Related papers: Isogeometric analysis using manifold-based smooth …
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…
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…
We propose a method to simultaneously compute scalar basis functions with an associated functional map for a given pair of triangle meshes. Unlike previous techniques that put emphasis on smoothness with respect to the Laplace--Beltrami…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
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…
We study approximation error bounds of isogeometric function spaces on a specific type of singularly parameterized domains. In this context an isogeometric function is the composition of a piecewise rational function with the inverse of a…
A particular class of planar two-patch geometries, called bilinear-like $G^{2}$ two-patch geometries, is introduced. This class includes the subclass of all bilinear two-patch parameterizations and possesses similar connectivity functions…
This work develops a computational framework that combines physics-informed neural networks with multi-patch isogeometric analysis to solve partial differential equations on complex computer-aided design geometries. The method utilizes…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…
In this paper, we propose a spectral method for deriving functions that are jointly smooth on multiple observed manifolds. This allows us to register measurements of the same phenomenon by heterogeneous sensors, and to reject…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
Subdivision surfaces are proven to be a powerful tool in geometric modeling and computer graphics, due to the great flexibility they offer in capturing irregular topologies. This paper discusses the robust and efficient implementation of an…
Reconstruction of a continuous surface of two-dimensional manifold from its raw, discrete point cloud observation is a long-standing problem. The problem is technically ill-posed, and becomes more difficult considering that various sensing…
We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
We present a practical approach for constructing meshes of general rough surfaces with given autocorrelation functions based on the unstructured meshes of nominally smooth surfaces. The approach builds on a well-known method to construct…
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.…
This paper is concerned with the construction of graded meshes for approximating so-called singular solutions of elliptic boundary value problems by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes. Such solutions…
This paper describes a framework for capturing geological structures in a 3D block model and improving its spatial fidelity given new mesh surfaces. Using surfaces that represent geological boundaries, the objectives are to identify areas…