Related papers: A fast boundary integral method for high-order mul…
In this paper, we describe a robust algorithm for 2-Manifold generation of various kinds of ShapeNet Models. The input of our pipeline is a triangle mesh, with a set of vertices and triangular faces. The output of our pipeline is a…
We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…
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…
The correct treatment of boundary conditions is a key step in the development of the SPH method. The SPH community has to face several challenges in this regard - in particular, a primordial aspect for any boundary formulation is to ensure…
Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two…
A triangulation of a surface is irreducible if there is no edge whose contraction produces another triangulation of the surface. In this work we propose an algorithm that constructs the set of irreducible triangulations of any surface with…
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…
This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh…
We present a new iterative technique based on radial basis function (RBF) interpolation and smoothing for the generation and smoothing of curvilinear meshes from straight-sided or other curvilinear meshes. Our technique approximates the…
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…
We present a high-order surface quadrature (HOSQ) for accurately approximating regular surface integrals on closed surfaces. The initial step of our approach rests on exploiting square-squeezing--a homeomorphic bilinear square-simplex…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…
Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific computing, but to date have ignored a very basic requirement: in many situations, surfaces must not pass through themselves or each…
This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its…
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 present a CUDA accelerated implementation of the Characteristic/Scan Conversion algorithm to generate narrow band signed distance fields in logically Cartesian grids. We outline an approach of task and data management on GPUs based on an…
This paper presents a method to generate high quality triangular or quadrilateral meshes that uses direction fields and a frontal point insertion strategy. Two types of direction fields are considered: asterisk fields and cross fields. With…
We provide a new approach for computing integrals over hypersurfaces in the level set framework. The method is based on the discretization (via simple Riemann sums) of the classical formulation used in the level set framework, with the…