the performance of several serial, space-parallelized and time-and-space-parallelized time-stepping numerical schemes in one-dimension and in two-dimensions are also presented.

Identiferoai:union.ndltd.org:UTENN/oai:trace.tennessee.edu:utk_graddiss-2263
Date01 August 2011
CreatorsLi, Chuan
PublisherTrace: Tennessee Research and Creative Exchange
Source SetsUniversity of Tennessee Libraries
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceDoctoral Dissertations

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