Search results for: Carla Manni

Items from 1 to 20 out of 57 results

article

NURBS in isogeometric discretization methods: A spectral analysis

Carlo Garoni, Carla Manni, Stefano Serra‐Capizzano, Hendrik Speleers

Numerical Linear Algebra with Applications > 27 > 6 > n/a - n/a

Nonuniform rational B‐splines (NURBS) are the most common representation form in isogeometric analysis. In this article, we study the spectral behavior of discretization matrices arising from isogeometric Galerkin and collocation methods based on d‐variate NURBS of degrees (p₁,…,p_d), and applied to general second‐order partial differential equations defined on a d‐dimensional domain. The spectrum...

article

Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis

Xiaodong Wei, Yongjie Jessica Zhang, Deepesh Toshniwal, Hendrik Speleers, more

Computer Methods in Applied Mechanics and Engineering > 2018 > 341 > C > 609-639

We present a novel blended B-spline method to construct bicubic/tricubic splines over unstructured quadrilateral and hexahedral meshes for isogeometric analysis. C 1 and (truncated) C 2 B-spline functions are used in regular elements, whereas C 0 and (truncated) C 1 B-spline functions are adopted in boundary elements and interior irregular elements around extraordinary...

article

Are the eigenvalues of the B‐spline isogeometric analysis approximation of −Δu = λu known in almost closed form?

Sven‐Erik Ekström, Isabella Furci, Carlo Garoni, Carla Manni, more

Numerical Linear Algebra with Applications > 25 > 5 > n/a - n/a

We consider the B‐spline isogeometric analysis approximation of the Laplacian eigenvalue problem −Δu = λu over the d‐dimensional hypercube (0,1)^d. By using tensor‐product arguments, we show that the eigenvalue–eigenvector structure of the resulting discretization matrix is completely determined by the eigenvalue–eigenvector structure of the matrix

L_{n}^{[p]}

arising from the isogeometric analysis approximation...

article

Numerical approximation of GB-splines by a convolutional approach

Fabio Roman, Carla Manni, Hendrik Speleers

Applied Numerical Mathematics > 2017 > 116 > C > 273-285

Generalized splines are smooth functions belonging piecewisely to spaces which are a natural generalization of algebraic polynomials. GB-splines are a B-spline-like basis for generalized splines, and they are usually defined by means of an integral recurrence relation which makes their evaluation quite cumbersome and computationally expensive. We present a simple strategy for approximating the values...

article

Lusin theorem, GLT sequences and matrix computations: An application to the spectral analysis of PDE discretization matrices

Carlo Garoni, Carla Manni, Stefano Serra-Capizzano, Debora Sesana, more

Journal of Mathematical Analysis and Applications > 2017 > 446 > 1 > 365-382

In this paper we consider a general d-dimensional second-order elliptic Partial Differential Equation (PDE) with variable coefficients, and we extend previous results on the spectral distribution of discretization matrices arising from B-spline Isogeometric Analysis (IgA). First, we provide the spectral symbol of the Galerkin B-spline IgA stiffness matrices, under the assumption that the PDE coefficients...

article

Splines over regular triangulations in numerical simulation

Francesca Pelosi, Carlotta Giannelli, Carla Manni, Maria Lucia Sampoli, more

Computer-Aided Design > 2017 > 82 > C > 100-111

We investigate the use of smooth spline spaces over regular triangulations as a tool in (isogeometric) Galerkin methods. In particular, we focus on box splines over three-directional meshes. Box splines are multivariate generalizations of univariate cardinal B-splines sharing the same properties. Tensor-product B-splines with uniform knots are a special case of box splines. The use of box splines...

chapter

Quasi-Interpolants with Tension Properties from and in CAGD

Carla Manni, Francesca Pelosi

Geometric Modelling > 143-160

We present _C ² quasi-interpolating schemes with tension properties. The B-splines like functions used in the quasi-interpolanting schemes are parametric cubic curves and their shape can be easily controlled via tension parameters which have an immediate geometric interpretation. Applications to the problem of approximation of curves with shape-constraints are discussed.

