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Center-based models are used to simulate the mechanical behavior ofbiological cells during embryonic development or cancer growth. To allow forthe simulation of biological populations potentially growing from a fewindividual cells to many thousands or more, these models have to be numericallyefficient, while being reasonably accurate on the level of individual celltrajectories. In this work, we increase the robustness, accuracy, andefficiency of the simulation of center-based models by choosing the time stepsadaptively in the numerical method. We investigate the gain in using singlerate time stepping for the forward and backward Euler methods, based on localestimates of the numerical errors and the stability of the method in the caseof the explicit forward Euler method. Furthermore, we propose a multirate timestepping scheme that simulates regions with high local force gradients (e.g. asthey happen after cell division) with multiple smaller time steps within alarger single time step for regions with smoother forces. These methods arecompared for different model systems in numerical experiments. We conclude thatthe adaptive single rate forward Euler method results in significant gains interms of reduced wall clock times for the simulation of a linearly growingtissue, while at the same time eliminating the need for manual determination ofa suitable time step size.

Adaptive time integration of mechanical forces in center-based models for biological cell populations