Related papers: Construction of Smooth Isogeometric Function Space…
This paper deals with a simple and straightforward procedure for automatic generation of finite-element or finite-volume meshes of spheroidal domains, consisting of tetrahedra. Besides the equation of the boundary, the generated meshes…
Decomposing the domain of a function into parts has many uses in mathematics. A domain may naturally be a union of pieces, a function may be defined by cases, or different boundary conditions may hold on different regions. For any…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit disk. Low rank approximations to functions in polar geometries are formed by synthesizing the disk analogue of the double Fourier…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
In this paper we develop the theory of equisingular deformations of plane curve singularities in arbitrary characteristic. We study equisingular deformations of the parametrization and of the equation and show that the base space of its…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…
In the framework of generalized finite element methods for elliptic equations with rough coefficients, efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
Through exploring the embedded transnormal systems of codimension 1, we show the existence of a transnormal function on a connected complete Riemannian manifold requires the underlying manifold to have a vector bundle structure or a linear…
Isogeometric Analysis is a spline-based discretization method to partial differential equations which shows the approximation power of a high-order method. The number of degrees of freedom, however, is as small as the number of degrees of…
This paper proposes an isogeometric boundary element method (IGBEM) to solve the electromagnetic scattering problems for three-dimensional doubly-periodic multi-layered structures. The main concerns are the constructions of (i) an open…
An extension of the Method of Regularized Stokeslets (MRS) in three dimensions is developed for triangulated surfaces with a piecewise linear force distribution. The method extends the regularized Stokeslet segment methodology used for…
An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth conformal multi-patch representation of their finite boundary surface.…
We consider the problem of characterizing entrywise functions that preserve the cone of positive definite matrices when applied to every off-diagonal element. Our results extend theorems of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J.…
A topological measure on a locally compact space is a set function on open and closed subsets which is finitely additive on the collection of open and compact sets, inner regular on open sets, and outer regular on closed sets. Almost all…
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.…
Infinite-dimensional manifolds modelled on arbitrary Hilbert spaces of functions are considered. It is shown that changes in model rather than changes of charts within the same model make coordinate formalisms on finite and…
In isogeometric analysis, it is frequently required to handle the geometric models enclosed by four-sided or non-four-sided boundary patches, such as trimmed surfaces. In this paper, we develop a Gregory solid based method to parameterize…