Related papers: Analysis-suitable $G^1$ multi-patch parametrizatio…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
In this paper, a novel isogeometric method for Biot's consolidation model is constructed and analyzed, using a four-field formulation where the unknown variables are the solid displacement, solid pressure, fluid flux, and fluid pressure.…
This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby…
The application of mortar methods in the framework of isogeometric analysis is investigated theoretically as well as numerically. For the Lagrange multiplier two choices of uniformly stable spaces are presented, both of them are spline…
Recently proposed as a stable means of evaluating geometric compactness, the isoperimetric profile of a planar domain measures the minimum perimeter needed to inscribe a shape with prescribed area varying from 0 to the area of the domain.…
Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener…
We present a novel method for isogeometric analysis (IGA) to directly work on geometries constructed by Boolean operations including difference (i.e., trimming), union and intersection. Particularly, this work focuses on the union…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…
In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…
In this work we define a spline complex preserving the cohomological structure of the continuous de Rham complex when the underlying physical domain is a toroidal solid. In the spirit of the isogeometric analysis, the spaces involved will…
Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem…
We investigate Sobolev regularity of bivariate functions obtained in Isogeometric Analysis when using geometry maps that are degenerate in the sense that the first partial derivatives vanish at isolated points. In particular, we show how…
We analyze the space of differentiable functions on a quad-mesh $\cM$, which are composed of 4-split spline macro-patch elements on each quadrangular face. We describe explicit transition maps across shared edges, that satisfy conditions…
Marching surfaces is a method for isosurface extraction and approximation based on a $G^1$ multi-sided patch interpolation scheme. Given a 3D grid of scalar values, an underlying curve network is formed using second order information and…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions of the parametric geometry diminish as the singularity is…
A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a spline-based representation of a…
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data,…
We present a systematic study on higher-order penalty techniques for isogeometric mortar methods. In addition to the weak-continuity enforced by a mortar method, normal derivatives across the interface are penalized. The considered…