Related papers: Generation of High-Order Coarse Quad Meshes on CAD…
This paper presents a novel intersection-based remapping method for isoparametric curvilinear meshes within the indirect arbitrary Lagrangian-Eulerian (ALE) framework, addressing the challenges of transferring physical quantities between…
Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing…
Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for…
This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
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…
Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in…
We present a novel approach named TBase for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element (square) can be virtually divided into a pair of equilateral right triangles by…
This paper presents a new method to generate iso-scallop tool paths for triangular mesh surfaces. With the popularity of 3D scanning techniques, scanning-derived mesh surfaces have seen a significant increase in their application to…
Computer-Aided Design (CAD) is essential in industrial design, but the complexity of traditional CAD modeling and workflows presents significant challenges for automating the generation of high-precision, editable CAD models. Existing…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual…
Constructing computer-aided design (CAD) models is labor-intensive but essential for engineering and manufacturing. Recent advances in Large Language Models (LLMs) have inspired the LLM-based CAD generation by representing CAD as command…
We consider algorithmic approaches to the D-optimality problem for cases where the input design matrix is large and highly structured, in particular implicitly specified as a full quadratic or linear response-surface model in several levels…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
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…
The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing…
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…