Related papers: Hybrid Optimization Techniques for Multi-State Opt…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology…
This work is concerned with the determination of the diffusion coefficient from distributed data of the state. This problem is related to homogenization theory on the one hand and to regularization theory on the other hand. An approach is…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
Artificially designed composite materials consist of microstructures, that exhibit various thermal properties depending on their shapes, such as anisotropic thermal conductivity. One of the representative applications of such composite…
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…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…
We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
This paper introduces a general modeling framework for a multi-type maximal covering location problem in which the position of facilities in different metric spaces are simultaneously decided to maximize the demand generated by a set of…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
We propose an unified algebraic approach for static condensation and hybridization, two popular techniques in finite element discretizations. The algebraic approach is supported by the construction of scalable solvers for problems involving…
We propose a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of…
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…
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…