Adaptive numerical simulation of intracellular calcium dynamics using domain decomposition methods

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-diffusions 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.