Related papers: A geometric mesh smoothing algorithm related to da…
Agglomeration techniques can be successfully employed to reduce the computational costs of numerical simulations and stand at the basis of multilevel algebraic solvers. To automatically perform mesh agglomeration, we propose a novel…
Textured 3D meshes jointly represent geometry, topology, and appearance, yet their irregular structure poses significant challenges for deep-learning-based semantic segmentation. While a few recent methods operate directly on meshes without…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…
Surfaces are typically represented as meshes, which can be extracted from volumetric fields via meshing or optimized directly as surface parameterizations. Volumetric representations occupy 3D space and have a large effective receptive…
A new semi-discrete finite element scheme for the evolution of three parametrized curves by curvature flow that are connected by a triple junction is presented and analyzed. In this triple junction, conditions are imposed on the angles at…
We introduce MeshGPT, a new approach for generating triangle meshes that reflects the compactness typical of artist-created meshes, in contrast to dense triangle meshes extracted by iso-surfacing methods from neural fields. Inspired by…
We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow,…
Parametric finite elements lead to very efficient numerical methods for surface evolution equations. We introduce several computational techniques for curvature driven evolution equations based on a weak formulation for the mean curvature.…
We consider a class of nonsmooth and nonconvex optimization problems over the Stiefel manifold where the objective function is the summation of a nonconvex smooth function and a nonsmooth Lipschitz continuous convex function composed with…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
We present a simple direct discretization for functionals used in the variational mesh generation and adaptation. Meshing functionals are discretized on simplicial meshes and the Jacobian matrix of the continuous coordinate transformation…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
We present a cut finite element method for the heat equation on two overlapping meshes: a stationary background mesh and an overlapping mesh that evolves inside/"on top" of it. Here the overlapping mesh is prescribed a simple discontinuous…
Textured meshes significantly enhance the realism and detail of objects by mapping intricate texture details onto the geometric structure of 3D models. This advancement is valuable across various applications, including entertainment,…
Deep learning-based medical image segmentation and surface mesh generation typically involve a sequential pipeline from image to segmentation to meshes, often requiring large training datasets while making limited use of prior geometric…
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…
We introduce a novel representation and optimization framework for discrete geodesics on triangle meshes that reduces artifacts of linear methods on uneven and coarse discretizations. Our method computes squared geodesic distances from…
The proposed two-dimensional geometrically exact beam element extends our previous work by including the effects of shear distortion, and also of distributed forces and moments acting along the beam. The general flexibility-based…
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…