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1. Li, Chuan. A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION.

Degree: 2011, University of Tennessee – Knoxville

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.

Subjects/Keywords: Luo-Rudy; action potential; cable equation; parallel computing; parareal algorithm; Biophysics; Molecular Biology; Numerical Analysis and Computation; Numerical Analysis and Scientific Computing; Partial Differential Equations

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APA (6th Edition):

Li, C. (2011). A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION. (Doctoral Dissertation). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_graddiss/1095

Chicago Manual of Style (16th Edition):

Li, Chuan. “A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION.” 2011. Doctoral Dissertation, University of Tennessee – Knoxville. Accessed November 13, 2019. https://trace.tennessee.edu/utk_graddiss/1095.

MLA Handbook (7th Edition):

Li, Chuan. “A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION.” 2011. Web. 13 Nov 2019.

Vancouver:

Li C. A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION. [Internet] [Doctoral dissertation]. University of Tennessee – Knoxville; 2011. [cited 2019 Nov 13]. Available from: https://trace.tennessee.edu/utk_graddiss/1095.

Council of Science Editors:

Li C. A TIME-AND-SPACE PARALLELIZED ALGORITHM FOR THE CABLE EQUATION. [Doctoral Dissertation]. University of Tennessee – Knoxville; 2011. Available from: https://trace.tennessee.edu/utk_graddiss/1095

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