Related papers: A simple technique for unstructured mesh generatio…
This paper presents a novel decoder-based approach for generating manufacturable 3D structures optimized for additive manufacturing. We introduce a deep learning framework that decodes latent representations into geometrically valid,…
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessary to introduce a truncation boundary, whereby only a…
We present a suite of techniques for jointly optimizing triangle meshes and shading models to match the appearance of reference scenes. This capability has a number of uses, including appearance-preserving simplification of extremely…
We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem may be singular, which has prompted us to conduct an a posteriori analysis of the method deriving residual based estimators to drive an…
We consider the problem of the construction of the nanophotonic structures of arbitrary geometry with prescribed desired properties. We reformulate this problem as an optimization problem for the Tikhonov functional which is minimized on…
3D Gaussian Splatting (3DGS) has enabled high-fidelity virtualization with fast rendering and optimization for novel view synthesis. On the other hand, triangle mesh models still remain a popular choice for surface reconstruction but suffer…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
Scaling artist-designed meshes to high triangle numbers remains challenging for autoregressive generative models. Existing transformer-based methods suffer from long-sequence bottlenecks and limited quantization resolution, primarily due to…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
Recent advances in differentiable rendering have sparked an interest in learning generative models of textured 3D meshes from image collections. These models natively disentangle pose and appearance, enable downstream applications in…
This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear…
Mesh adaptation for finite element approximation is a procedure used in numerous applications. The use of thin and long anisotropic triangles improves the efficiency of the procedure. When piecewise linear finite elements are used, the…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
We shall establish the convergence of an adaptive conforming finite element method for the reconstruction of the distributed flux in a diffusion system. The adaptive method is based on a posteriori error estimators for the distributed flux,…
In moving mesh methods, the underlying mesh is dynamically adapted without changing the connectivity of the mesh. We specifically consider the generation of meshes which are adapted to a scalar monitor function through equidistribution.…
The paper is concerned with the adaptive finite element solution of linear elliptic differential equations using equidistributing meshes. A strategy is developed for defining this type of mesh based on residual-based a posteriori error…