Related papers: Topology Optimization through Differentiable Finit…
In this work we consider the numerical solution of incompressible flows on two-dimensional manifolds. Whereas the compatibility demands of the velocity and the pressure spaces are known from the flat case one further has to deal with the…
In the present work, a highly efficient Moving Morphable Component (MMC) based approach for multi-resolution topology optimization is proposed. In this approach, high-resolution optimization results can be obtained with much less number of…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…
This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can…
Recent works in deep learning have shown that integrating differentiable physics simulators into the training process can greatly improve the quality of results. Although this combination represents a more complex optimization task than…
We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization…
Using Domain Decomposition (DD) algorithm on non--overlapping domains, we compare couplings of different discretisation models, such as Finite Element (FEM) and Reduced Order (ROM) models for separate subcomponents. In particular, we…
A memetic framework for optimal inverse design is proposed by combining a local gradient-based procedure and a robust global scheme. The procedure is based on method-of-moments matrices and does not demand full inversion of a system matrix.…
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…
Optimization is finding the best solution, which mathematically amounts to locating the global minimum of some cost function. Optimization is traditionally automated with digital or quantum computers, each having their limitations and none…
We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…
New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specifications. Our approach utilizes multi-material microstructures as low-level building blocks…
Photonic topology optimization is a technique used to find the electric permittivity distribution of a device that optimizes an electromagnetic figure-of-merit. Two common techniques are used: continuous density-based optimizations that…
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. The DP scheme for the numerical…
This paper presents an algorithm for reliability-based topology optimization of linear elastic continua under random-field material model. The modelling random field is discretized into a small number of random variables, and then the…
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for…