article

On the dimension of Tchebycheffian spline spaces over planar T-meshes

Cesare Bracco, Tom Lyche, Carla Manni, Fabio Roman, more

Computer Aided Geometric Design > 2016 > 45 > C > 151-173

In this paper we define Tchebycheffian spline spaces over planar T-meshes and we address the problem of determining their dimension. We extend to the Tchebycheffian spline context the homological approach previously used to characterize polynomial spline spaces over T-meshes, and we exploit this characterization in the study of the dimension. In particular, we give combinatorial lower and upper bounds...

article

Spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness

Fabio Roman, Carla Manni, Hendrik Speleers

Numerische Mathematik > 2017 > 135 > 1 > 169-216

We present a first step towards the spectral analysis of matrices arising from IgA Galerkin methods based on hyperbolic and trigonometric GB-splines. Second order differential problems with constant coefficients are considered and discretized by means of sequences of both nested and non-nested spline spaces. We prove that there always exists an asymptotic eigenvalue distribution which can be compactly...

article

Effortless quasi-interpolation in hierarchical spaces

Hendrik Speleers, Carla Manni

Numerische Mathematik > 2016 > 132 > 1 > 155-184

We present a general and simple procedure to construct quasi-interpolants in hierarchical spaces. Such spaces are composed of a hierarchy of nested spaces and provide a flexible framework for local refinement. The proposed hierarchical quasi-interpolants are described in terms of the so-called truncated hierarchical basis. Assuming a quasi-interpolant is selected for each space associated with a particular...

article

Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines

Cesare Bracco, Tom Lyche, Carla Manni, Fabio Roman, more

Applied Mathematics and Computation > 2016 > 272 > P1 > 187-198

Univariate generalized splines are smooth piecewise functions with sections in certain extended Tchebycheff spaces. They are a natural extension of univariate (algebraic) polynomial splines, and enjoy the same structural properties as their polynomial counterparts. In this paper, we consider generalized spline spaces over planar T-meshes, and we deepen their parallelism with polynomial spline spaces...

article

Optimizing domain parameterization in isogeometric analysis based on Powell–Sabin splines

Hendrik Speleers, Carla Manni

Journal of Computational and Applied Mathematics > 2015 > 289 > Complete > 68-86

We address the problem of constructing a high-quality parameterization of a given planar physical domain, defined by means of a finite set of boundary curves. We look for a geometry map represented in terms of Powell–Sabin B-splines. Powell–Sabin splines are C1 quadratic splines defined on a triangulation, and thus the parameter domain can be any polygon.The geometry map is generated by the following...

article

Isogeometric collocation methods with generalized B-splines

Carla Manni, Alessandro Reali, Hendrik Speleers

Computers and Mathematics with Applications > 2015 > 70 > 7 > 1659-1675

We introduce isogeometric collocation methods based on generalized B-splines and we analyze their performance through numerical examples for univariate and multivariate scalar- and vector-valued problems. In particular, advection–diffusion and linear elasticity model problems are addressed. The resulting method combines the favorable properties of isogeometric collocation and the geometrical and analytical...

article

Computation of quadrature rules for integration with respect to refinable functions on assigned nodes

Francesco Calabrò, Carla Manni, Francesca Pitolli

Applied Numerical Mathematics > 2015 > 90 > Complete > 168-189

Integrals involving refinable functions are of interest in several applications ranging from discretization of PDEs to wavelet analysis. We present a procedure to construct quadrature rules with assigned nodes for these integrals. The process requires in input the refinement mask coefficients and the sequence of nodes only. The corresponding weights are computed by an iterative procedure that does...

article

BS2 methods for semi-linear second order boundary value problems

Carla Manni, Francesca Mazzia, Alessandra Sestini, Hendrik Speleers

Applied Mathematics and Computation > 2015 > 255 > Complete > 147-156

A new class of Linear Multistep Methods based on B-splines for the numerical solution of semi-linear second order Boundary Value Problems is introduced. The presented schemes are called BS2 methods, because they are connected to the BS (B-spline) methods previously introduced in the literature to deal with first order problems. We show that, when using an even number of steps, schemes with good general...

