Related papers: Adaptive Quadrilateral Mesh in Curved Domains
We use circle-packing methods to generate quadrilateral meshes for polygonal domains, with guaranteed bounds both on the quality and the number of elements. We show that these methods can generate meshes of several types: (1) the elements…
We propose an end-to-end pipeline to robustly generate high-quality, high-order and coarse quadrilateral meshes on CAD models. This kind of mesh enables the use of high-order analysis techniques such as high-order finite element methods or…
We propose a two dimensional (2D) adaptive nodes technique for irregular regions. The method is based on equi-distribution principal and dimension reduction. The mesh generation is carried out by first producing some adaptive nodes in a…
Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first…
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…
Rendering techniques based on a random grid can be improved by adapting brushstrokes to the shape of different areas of the original picture. In this paper, the concept of Coherence Length Diagram is applied to determine the adaptive…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
An implementation of adaptive mesh refinement algorithms is presented for use with multilayer shallow water equations. Currently, adaptive mesh refinement is implemented with a single layer shallow water model in the GeoClaw framework. This…
The high computational demands of multiscale modeling necessitate advanced parallel and adaptive strategies. To address this challenge, we introduce an adaptive method that utilizes two microscale models based on an offline database for…
Strip-decomposable quadrilateral (SDQ) meshes, i.e., quad meshes that can be decomposed into two transversal strip networks, are vital in numerous fabrication processes; examples include woven structures, surfaces from sheets, custom rebar,…
We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature…
This paper introduces the MeshAC package, which generates three-dimensional adaptive meshes tailored for the efficient and robust implementation of multiscale coupling methods. While Delaunay triangulation is commonly used for mesh…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
Introduction of curvilinear coordinates might be very convenient in many cases. Theoretically, tensor analysis would be most suited. However, tensor notation can't be used in numerical procedure. For example, the strict discrimination of…
Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the…
Emerging AI applications such as ChatGPT, graph convolutional networks, and other deep neural networks require massive computational resources for training and inference. Contemporary computing platforms such as CPUs, GPUs, and TPUs are…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
A general approach for transforming phase field equations into generalized curvilinear coordinates is proposed in this work. The proposed transformation can be applied to isotropic, non-isotropic, and curvilinear grids without adding any…
We propose a concise approximate description, and a method for efficiently obtaining this description, via adaptive random sampling of the performance (running time, memory consumption, or any other profileable numerical quantity) of a…