Related papers: Weak Scalability of time parallel Schwarz methods …
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…
In this paper, we propose an efficient two-level additive Schwarz method for solving large-scale eigenvalue problems arising from the finite element discretization of symmetric elliptic operators, which may compute efficiently more interior…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. Specifically in the optimal control minimization problem, a tracking-type cost functional is minimized to steer the…
Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…
Parabolic optimal control problems with control constraints are generally challenging, from either theoretical analysis or algorithmic design perspectives. Conceptually, the well-known alternating direction method of multipliers (ADMM) can…
The time domain analysis of eddy current problems often requires the simulation of long time intervals, e.g. until a steady state is reached. Fast-switching excitations e.g. in pulsedwidth modulated signals require in addition very small…
Using a high degree of parallelism is essential to perform data assimilation efficiently. The state formulation of the incremental weak constraint four-dimensional variational data assimilation method allows parallel calculations in the…
In the present work, we study and analyze an efficient iterative coupling method for a dimensionally heterogeneous problem . We consider the case of 2-D Laplace equation with non symmetric boundary conditions with a corresponding 1-D…
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…
The core of the Model Predictive Control (MPC) method in every step of the algorithm consists in solving a time-dependent optimization problem on the prediction horizon of the MPC algorithm, and then to apply a portion of the optimal…
In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…
We develop a novel parallel decomposition strategy for unweighted, undirected graphs, based on growing disjoint connected clusters from batches of centers progressively selected from yet uncovered nodes. With respect to similar previous…
In this paper, we determine the convergence speed of an upscaling of a pseudo-parabolic system containing drift terms with scale separation of size $\epsilon \ll 1$. Both the upscaling and convergence speed determination exploit a natural…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, which is closely related to iterated Runge-Kutta methods…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
The numerical simulation of atherosclerotic plaque growth is computationally prohibitive, since it involves a complex cardiovascular fluid-structure interaction (FSI) problem with a characteristic time scale of milliseconds to seconds, as…