
Magnetic Field Simulations Using Explicit Time Integration With Higher Order Schemes
A transient magnetoquasistatic vector potential formulation involving n...
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Implicit Temporal Differences
In reinforcement learning, the TD(λ) algorithm is a fundamental policy e...
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Optimized RungeKutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics
We develop errorcontrol based time integration algorithms for compressi...
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Inflight range optimization of multicopters using multivariable extremum seeking with adaptive step size
Limited flight range is a common problem for multicopters. To alleviate ...
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Exponential methods for solving hyperbolic problems with application to kinetic equations
The efficient numerical solution of many kinetic models in plasma physic...
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Finite element solution of nonlocal CahnHilliard equations with feedback control time step size adaptivity
In this study, we evaluate the performance of feedback controlbased tim...
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Calibrated Adaptive Probabilistic ODE Solvers
Probabilistic solvers for ordinary differential equations (ODEs) assign ...
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Efficient adaptive step size control for exponential integrators
Traditional step size controllers make the tacit assumption that the cost of a time step is independent of the step size. This is reasonable for explicit and implicit integrators that use direct solvers. In the context of exponential integrators, however, an iterative approach, such as Krylov methods or polynomial interpolation, to compute the action of the required matrix functions is usually employed. In this case, the assumption of constant cost is not valid. This is, in particular, a problem for higherorder exponential integrators, which are able to take relatively large time steps based on accuracy considerations. In this paper, we consider an adaptive step size controller for exponential Rosenbrock methods that determines the step size based on the premise of minimizing computational cost. The largest allowed step size, given by accuracy considerations, merely acts as a constraint. We test this approach on a range of nonlinear partial differential equations. Our results show significant improvements (up to a factor of 4 reduction in the computational cost) over the traditional step size controller for a wide range of tolerances.
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