scholarly journals Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis

2016 ◽  
Vol 305 ◽  
pp. 217-240 ◽  
Author(s):  
Michael Bartoň ◽  
Victor Manuel Calo
Keyword(s):  
Tensor Product ◽  
Isogeometric Analysis ◽  
Quadrature Rules ◽  
Optimal Quadrature ◽  
Odd Degree

scholarly journals Optimal and reduced quadrature rules for tensor product and hierarchically refined splines in isogeometric analysis

2017 ◽  
Vol 316 ◽  
pp. 966-1004 ◽  
Author(s):  
René R. Hiemstra ◽  
Francesco Calabrò ◽  
Dominik Schillinger ◽  
Thomas J.R. Hughes
Keyword(s):  
Tensor Product ◽  
Isogeometric Analysis ◽  
Quadrature Rules

Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization

2015 ◽  
Vol 285 ◽  
pp. 817-828 ◽  
Author(s):  
P. Antolin ◽  
A. Buffa ◽  
F. Calabrò ◽  
M. Martinelli ◽  
G. Sangalli
Keyword(s):  
Tensor Product ◽  
Isogeometric Analysis ◽  
Matrix Computation

scholarly journals Near optimal angular quadratures for polarised radiative transfer

2020 ◽  
Vol 636 ◽  
pp. A24 ◽  
Author(s):  
Jiří Štěpán ◽  
Jaume Jaume Bestard ◽  
Javier Trujillo Bueno
Keyword(s):  
Numerical Calculation ◽  
Radiative Transfer ◽  
Tensor Product ◽  
Radiation Field ◽  
Computing Time ◽  
Three Dimensional ◽  
Quadrature Rules ◽  
Thermodynamical Equilibrium ◽  
Angular Integration ◽  
Local Thermodynamical Equilibrium

In three-dimensional (3D) radiative transfer (RT) problems, the tensor product quadratures are generally not optimal in terms of the number of discrete ray directions needed for a given accuracy of the angular integration of the radiation field. In this paper, we derive a new set of angular quadrature rules that are more suitable for solving 3D RT problems with the short- and long-characteristics formal solvers. These quadratures are more suitable than the currently used ones for the numerical calculation of the radiation field tensors that are relevant in the problem of the generation and transfer of polarised radiation without assuming local thermodynamical equilibrium (non-LTE). We show that our new quadratures can save up to about 30% of computing time with respect to the Gaussian-trapezoidal product quadratures with the same accuracy.

scholarly journals Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis

2018 ◽  
Vol 328 ◽  
pp. 554-564 ◽  
Author(s):  
Quanling Deng ◽  
Michael Bartoň ◽  
Vladimir Puzyrev ◽  
Victor Calo
Keyword(s):  
Isogeometric Analysis ◽  
Quadrature Rules
Sign in / Sign up

Export Citation Format

Share Document