Hartung-Gorre Verlag
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Renate Gorre D-78465
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Series in Computational Science
edited by Illia Horenka,
Rolf Krause, Olaf Schenk
Volume 4
Dorian Krause
Scalable
Space-Time Adaptive Simulation Tools for
Computational Electrocardiology
First Edition 2014. 184
pages, EUR 64,00
ISBN 978-3-86628-494-4
This work is
concerned with the development of computational tools for the solution of
reaction-diffusion equations from the field of computational electrocardiology. We designed lightweight spatially and
space-time adaptive schemes for large-scale parallel simulations. We propose
two different adaptive schemes based on locally structured meshes, managed
either via a conforming coarse tessellation or a forest of shallow trees. A
crucial ingredient of our approach is a non-conforming mortar element discretization
which is used to glue together individually structured meshes by means of
constraints. For the solution of variational problems
in the proposed trial spaces we investigate two diametrically opposite
approaches. First, we discuss the implementation of a matrix-free scheme for
the solution of the monodomain equation on patch-wise
adaptive meshes. Second, an approach to the construction of standard linear
algebra data structures on tree-based meshes is considered. In particular, we
address the element-wise assembly of stiffness matrices on constrained spaces
via an algebraic representation of the inclusion map. We evaluate the
performance of our adaptive schemes and demonstrate their applicability to the
design of realistic large-scale heart models. In order to enable local time
stepping in the context of (semi-)implicit integration schemes, we present a
space-time discretization based on the proposed lightweight adaptive mesh data
structures. By means of a discontinuous Galerkin
method in time, the solution of the linear or non-linear system of equations is
reduced to a sequence of smaller systems of adjustable size. We discuss the
stabilization of the arising discrete problems and present extensive numerical
evaluations of the space-time adaptive solution of the (1+1)-, (2+1)- and (3+1)-dimensional heat equation as well as the monodomain equation. Our results show both feasibility and
potential of adaptive space-time discretizations for
the solution of reaction-diffusion equations in computational electrocardiology.
Keywords: Computational Science;
Computational electrocardiology; High performance
computing; Parallel computing; Space-time adaptivity;
Lightweight adaptive mesh data structures; Non-conforming discretizations;
Fast solution techniques for reaction-diffusion equations; Large-scale heart
models
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