Related papers: Multiphase shape optimization problems
Computational meshes arising from shape optimization routines commonly suffer from decrease of mesh quality or even destruction of the mesh. In this work, we provide an approach to regularize general shape optimization problems to increase…
The thesis is about an application of the shape optimization to the morphological evolution of Golgi stack. Golgi stack consists of multiple layers of cisternae. It is an organelle in the biological cells. Inspired by the Helfrich Model…
Let $(M^{n+1},g)$ be a closed Riemannian manifold of dimension $3\le n+1\le 5$. We show that, if the metric $g$ is generic or if the metric $g$ has positive Ricci curvature, then $M$ contains infinitely many geometrically distinct constant…
Isogeometric analysis (IGA) has emerged as a promising approach in the field of structural optimization, benefiting from the seamless integration between the computer-aided design (CAD) geometry and the analysis model by employing…
The free-form deformation model can represent a wide range of non-rigid deformations by manipulating a control point lattice over the image. However, due to a large number of parameters, it is challenging to fit the free-form deformation…
We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane…
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…
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding to the portion of the habitat which is favorable to the…
We consider the method of mappings for performing shape optimization for unsteady fluid-structure interaction (FSI) problems. In this work, we focus on the numerical implementation. We model the optimization problem such that it takes…
Shape optimization problems constrained by variational inequalities (VI) are non-smooth and non-convex optimization problems. The non-smoothness arises due to the variational inequality constraint, which makes it challenging to derive…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
Future e-mobility calls for efficient electrical machines. For different areas of operation, these machines have to satisfy certain desired properties that often depend on their design. Here we investigate the use of multipatch Isogeometric…
Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However,…
We study a general version of the Cheeger inequality by considering the shape functional $\mathcal{F}_{p,q}(\Omega)=\lambda_p^{1/p}(\Omega)/\lambda_q(\Omega)^{1/q}$. The infimum and the supremum of $\mathcal{F}_{p,q}$ are studied in the…
Construction of optimal deformations is one of the long standing problems of computational mathematics. We consider the problem of computing quasi-isometric deformations with minimal possible quasi-isometry constant (global estimate for…
Minima of functionals of the type $$ w\mapsto \int_{\Omega}\left[\snr{Dw}\log(1+\snr{Dw})+a(x)\snr{Dw}^{q}\right] \dx\,, \quad 0\leq a(\cdot) \in C^{0, \alpha}\,,$$ with $\Omega \subset \er^n$, have locally H\"older continuous gradient…
We study the Dirichlet problem for systems of the form -\Delta u^k=f^k(x,u)+\mu^k, x\in\Omega, k=1,...,n, where \Omega\subset R^d$ is an open (possibly nonregular) bounded set, \mu^1,...,\mu^n are bounded diffuse measures on \Omega,…
We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimise the sum of the first Dirichlet Laplace--Beltrami operator eigenvalues over a given number of partitions of a surface. We consider…
A fast and reliable geometry optimization algorithm is presented that optimizes atomic positions and lattice vectors simultaneously. Using a series of benchmarks, it is shown that the method presented in this paper outperforms in most cases…
Multistage stochastic optimization problems are oftentimes formulated informally in a pathwise way. These are correct in a discrete setting and suitable when addressing computational challenges, for example. But the pathwise problem…