Related papers: First and Second Order Shape Optimization based on…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
We study the problem of 3D shape reconstruction from 2D landmarks extracted in a single image. We adopt the 3D deformable shape model and formulate the reconstruction as a joint optimization of the camera pose and the linear shape…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
We propose a novel early-terminating mesh refinement strategy using an integrated residual method to solve dynamic feasibility problems. As a generalization of direct collocation, the integrated residual method is used to approximate an…
Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…
As humans, we regularly associate shape of an object with its built material. In the context of geometric modeling, however, this interrelation between form and material is rarely explored. In this work, we propose a novel data-driven…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
We present 2-D, 3-D, and spherical mesh generators for the Finite Element Method (FEM) using triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke's law. Given the desired…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
We propose a numerical method for fluid deformable surfaces governed by surface Stokes flow and Helfrich bending energy under active growth, aiming to model shape evolution of the epithelium in developmental processes. To prevent…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
This paper presents a theory of optimization fabrics, second-order differential equations that encode nominal behaviors on a space and can be used to define the behavior of a smooth optimizer. Optimization fabrics can encode commonalities…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
Mesh numbering is a critical issue in Finite Element Methods, as the computational cost of one analysis is highly dependent on the order of the nodes of the mesh. This paper presents some preliminary investigations on the problem of mesh…
In this article, we improve the convergence order of some finite volume solutions approximating some second order elliptic problems. We prove that finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be obtained after…
The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model…
We introduce a numerical framework to verify the finite step convergence of first-order methods for parametric convex quadratic optimization. We formulate the verification problem as a mathematical optimization problem where we maximize a…
In this work, we study the design and analysis of a novel hybrid high-order (HHO) method on unfitted meshes. HHO methods rely on a pair of unknowns, combining polynomials attached to the mesh faces and the mesh cells. In the unfitted…