A review of finite-element methods for time-harmonic acoustics, Journal of the Acoustical Society of America, vol.119, issue.3, 2006. ,
Numerical methods for noise propagation in moving flows, with application to turbofan engines, Acoustical Science and Technology, vol.30, issue.4, pp.227-239, 2009. ,
Efficient finite element methods for aircraft engine noise prediction, 2014. ,
Assessment of finite and spectral element shape functions for efficient iterative simulations of interior acoustics, Computer Methods in Applied Mechanics and Engineering, vol.195, pp.6463-6478, 2006. ,
, Chebyshev and Fourier Spectral Methods, 2000.
Higher-Order Finite Element Methods, 2004. ,
, Spectral/hp element methods for computational fluid dynamics, 2013.
DOI : 10.1093/acprof:oso/9780198528692.001.0001
Discrete dispersion relation for hp-version finite element approximation at high wave number, SIAM Journal on Numerical Analysis, vol.42, issue.2, pp.553-575, 2004. ,
DOI : 10.1137/s0036142903423460
From h to p efficiently: Implementing finite and spectral/h-p element methods to achieve optimal performance for low-and high-order discretisations, Journal of Computational Physics, vol.229, issue.13, pp.5161-5181, 2010. ,
DOI : 10.1016/j.jcp.2010.03.031
URL : http://spiral.imperial.ac.uk/bitstream/10044/1/14735/2/Journal%20of%20Computational%20Physics_229_13_2010.pdf
Efficient implementation of high-order finite elements for Helmholtz problems, International Journal for Numerical Methods in EngineeringIn ,
The h, p and h-p version of the finite element method-Basis theory and applications, Advances in Engineering Software, vol.15, issue.3-4, pp.159-174, 1992. ,
A survey of Trefftz methods for the Helmholtz equation ,
The ultra weak variational formulation using Bessel basis functions, Communications in Computational Physics, vol.11, issue.2, pp.400-414, 2012. ,
DOI : 10.4208/cicp.121209.040111s
Application of an ultra weak variational formulation of elliptic PDEs to the two-dimensional Helmholtz problem, SIAM Journal on Numerical Analysis, vol.35, issue.1, pp.255-299, 1998. ,
Computational aspects of the ultra-weak variational formulation, Journal of Computational Physics, vol.182, issue.1, pp.27-46, 2002. ,
DOI : 10.1006/jcph.2002.7148
Using plane waves as base functions for solving time harmonic equations with the ultra weak variational formulation, Journal of Computational Acoustics, vol.11, issue.2, pp.227-238, 2003. ,
DOI : 10.1142/s0218396x03001912
A least-squares method for the Helmholtz equation, Computer Methods in Applied Mechanics and Engineering, vol.175, issue.1-2, pp.121-136, 1999. ,
Discontinuous Galerkin methods with plane waves for time-harmonic problems, Journal of Computational Physics, vol.225, issue.2, pp.1961-1984, 2007. ,
DOI : 10.1016/j.jcp.2007.02.030
A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems, International Journal for Numerical Methods in Engineering, vol.85, issue.3, pp.380-402, 2011. ,
Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM Journal on Numerical Analysis, vol.49, issue.1, pp.264-284, 2011. ,
Dispersion analysis of plane wave discontinuous Galerkin methods, International Journal for Numerical Methods in Engineering, vol.98, issue.5, pp.313-323, 2014. ,
DOI : 10.1002/nme.4626
Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes, Applied Numerical Mathematics, vol.79, pp.79-91, 2014. ,
Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM, ESAIM: Mathematical Modelling and Numerical Analysis, vol.48, issue.03, 2014. ,
, Plane wave discontinuous Galerkin methods: exponential convergence of the hp-version, p.1, 2015.
