Related papers: A numerical procedure and unified formulation for …
We provide a framework for the numerical approximation of distributed optimal control problems, based on least-squares finite element methods. Our proposed method simultaneously solves the state and adjoint equations and is $\inf$--$\sup$…
In this paper, the SQP method applied to a hyperbolic PDE-constrained optimization problem is considered. The model arises from the acoustic full waveform inversion in the time domain. The analysis is mainly challenging due to the involved…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
We use the adjoint methods to study the static Hamilton-Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of…
This paper focusses on the optimal control problems governed by fourth-order linear elliptic equations with clamped boundary conditions in the framework of the Hessian discretisation method (HDM). The HDM is an abstract framework that…
In this paper, we propose an unfitted finite element method to solve PDE-constrained shape optimization problems via shape gradient flow. The shape gradient flow system consists of the state equation, the adjoint equation, the velocity…
This paper presents a systematic approach for computing local solutions to motion planning problems in non-convex environments using numerical optimal control techniques. It extends the range of use of state-of-the-art numerical optimal…
In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \begin{eqnarray*} \frac{\partial y}{\partial t} + A y &=& \int_0^t B(t, s) y(s) ds + Gu,…
Achieving robust control and optimization in high-fidelity physics simulations is extremely challenging, especially for evolutionary systems whose solutions span vast scales across space, time, and physical variables. In conjunction with…
In this paper we introduce a new procedure to solve nonlinear optimal control problems with delays which exploits indirect methods combined with numerical homotopy procedures. It is known that solving this kind of problems via indirect…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
PDE-constrained optimization aims at finding optimal setups for partial differential equations so that relevant quantities are minimized. Including sparsity promoting terms in the formulation of such problems results in more practically…
This paper presents a safe output regulation control strategy for a class of systems modeled by a coupled $2\times 2$ hyperbolic PDE-ODE structure, subject to fully distributed disturbances throughout the system. A state-feedback controller…
We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume…
A solid system consisting of two heat conducting cylinders with a thermoelectric converter (Peltier element) between them is considered. A nonlinear model, which was previously verified by authors, is used to design a constrained control…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
We study a PDE-constrained optimal control problem that involves functions of bounded variation as controls and includes the TV seminorm of the control in the objective. We apply a path-following inexact Newton method to the problems that…