Related papers: Topological derivative for PDEs on surfaces
We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
This paper implements topology optimization on two-dimensional manifolds. In this paper, the material interpolation is implemented on a material parameter in the partial differential equation used to describe a physical field, when this…
Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
We consider the topology optimization problem of a 2d permanent magnet synchronous machine in magnetostatic operation with demagnetization. This amounts to a PDE-constrained multi-material design optimization problem with an additional…
We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…
The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical…
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…
In this paper, we perform a rigourous version of shape and topological derivatives for optimizations problems under constraint Helmoltz problems. A shape and topological optimization problem is formulated by introducing cost functional. We…
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…
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…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…
In this paper we introduce the topological state derivative for general topological dilatations and explore its relation to standard optimal control theory. We show that for a class of partial differential equations, the shape dependent…
In this paper, a topology optimization framework utilizing automatic differentiation is presented as an efficient way for solving 2D density-based topology optimization problem by calculating gradients through the fully differentiable…
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…
Shape optimization involves the minimization of a cost function defined over a set of shapes, often governed by a partial differential equation (PDE). In the absence of closed-form solutions, one relies on numerical methods to approximate…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
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…