Residual-based adaptivity and pwdg methods for the helmholtz equation, SIAM Journal on Scientific Computing, vol.37, issue.3, 2015. ,
A comparison of two Trefftz-type methods: the ultraweak variational formulation and the least-squares method, for solving shortwave 2-D Helmholtz problems, International journal for numerical methods in engineering, vol.71, issue.4, pp.406-432, 2007. ,
The discontinuous enrichment method, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.48, pp.6455-6479, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-02012889
A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime, Computer Methods in Applied Mechanics and Engineering, vol.192, pp.646-647, 2003. ,
A discontinuous enrichment method for three-dimensional multiscale harmonic wave propagation problems in multi-fluid and fluid-solid media, International Journal for Numerical Methods in Engineering, vol.76, issue.3, pp.400-425, 2008. ,
Higher-order extensions of a discontinuous Galerkin method for mid-frequency Helmholtz problems, International Journal for Numerical Method in Engineering, vol.61, issue.11, pp.1938-1956, 2004. ,
Three-dimensional discontinuous Galerkin elements with plane waves and lagrange multipliers for the solution of midfrequency helmholtz problems, International Journal for Numerical Methods in Engineering, vol.66, issue.5, pp.796-815, 2006. ,
A wave based prediction technique for coupled vibro-acoustic analysis, 1998. ,
The variational theory of complex rays for the calculation of medium-frequency vibrations, Engineering Computations, vol.18, issue.1, pp.193-214, 2001. ,
A weighted variational formulation based on plane wave basis for discretization of Helmholtz equations, International Journal of Numerical Analysis and Modeling, vol.11, issue.3, pp.587-607, 2014. ,
The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.139, issue.1-4, pp.289-314, 1996. ,
Comparison of two wave element methods for the Helmholtz problem, Communications in Numerical Methods in Engineering, vol.25, issue.1, pp.35-52, 2009. ,
Overview of the discontinuous enrichment method, the ultra-weak variational formulation, and the partition of unity method for acoustic scattering in the medium frequency regime and performance comparisons, International Journal for Numerical Methods in Engineering, vol.89, pp.403-420, 2012. ,
Symmetric hierarchical polynomials for the h-p-version of finite elements ,
Finite element solution of the Helmholtz equation with high wave number part ii: the h-p version of the fem, SIAM Journal on Numerical Analysis, vol.34, issue.1, pp.315-358, 1997. ,
The p and hp versions of the finite element method, basic principles and properties, SIAM review, vol.36, issue.4, pp.578-632, 1994. ,
Analysis of high-order finite elements for convected wave propagation, International Journal for Numerical Methods in Engineering, vol.96, issue.11, pp.665-688, 2013. ,
Finite volume methods for hyperbolic problems, 2002. ,
Linear and nonlinear waves, 1999. ,
A discontinuous Galerkin method with plane waves for sound absorbing materials, International Journal for Numerical Methods in Engineeringdoi ,
A discontinuous enrichment method for capturing evanescent waves in multiscale fluid and fluid/solid problems, Computer Methods in Applied Mechanics and Engineering, vol.197, pp.1680-1698, 2008. ,
Improvements for the ultra weak variational formulation, International Journal for Numerical Methods in Engineering, vol.94, issue.6, pp.598-624, 2013. ,
Green function discretization for numerical solution of the Helmholtz equation, Journal of Sound And Vibration, vol.187, issue.4, pp.553-568, 1995. ,
A comparison of two Trefftz-type methods: the ultraweak variational formulation and the least-squares method, for solving shortwave 2-D Helmholtz problems, International Journal for Numerical Methods in Engineering, vol.71, issue.4, pp.406-432, 2007. ,
Physics-based computational methods for aero-acoustics, IUTAM Symposium on computational aero-acoustics for aircraft noise prediction, vol.6, pp.183-192, 2010. ,
, Plane wave discontinuous Galerkin methods: analysis of the h-version, vol.43, pp.297-331, 2009.
Error estimates for the ultra weak variational formulation of the helmholtz equation, ESAIM: Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique, vol.42, issue.6, pp.925-940, 2008. ,
Acoustics: An introduction to its physical principles and applications, 1989. ,
Finite element method for solving problems with singular solutions, Journal of Computational and Applied Mathematics, vol.74, issue.1-2, pp.51-70, 1996. ,
Preconditioning Helmholtz linear systems, Applied Numerical Mathematics, vol.60, issue.4, pp.420-431, 2010. ,
An eigen-based high-order expansion basis for structured spectral elements, Journal of Computational Physics, vol.230, issue.23, pp.8573-8602, 2011. ,
Construction of minimum energy high-order Helmholtz bases for structured elements, Journal of Computational Physics, vol.306, pp.269-290, 2016. ,
Modelling of short wave diffraction problems using approximating systems of plane waves, International Journal for Numerical Methods in Engineering, vol.54, issue.10, pp.1501-1533, 2002. ,
Sparse direct factorizations through unassembled hyper-matrices, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.912, pp.430-438, 2010. ,
Impact of element-level static condensation on iterative solver performance, Computers & Mathematics with Applications, vol.70, issue.10, pp.2331-2341, 2015. ,
A generalized plane-wave numerical method for smooth nonconstant coefficients, IMA Journal of Numerical Analysis, vol.34, issue.3, pp.1072-1103, 2014. ,
Numerical simulation of wave propagation in inhomogeneous media using Generalized Plane Waves ,
A new method of fundamental solutions applied to nonhomogeneous elliptic problems, Advances in Computational Mathematics, vol.23, issue.1-2, pp.125-142, 2005. ,