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We consider the inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary…

Analysis of PDEs · Mathematics 2019-09-23 Ugur G. Abdulla , Bruno Poggi

We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…

Methodology · Statistics 2018-10-11 Quentin Clairon

Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…

Optimization and Control · Mathematics 2020-01-23 Jorn Baayen , Jakub Marecek

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

Optimization and Control · Mathematics 2023-10-18 Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen , Trang Nguyen

Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper, we derive explicit stabilized integrators of orders one and…

Numerical Analysis · Mathematics 2023-06-09 Ibrahim Almuslimani , Gilles Vilmart

The paper is concerned with a kind of minimal time control problem for the heat equation with impulse controls. The purpose of such a problem is to find an optimal impulse control (among certain control constraint set) steering the solution…

Optimization and Control · Mathematics 2018-06-19 Yueliang Duan , Lijuan Wang , Can Zhang

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…

We consider the inverse multiphase Stefan problem with homogeneous Dirichlet boundary condition on a bounded Lipschitz domain, where the density of the heat source is unknown in addition to the temperature and the phase transition…

Analysis of PDEs · Mathematics 2020-05-12 Ugur G. Abdulla , Bruno Poggi

Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…

Computational Physics · Physics 2018-07-26 Mehran Makhtoumi

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…

Numerical Analysis · Mathematics 2022-12-14 Devika Shylaja

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…

Optimization and Control · Mathematics 2023-04-06 Caroline Geiersbach , Teresa Scarinci

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of…

Optimization and Control · Mathematics 2021-07-02 Moira MacNeil , Merve Bodur

We introduce two models of industrial drying - a simplified one-equation model, and a detailed three-equation model. The purpose of the simplified model is rigorous validation of numerical methods for PDE-constrained optimal control. The…

Optimization and Control · Mathematics 2024-04-26 Lennon Ó Náraigh

We introduce a time-implicit, finite-element based space-time discretization scheme for the backward stochastic heat equation, and for the forward-backward stochastic heat equation from stochastic optimal control, and prove strong rates of…

Optimization and Control · Mathematics 2020-12-21 Andreas Prohl , Yanqing Wang

In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…

Numerical Analysis · Mathematics 2021-06-08 J. A. Fiordilino , M. Winger

We consider the optimal control problem of minimizing some quadratic functional over all possible solutions of an internally controlled multi-dimensional heat equation with a periodic terminal state constraint. This problem has a unique…

Optimization and Control · Mathematics 2015-09-22 Emmanuel Trélat , Lijuan Wang , Yubiao Zhang

We provide an a priori analysis of collocation methods for solving elliptic boundary value problems. They begin with information in the form of point values of the data and utilize only this information to numerically approximate the…

Numerical Analysis · Mathematics 2025-01-08 Andrea Bonito , Ronald DeVore , Guergana Petrova , Jonathan W. Siegel

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…

Numerical Analysis · Mathematics 2014-11-19 C. Brett , A. S. Dedner , C. M. Elliott

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…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…

Optimization and Control · Mathematics 2020-12-09 Andreas Prohl , Yanqing Wang