Related papers: Computational Shape Derivatives in Heat Conduction…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we…
We analyze the theoretical framework of a shape optimization problem for a microchannel cooling system. To this end, a cost functional based on the tracking of absorbed energy by the cooler as well as some desired flow on a subdomain of the…
We model a microchannel cooling system and consider the optimization of its shape by means of shape calculus. A three-dimensional model covering all relevant physical effects and three reduced models are introduced. The latter are derived…
This article is concerned with the solution of a time-dependent shape identification problem. Specifically we consider the heat equation in a domain, which contains a time-dependent inclusion of zero temperature. The objective is to detect…
A support structure is required to successfully create structural parts in the powder bed fusion process for additive manufacturing. In this study, we present the topology optimization of a support structure that improves the heat…
In this paper we derive rigorously the derivative of the Dirichlet to Neumann map and of the Neumann to Dirichlet map of the conductivity equation with respect to movements of vertices of triangular conductivity inclusions. We apply this…
This paper is devoted to the study of gradient estimates for the Dirichlet problem of the heat equation in the exterior domain of a compact set. Our results describe the time decay rates of the derivatives of solutions to the Dirichlet…
Thermal conductivities are routinely calculated in molecular dynamics simulations by keeping the boundaries at different temperatures and measuring the slope of the temperature profile in the bulk of the material, explicitly using Fourier's…
In this paper, we study optimization of the first eigenvalue of the heat equation with spatially nonuniform conductivity on a bounded domain under several constraints for the conductivity. We consider this problem in various boundary…
In this paper, we study an insulation problem that seeks to determine the optimal distribution of a given amount $m>0$ of insulating material coating an insulated boundary part $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape which minimizes a certain cost…
Recently, gradient-based discrete sampling has emerged as a highly efficient, general-purpose solver for various combinatorial optimization (CO) problems, achieving performance comparable to or surpassing the popular data-driven approaches.…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the…