## Editorial

Published in Computing and Visualization in Science

Published in Computing and Visualization in Science

Published in Computing and Visualization in Science

We develop new error estimates for the one-dimensional advection equation, considering general space-time discretization schemes based on Runge–Kutta methods and finite difference discretizations. We then derive conditions on the number of points per wavelength for a given error tolerance from these new estimates. Our analysis also shows the existe...

Published in Computing and Visualization in Science

The Poisson–Boltzmann equation (PBE) is a nonlinear elliptic parametrized partial differential equation that arises in biomolecular modeling and is a fundamental tool for structural biology. It is used to calculate electrostatic potentials around an ensemble of fixed charges immersed in an ionic solution. Efficient numerical computation of the PBE ...

Published in Computing and Visualization in Science

We apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To resolve the fast-switching excitations, small time steps are needed, such that parallelization in time becomes highly relevant for reducing the simulation time. The MGRIT alg...

Published in Computing and Visualization in Science

This paper describes a space-time parallel algorithm with space-time adaptive mesh refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in order to provide solution efficient adaptive grids with a reduction in work performed on coarser grids. This algorithm is achieved by integrating two software libraries: XBraid (...

Published in Computing and Visualization in Science

To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to space–time multigrid, PFASST is able to compute multiple time-steps simultaneously and is therefore in particular s...

Published in Computing and Visualization in Science

This review article serves to summarize the many advances in time-parallel computations since the excellent review article by Gander, “50 years of Time Parallel Integration” (Gander, in: 50 years of time parallel time integration. Multiple shooting and time domain decomposition, Springer, Berlin, 2015). We focus, when possible, on applications of t...

Published in Computing and Visualization in Science

Rayleigh–Bénard convection (RBC) is a fundamental problem of fluid dynamics, with many applications to geophysical, astrophysical, and industrial flows. Understanding RBC at parameter regimes of interest requires complex physical or numerical experiments. Numerical simulations require large amounts of computational resources; in order to more effic...

Published in Computing and Visualization in Science

A key component of many robotics model-based planning and control algorithms is physics predictions, that is, forecasting a sequence of states given an initial state and a sequence of controls. This process is slow and a major computational bottleneck for robotics planning algorithms. Parallel-in-time integration methods can help to leverage parall...

Published in Computing and Visualization in Science

The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine propagator is based on a (high-dimensional, slow-fast) stochastic microscopic model, and the coarse propagator i...