Related papers: New time domain decomposition methods for paraboli…
A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We present the spatial DG discretization based on a mixed…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
In this paper, we study several theoretical and numerical questions concerning the null controllability problems for linear parabolic equations and systems for several dimensions. The control is distributed and acts on a small subset of the…
We consider parabolic evolution equations with Lipschitz continuous and strongly monotone spatial operators. By introducing an additional variable, we construct an equivalent system where the operator is a Lipschitz continuous mapping from…
We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
We prove the convergence of the fixed-point (also called thresholding) algorithm in three optimal control problems under large volume constraints. This algorithm was introduced by C\'ea, Gioan and Michel, and is of constant use in the…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…
We present non-overlapping Domain Decomposition Methods (DDM) based on quasi-optimal transmission operators for the solution of Helmholtz transmission problems with piece-wise constant material properties. The quasi-optimal transmission…
Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the…
In this work, we consider the time-harmonic Maxwell's equations and their numerical solution with a domain decomposition method. As an innovative feature, we propose a feedforward neural network-enhanced approximation of the interface…
Understanding how systems built out of modular components can be jointly optimized is an important problem in biology, engineering, and machine learning. The backpropagation algorithm is one such solution and has been instrumental in the…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…
In this paper, we aim to solve the system of equations governing linear elasticity in parallel using domain decomposition. Through a non-overlapping decomposition of the domain, our approach aims to target the resulting interface problem,…
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation of parabolic problems with moving domains or interfaces. We…
The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of linear parabolic equations with time-dependent…
In this paper we develop an adaptive procedure for the numerical solution of semilinear parabolic problems, with possible singular perturbations. Our approach combines a linearization technique using Newton's method with an adaptive…
We present a time-parallelization method that enables to accelerate the computation of quantum optimal control algorithms. We show that this approach is approximately fully efficient when based on a gradient method as optimization solver:…
We examine the problem of two-point boundary optimal control of nonlinear systems over finite-horizon time periods with unknown model dynamics by employing reinforcement learning. We use techniques from singular perturbation theory to…
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…