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Mathematical analysis of variational isogeometric methods
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 …
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 …
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
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 …
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
Fractional partial order diffusion equations are a generalization of classical partial
differential equations, used to model anomalous diffusion phenomena. When using the …
differential equations, used to model anomalous diffusion phenomena. When using the …
Foundations of spline theory: B-splines, spline approximation, and hierarchical refinement
This chapter presents an overview of polynomial spline theory, with special emphasis on the
B-spline representation, spline approximation properties, and hierarchical spline refinement …
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
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 …
spectral analysis. We consider constant-and variable-coefficient, second-order eigenvalue …
Robust and optimal multi-iterative techniques for IgA Galerkin linear systems
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 …
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
Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced
as a generalization both of classical Toeplitz sequences and of variable coefficient …
as a generalization both of classical Toeplitz sequences and of variable coefficient …
Block generalized locally Toeplitz sequences: theory and applications in the multidimensional case
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 …
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
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 …
fractional diffusion equation (FDE) of order 2-α with 0<α<1. By using a finite volume …