Related papers: Isogeometric analysis with $C^1$ hierarchical func…
An adaptive isogeometric method based on $d$-variate hierarchical spline constructions can be derived by considering a refine module that preserves a certain class of admissibility between two consecutive steps of the adaptive loop [6]. In…
The de Rham complex arises naturally when studying problems in electromagnetism and fluid mechanics. Stable numerical methods to solve these problems can be obtained by using a discrete de Rham complex that preserves the structure of the…
The perfectly matched layer (PML) formulation is a prominent way of handling radiation problems in unbounded domain and has gained interest due to its simple implementation in finite element codes. However, its simplicity can be advanced…
Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get…
Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
In this paper hierarchical analysis-suitable T-splines (HASTS) are developed. The resulting spaces are a superset of both analysis-suitable T-splines and hierarchical B-splines. The additional flexibility provided by the hierarchy of…
The local refinement of PHT-splines (polynomial splines over hierarchical T-meshes) is achieved by a simple cross insertion, which may introduce superfluous control points or coefficients. By allowing split-in-half in mesh refinement,…
We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local $h$-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is…
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condition number of the system matrix not only grows with the…
Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…
We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The…
In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…
Polynomial splines are ubiquitous in the fields of computer aided geometric design and computational analysis. Splines on T-meshes, especially, have the potential to be incredibly versatile since local mesh adaptivity enables efficient…
Under consideration methods of constructing trigonometric interpolation splines of two variables on rectangular areas. These methods are easily generalized to the case of trigonometric interpolation splines of several variables on such…
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…
We present a semi-Lagrangian method for the numerical resolution of Vlasov-type equations on multi-patch meshes. Following N. Crouseilles et al. [A parallel Vlasov solver based on local cubic spline interpolation on patches. Journal of…
In this paper, we investigate $C^2$ super-smoothness of the full $C^1$ cubic spline space on a Powell-Sabin refined triangulation, for which a B-spline basis can be constructed. Blossoming is used to identify the $C^2$ smoothness conditions…