Mattia Tani
Publications
2022, Journal article
Weighted quadrature for hierarchical B-splines
C. Giannelli, T. Kanduc, M. Martinelli, G. Sangalli and M. Tani
We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded hierarchical meshes....
CNR@People | DOI: 10.1016/j.cma.2022.115465
2020, Journal article
Compressive isogeometric analysis
S. Brugiapaglia, L. Tamellini, and M. Tani
This work is motivated by the difficulty in assembling the Galerkin matrix when solving Partial Differential Equations (PDEs) with Isogeometric Analysis (IGA) using B-splines of moderate-to-high polyn...
CNR@People | DOI: 10.1016/j.camwa.2020.11.004
2020, Journal article
Space-time least-squares isogeometric method and efficient solver for parabolic problems
M. Montardini, M. Negri, G. Sangalli, and M. Tani
In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the lin...
CNR@People | DOI: 10.1090/mcom/3471
2019, Journal article
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity
R.R. Hiemstra, G. Sangalli, M. Tani, F. Calabro, and T.J.R. Hughes
Recently, a new formation and assembly strategy was proposed in [1], which resulted in significant speedups in the formation and assembly time of the Galerkin mass matrix in isogeometric analysis. The...
CNR@People | DOI: 10.1016/j.cma.2019.06.020
2018, Journal article
Isogeometric analysis: Mathematical and implementational aspects, with applications
T.J.R. Hughes, G. Sangalli, and M. Tani
Isogeometric analysis (IGA) is a recent and successful extension of classical finite element analysis. IGA adopts smooth splines, NURBS and generalizations to approximate problem unknowns, in order to...
CNR@People | DOI: 10.1007/978-3-319-94911-6_4
2018, Journal article
Matrix-free weighted quadrature for a computationally efficient isogeometric k-method
G. Sangalli and M. Tani
The k-method is the isogeometric method based on splines (or NURBS, etc.) with maximum regularity. When implemented following the paradigms of classical finite element methods, the computational resou...
CNR@People | DOI: 10.1016/j.cma.2018.04.029
2018, Journal article
Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method
M. Montardini, G. Sangalli, and M. Tani
In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be don...
CNR@People | DOI: 10.1016/j.cma.2018.04.017
2017, Journal article
Fast formation of isogeometric Galerkin matrices by weighted quadrature
F. Calabrò, G. Sangalli, and M. Tani
In this paper we propose an algorithm for the formation of matrices of isogeometric Galerkin methods. The algorithm is based on three ideas. The first is that we perform the external loop over the row...
CNR@People | DOI: 10.1016/j.cma.2016.09.013
2016, Journal article
Isogeometric preconditioners based on fast solvers for the Sylvester equation
G. Sangalli and M. Tani
We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, ...
CNR@People | DOI: 10.1137/16M1062788
Weighted quadrature for hierarchical B-splines
C. Giannelli, T. Kanduc, M. Martinelli, G. Sangalli and M. Tani
We present weighted quadrature for hierarchical B-splines to address the fast formation of system matrices arising from adaptive isogeometric Galerkin methods with suitably graded hierarchical meshes....
CNR@People | DOI: 10.1016/j.cma.2022.115465
2020, Journal article
Compressive isogeometric analysis
S. Brugiapaglia, L. Tamellini, and M. Tani
This work is motivated by the difficulty in assembling the Galerkin matrix when solving Partial Differential Equations (PDEs) with Isogeometric Analysis (IGA) using B-splines of moderate-to-high polyn...
CNR@People | DOI: 10.1016/j.camwa.2020.11.004
2020, Journal article
Space-time least-squares isogeometric method and efficient solver for parabolic problems
M. Montardini, M. Negri, G. Sangalli, and M. Tani
In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the lin...
CNR@People | DOI: 10.1090/mcom/3471
2019, Journal article
Fast formation and assembly of finite element matrices with application to isogeometric linear elasticity
R.R. Hiemstra, G. Sangalli, M. Tani, F. Calabro, and T.J.R. Hughes
Recently, a new formation and assembly strategy was proposed in [1], which resulted in significant speedups in the formation and assembly time of the Galerkin mass matrix in isogeometric analysis. The...
CNR@People | DOI: 10.1016/j.cma.2019.06.020
2018, Journal article
Isogeometric analysis: Mathematical and implementational aspects, with applications
T.J.R. Hughes, G. Sangalli, and M. Tani
Isogeometric analysis (IGA) is a recent and successful extension of classical finite element analysis. IGA adopts smooth splines, NURBS and generalizations to approximate problem unknowns, in order to...
CNR@People | DOI: 10.1007/978-3-319-94911-6_4
2018, Journal article
Matrix-free weighted quadrature for a computationally efficient isogeometric k-method
G. Sangalli and M. Tani
The k-method is the isogeometric method based on splines (or NURBS, etc.) with maximum regularity. When implemented following the paradigms of classical finite element methods, the computational resou...
CNR@People | DOI: 10.1016/j.cma.2018.04.029
2018, Journal article
Robust isogeometric preconditioners for the Stokes system based on the Fast Diagonalization method
M. Montardini, G. Sangalli, and M. Tani
In this paper we propose a new class of preconditioners for the isogeometric discretization of the Stokes system. Their application involves the solution of a Sylvester-like equation, which can be don...
CNR@People | DOI: 10.1016/j.cma.2018.04.017
2017, Journal article
Fast formation of isogeometric Galerkin matrices by weighted quadrature
F. Calabrò, G. Sangalli, and M. Tani
In this paper we propose an algorithm for the formation of matrices of isogeometric Galerkin methods. The algorithm is based on three ideas. The first is that we perform the external loop over the row...
CNR@People | DOI: 10.1016/j.cma.2016.09.013
2016, Journal article
Isogeometric preconditioners based on fast solvers for the Sylvester equation
G. Sangalli and M. Tani
We consider large linear systems arising from the isogeometric discretization of the Poisson problem on a single-patch domain. The numerical solution of such systems is considered a challenging task, ...
CNR@People | DOI: 10.1137/16M1062788
2019, Conference proceedings
Quadrature rules in the isogeometric Galerkin method: State of the art and an introduction to weighted quadrature
F. Calabro, G. Loli, G. Sangalli, and M. Tani
In this paper we introduce the quadrature needed in the isogeometric Galerkin method. Quadrature rules affect the cost of the assembly of the discrete counterpart of the IGA method, so that the search...
CNR@People | DOI: 10.1007/978-3-030-27331-6_3
Quadrature rules in the isogeometric Galerkin method: State of the art and an introduction to weighted quadrature
F. Calabro, G. Loli, G. Sangalli, and M. Tani
In this paper we introduce the quadrature needed in the isogeometric Galerkin method. Quadrature rules affect the cost of the assembly of the discrete counterpart of the IGA method, so that the search...
CNR@People | DOI: 10.1007/978-3-030-27331-6_3
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