article

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

Marco Donatelli, Carlo Garoni, Carla Manni, Stefano Serra-Capizzano, more

Computer Methods in Applied Mechanics and Engineering > 2015 > 284 > Complete > 1120-1146

We consider fast solvers for the large linear systems coming from the Isogeometric Analysis (IgA) collocation approximation based on B-splines of full elliptic d-dimensional Partial Differential Equations (PDEs). We are interested in designing iterative algorithms which are optimal and robust. The former property implies that the computational cost is linear with respect to the number of degrees of...

article

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

Marco Donatelli, Carlo Garoni, Carla Manni, Stefano Serra-Capizzano, more

Computer Methods in Applied Mechanics and Engineering > 2015 > 284 > Complete > 230-264

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 isogeometric analysis. Our ultimate goal is to design iterative algorithms with the following two properties. First, their computational cost is optimal, that is linear with respect to the number of degrees of freedom, i.e...

article

Two-grid optimality for Galerkin linear systems based on B-splines

Marco Donatelli, Carlo Garoni, Carla Manni, Stefano Serra-Capizzano, more

Computing and Visualization in Science > 2015 > 17 > 3 > 119-133

A multigrid method for linear systems stemming from the Galerkin B-spline discretization of classical second-order elliptic problems is considered. The spectral features of the involved stiffness matrices, as the fineness parameter h tends to zero, have been deeply studied in previous works, with particular attention to the dependencies of the spectrum on the degree p of the B-splines used in the...

article

Shape preserving $$HC^2$$ H C 2 interpolatory subdivision

Davide Lettieri, Carla Manni, Francesca Pelosi, Hendrik Speleers

BIT Numerical Mathematics > 2015 > 55 > 3 > 751-779

A subdivision procedure is developed to solve a $$C^2$$ C 2 Hermite interpolation problem with the further request of preserving the shape of the initial data. We consider a specific non-stationary and non-uniform variant of the Merrien $$HC^2$$ H C 2 subdivision family, and we provide a data dependent strategy to select the related parameters which ensures convergence and...

article

A fully data-dependent criterion for free angles selection in spatial PH cubic biarc Hermite interpolation

Alessandra Sestini, Karla Ferjančič, Carla Manni, Maria Lucia Sampoli

Computer Aided Geometric Design > 2014 > 31 > 7-8 > 398-411

Cubic biarcs are the natural counterpart, in the context of the PH spatial Hermite interpolation, of piecewise quadratics for Hermite interpolation of standard parametric curves. Recently, it has been shown that, spatial Hermite interpolation can be always treated with PH cubic biarcs, providing an interesting alternative to the use of higher degrees, see Bastl et al. (2014). Beside the parameter...

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INFONA - science communication portal

Search results for: Carla Manni

NURBS in isogeometric discretization methods: A spectral analysis

Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis

Are the eigenvalues of the B‐spline isogeometric analysis approximation of −Δu = λu known in almost closed form?

Numerical approximation of GB-splines by a convolutional approach

Lusin theorem, GLT sequences and matrix computations: An application to the spectral analysis of PDE discretization matrices

Splines over regular triangulations in numerical simulation

Quasi-Interpolants with Tension Properties from and in CAGD

On the dimension of Tchebycheffian spline spaces over planar T-meshes

Spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness

Effortless quasi-interpolation in hierarchical spaces

Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines

Optimizing domain parameterization in isogeometric analysis based on Powell–Sabin splines

Isogeometric collocation methods with generalized B-splines

Computation of quadrature rules for integration with respect to refinable functions on assigned nodes

BS2 methods for semi-linear second order boundary value problems

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

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

Two-grid optimality for Galerkin linear systems based on B-splines

Shape preserving $$HC^2$$ H C 2 interpolatory subdivision

A fully data-dependent criterion for free angles selection in spatial PH cubic biarc Hermite interpolation

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