Data di Pubblicazione:
2021
Citazione:
Isogeometric collocation approximations of acoustic wave problems / E. Zampieri. ((Intervento presentato al convegno Virtual International Conference on Isogeometric Analysis-VIGA tenutosi a Lyon-online nel 2021.
Abstract:
In the last decades there has been an increasing attention to high order simulation of acoustic wave
propagation by considering spectral, spectral elements and isogeometric (IGA) discretizations. Our
previous work [1] investigated the approximation of 2D acoustic wave problems with proper
absorbing boundary conditions by Galerkin IGA methods in space and Newmark’s explicit schemes
in time.
We extend now our study to IGA collocation explicit and implicit methods [2] in order to optimize
the storage of stiffness and mass matrices and the computational costs. A detailed numerical study on
both Cartesian and NURBS domains illustrate the stability and convergence properties of the IGA
Newmark Collocation method with respect to all the IGA parameters, namely the local polynomial
degree p, regularity k, mesh size h, and to the Newmark parameters t, β and γ.
The results show that the stability thresholds of the method depend linearly on h and inversely on p,
confirming that the proposed IGA Collocation method retains the good convergence and stability
properties of standard IGA Galerkin and spectral element discretizations of acoustic problems.
Moreover, a detailed comparison of convergence errors, computational times, and matrix sparsity
patterns show that IGA Collocation often outperforms IGA Galerkin, in particular in the case of
maximal regularity k = p - 1 and for increasing NURBS degree p.
REFERENCES
[1] E. Zampieri and L. F. Pavarino. Explicit second order isogeometric discretizations for acoustic
wave problems. Computer Methods in Applied Mechanics and Engineering, 348:776– 795,
2019.
[2] E. Zampieri and L. F. Pavarino. Isogeometric collocation discretizations for acoustic wave
problems. Computer Methods in Applied Mechanics and Engineering, to appear, 2021.
Tipologia IRIS:
14 - Intervento a convegno non pubblicato
Elenco autori:
E. Zampieri
Link alla scheda completa: