Scalable approximation and solvers for ionic electrodiffusion in cellular geometries
CoRR(2024)
摘要
The activity and dynamics of excitable cells are fundamentally regulated and
moderated by extracellular and intracellular ion concentrations and their
electric potentials. The increasing availability of dense reconstructions of
excitable tissue at extreme geometric detail pose a new and clear scientific
computing challenge for computational modelling of ion dynamics and transport.
In this paper, we design, develop and evaluate a scalable numerical algorithm
for solving the time-dependent and nonlinear KNP-EMI equations describing ionic
electrodiffusion for excitable cells with an explicit geometric representation
of intracellular and extracellular compartments and interior interfaces. We
also introduce and specify a set of model scenarios of increasing complexity
suitable for benchmarking. Our solution strategy is based on an
implicit-explicit discretization and linearization in time, a mixed finite
element discretization of ion concentrations and electric potentials in
intracellular and extracellular domains, and an algebraic multigrid-based,
inexact block-diagonal preconditioner for GMRES. Numerical experiments with up
to 10^8 unknowns per time step and up to 256 cores demonstrate that this
solution strategy is robust and scalable with respect to the problem size, time
discretization and number of cores.
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