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We consider the dunking problem: a solid body at uniform temperature $T_{\text i}$ is placed in a environment characterized by farfield temperature $T_\infty$ and spatially uniform time-independent heat transfer coefficient. We permit…
We consider a second order singularly perturbed boundary value problem, of reaction-convection-diffusion type with two small parameters, and the approximation of its solution by the $hp$ version of the Finite Element Method on the so-called…
The increasing recognition of the association between adverse human health conditions and many environmental substances as well as processes has led to the need to monitor them. An important problem that arises in environmental statistics…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
In this paper we show how to efficiently achieve thermal cloaking from a computational standpoint in several virtual scenarios by controlling a distribution of active heat sources. We frame this problem in the setting of PDE-constrained…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
In this article we consider the Dirichlet problem on a bounded domain $\Omega \subset {\bf R}^d$ with respect to a second-order elliptic differential operator in divergence form. We do not assume a divergence condition as in the pioneering…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…
In this paper, we first design a time optimal control problem for the heat equation with sampled-data controls, and then use it to approximate a time optimal control problem for the heat equation with distributed controls. Our design is…
We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic…
We consider the thermal dunking problem, in which a solid body is suddenly immersed in a fluid of different temperature, and study both the temporal evolution of the solid and the associated Biot number -- a non-dimensional heat transfer…
In this article we develop a duality principle and concerning computational method for a structural optimization problem in elasticity. We consider the problem of finding the optimal topology for an elastic solid which minimizes its…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
In this paper, we present a novel tolerance allocation algorithm for the assessment and control of geometric variation on system performance that is applicable to any system of partial differential equations. In particular, we parameterize…
We consider the problem of optimal distribution of a limited amount of conductive material in systems governed by local and non-local scalar diffusion laws. Of particular interest for these problems is the study of the limiting case, which…
An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, of negligible diameter, made up of two consecutive sections of different, isotropic and homogeneous materials. At the…
This paper is concerned with the two--phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A…
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…
We present a space-time finite element method for the heat equation that computes quasi-optimal approximations with respect to natural norms while incorporating local mesh refinements in space-time. The discretized problem is solved with a…