SIAM Journal on Scientific and Statistical Computing
Matrix-free W-methods using a multiple Arnoldi iteration
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
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In this paper we present adaptive numerical simulations of intracellular calcium dynamics using domain decomposition methods. The modeling of diffusion, binding and membrane transport of calcium ions in cells leads to a system of reaction-diffusion equations. We describe the modulation of cytosolic and ER calcium concentration close to the membrane of the cell organelle. This leads to a two-dimensional model. Local grid refinement is adjusted to the strongly local effects of the calcium dynamics. A finite element method is used for spatial discretization and a Rosenbrock solver for time integration which is third-order accurate and very suitable for nonlinear parabolic problems. We present sequential and parallelized numerical results. The latter are based on domain decomposition methods.