Math @ Duke
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Publications [#28834] of John A. Trangenstein
Papers Published
- with John A. Trangenstein and Chisup Kim, Operator Splitting and Adaptive Mesh Refinement for the Luo-Rudy I Model,
Journal of Computational Physics, vol. 196
(2004),
pp. 645-679, Elsevier
(last updated on 2004/12/10)
Abstract: We apply second-order operator splitting to
the Luo-Rudy I model for
electrical wave propagation in the heart.
The purpose of the operator splitting is to
separate the nonlinear
but local reaction computations from the
linear but globally coupled
diffusion computations.
This approach allows us to use {\em local
nonlinear} iterations for
the stiff nonlinear reactions, and to solve
{\em global linear}
systems for the implicit treatment of
diffusion.
For computational efficiency, we use
dynamically adaptive mesh
refinement (AMR), involving hierarchies of
unions of grid patches
on distinct levels of refinement.
The linear system for the discretization of
the diffusion on the
composite AMR grid is formulated via
standard conforming finite
elements on unions grid patches within a
level of refinement, and
aligned mortar elements along interfaces
between levels of refinement.
The linear systems are solved iteratively
by preconditioned conjugate
gradients.
Our preconditioner uses multiplicative
domain decomposition between
levels of refinement;
the smoother involves algebraic additive
domain decomposition between
patches within a level of refinement, and
Gauss-Seidel iteration
within grid patches.
Numerical results are presented in 1D and
2D, including spiral waves.
Keywords: reaction-diffusion, • excitable media, • adaptive mesh refinement, • operator splitting, • finite elements, • multigrid, • domain decomposition
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