Related papers: A Novel Deformation Method for Higher Order Mesh G…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
We present a new approach to discretizing shape optimization problems that generalizes standard moving mesh methods to higher-order mesh deformations and that is naturally compatible with higher-order finite element discretizations of…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
Computational mathematics plays an increasingly important role in computational fluid dynamics (CFD). The aeronautics and aerospace re- search community is working on next generation of CFD capacity that is accurate, automatic, and fast. A…
High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve…
We describe a high order technique to generate quadrilateral decompositions and meshes for complex two dimensional domains using spectral elements in a field guided procedure. Inspired by cross field methods, we never actually compute…
We present PhyDeformer, a new deformation method for high-quality garment mesh registration. It operates in two phases: In the first phase, a garment grading is performed to achieve a coarse 3D alignment between the mesh template and the…
Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in…
We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…
We present a technique for automatically producing a deformation of an input triangle mesh, guided solely by a text prompt. Our framework is capable of deformations that produce both large, low-frequency shape changes, and small…
We propose a class of temporally high-order parametric finite element methods for simulating solid-state dewetting of thin films in two dimensions using a sharp-interface model. The process is governed by surface diffusion and contact point…
We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…
We study the problem of shape generation in 3D mesh representation from a few color images with known camera poses. While many previous works learn to hallucinate the shape directly from priors, we resort to further improving the shape…
Fluid-structure interactions are a widespread phenomenon in nature. Although their numerical modeling have come a long way, the application of numerical design tools to these multiphysics problems is still lagging behind. Gradient-based…
In this paper, gradient-based optimization methods are combined with finite-element modeling for improving electric devices. Geometric design parameters are considered by affine decomposition of the geometry or by the design element…
A method for performing high order mesh refinement multigrid computations is presented. The Full Approximation Scheme (FAS) multigrid technique is utilized for a sequence of nested patches of increasing resolution. Conservation forms are…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
This paper presents a new progressive compression method for triangular meshes. This method, in fact, is based on a schema of irregular multi-resolution analysis and is centered on the optimization of the rate-distortion trade-off. The…