Related papers: Efficient adaptive step size control for exponenti…
We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…
This paper studies economic model predictive Control (EMPC) schemes, where the stage cost depends only on control inputs. Such problems arise in applications like water distribution networks and differ from standard EMPC since multiple…
Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as…
Recently, our group developed explicit symplectic methods for curved spacetimes that are not split into several explicitly integrable parts, but are via appropriate time transformations. Such time-transformed explicit symplectic integrators…
We investigate time-adaptive Magnus-type integrators for the numerical approximation of a Mott transistor. The rapidly attenuating electromagnetic field calls for adaptive choice of the time steps. As a basis for step selection,…
Many common Markov chain Monte Carlo (MCMC) kernels can be formulated using a deterministic involutive proposal with a step size parameter. Selecting an appropriate step size is often a challenging task in practice; and for complex…
We review error estimation methods for co-simulation, in particular methods that are applicable when the subsystems provide minimal interfaces. By this, we mean that subsystems do not support rollback of time steps, do not output…
Recently, many machine learning optimizers have been analysed considering them as the asymptotic limit of some differential equations when the step size goes to zero. In other words, the optimizers can be seen as a finite difference scheme…
Extremum Seeking Control (ESC) is a well-known set of continuous time algorithms for model-free optimization of a cost function. One issue for ESCs is the convergence rates of parameters to extrema of unknown cost functions. The local…
Prior work on computable defect-based local error estimators for (linear) time-reversible integrators is extended to nonlinear and nonautonomous evolution equations. We prove that the asymptotic results from the linear case [W. Auzinger and…
We give an algorithm for efficient step size control in numerical integration of non-stiff initial value problems, based on a formula tailormade to methods where the numerical solution is compared with a solution of lower order.
In symmetric block eigenvalue algorithms, such as the subspace iteration algorithm and the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm, a large block size is often employed to achieve robustness and rapid…
This paper presents a systematic method for the selection of the Model Predictive Control (MPC) stage cost. We match the MPC feedback law to a proportional-integral (PI) controller, which we efficiently tune by high-performance Monte Carlo…
This paper is concerned with the development and testing of advanced time-stepping methods suited for the integration of time-accurate, real-world applications of computational fluid dynamics (CFD). The performance of several time…
Recently path integral methods have been developed for stochastic optimal control for a wide class of models with non-linear dynamics in continuous space-time. Path integral methods find the control that minimizes the expected cost-to-go.…
This paper is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the pulsating and exploding soliton…
Recent method developments involving path integral simulations have come a long way in making these techniques practical for studying condensed phase non-equilibrium phenomena. One of the main difficulties that still needs to be surmounted…
This work presents a new algorithm to compute the matrix exponential within a given tolerance. Combined with the scaling and squaring procedure, the algorithm incorporates Taylor, partitioned and classical Pad\'e methods shown to be…
Exponential integrators have been introduced as an efficient alternative to explicit and implicit methods for integrating large stiff systems of differential equations. Over the past decades these methods have been studied theoretically and…