Mathematical analysis of variational isogeometric methods

LB Da Veiga, A Buffa, G Sangalli, R Vázquez - Acta Numerica, 2014‏ - cambridge.org
This review paper collects several results that form part of the theoretical foundation of
isogeometric methods. We analyse variational techniques for the numerical resolution of …

[کتاب][B] Generalized locally Toeplitz sequences: theory and applications

C Garoni, S Serra-Capizzano - 2017‏ - Springer
Sequences of matrices with increasing size naturally arise in several contexts and especially
in the discretization of continuous problems, such as integral and differential equations. The …

On the similarities and differences between Classical Hierarchical, Truncated Hierarchical and LR B-splines

KA Johannessen, F Remonato, T Kvamsdal - Computer Methods in Applied …, 2015‏ - Elsevier
Smooth spline functions such as B-splines and NURBS are already an established
technology in the field of computer-aided design (CAD) and have in recent years been given …

Spectral analysis and structure preserving preconditioners for fractional diffusion equations

M Donatelli, M Mazza, S Serra-Capizzano - Journal of Computational …, 2016‏ - Elsevier
Fractional partial order diffusion equations are a generalization of classical partial
differential equations, used to model anomalous diffusion phenomena. When using the …

Foundations of spline theory: B-splines, spline approximation, and hierarchical refinement

A Kunoth, T Lyche, G Sangalli… - Splines and PDEs: From …, 2018‏ - Springer
This chapter presents an overview of polynomial spline theory, with special emphasis on the
B-spline representation, spline approximation properties, and hierarchical spline refinement …

Symbol-based analysis of finite element and isogeometric B-spline discretizations of eigenvalue problems: exposition and review

C Garoni, H Speleers, SE Ekström, A Reali… - … Methods in Engineering, 2019‏ - Springer
We present an example-based exposition and review of recent advances in symbol-based
spectral analysis. We consider constant-and variable-coefficient, second-order eigenvalue …

Robust and optimal multi-iterative techniques for IgA Galerkin linear systems

M Donatelli, C Garoni, C Manni… - Computer Methods in …, 2015‏ - Elsevier
We consider fast solvers for large linear systems arising from the Galerkin approximation
based on B-splines of classical d-dimensional elliptic problems, d≥ 1, in the context of …

The GLT class as a generalized Fourier analysis and applications

S Serra-Capizzano - Linear Algebra and its Applications, 2006‏ - Elsevier
Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced
as a generalization both of classical Toeplitz sequences and of variable coefficient …

Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case

G Barbarino, C Garoni… - Electronic Transactions on …, 2020‏ - ricerca.sns.it
In computational mathematics, when dealing with a large linear discrete problem (eg, a
linear system) arising from the numerical discretization of a partial differential equation …

Spectral analysis and multigrid methods for finite volume approximations of space-fractional diffusion equations

M Donatelli, M Mazza, S Serra-Capizzano - SIAM Journal on Scientific …, 2018‏ - SIAM
We consider a boundary value problem in weak form of a steady-state Riesz space-
fractional diffusion equation (FDE) of order 2-α with 0<α<1. By using a finite volume …