scholarly journals A quasi-optimal coarse problem and an augmented Krylov solver for the variational theory of complex rays

2016 ◽  
Vol 107 (11) ◽  
pp. 903-922
Author(s):  
Louis Kovalevsky ◽  
Pierre Gosselet
Keyword(s):  
Variational Theory ◽  
Complex Rays

scholarly journals Extended variational theory of complex rays in heterogeneous Helmholtz problem

2017 ◽  
Vol 59 (6) ◽  
pp. 909-918 ◽  
Author(s):  
Hao Li ◽  
Pierre Ladeveze ◽  
Hervé Riou
Keyword(s):  
Variational Theory ◽  
Helmholtz Problem ◽  
Complex Rays

scholarly journals AN ADAPTIVE NUMERICAL STRATEGY FOR THE MEDIUM-FREQUENCY ANALYSIS OF HELMHOLTZ'S PROBLEM

2012 ◽  
Vol 20 (01) ◽  
pp. 1250001 ◽  
Author(s):  
HERVÉ RIOU ◽  
PIERRE LADEVÈZE ◽  
BENJAMIN SOURCIS ◽  
BÉATRICE FAVERJON ◽  
LOUIS KOVALEVSKY
Keyword(s):  
Degrees Of Freedom ◽  
Acoustic Vibration ◽  
Accurate Solution ◽  
Variational Theory ◽  
Wave Shape ◽  
Medium Frequency ◽  
Governing Differential Equation ◽  
Vibration Problems ◽  
Complex Rays ◽  
Numerical Strategy

The variational theory of complex rays (VTCR) is a wave-based predictive numerical tool for medium-frequency problems. In order to describe the dynamic field variables within the substructures, this approach uses wave shape functions which are exact solutions of the governing differential equation. The discretized parameters are the number of substructures (h) and the number of wavebands (p) which describe the amplitude portraits. Its capability to produce an accurate solution with only a few degrees of freedom and the absence of pollution error make the VTCR a suitable numerical strategy for the analysis of vibration problems in the medium-frequency range. This approach has been developed for structural and acoustic vibration problems. In this paper, an error indicator which characterizes the accuracy of the solution is introduced and is used to define an adaptive version of the VTCR. Numerical illustrations are given.

Analysis of Medium-Frequency Vibrations in a Frequency Range

2003 ◽  
Vol 11 (02) ◽  
pp. 255-283 ◽  
Author(s):  
P. Ladevèze ◽  
P. Rouch ◽  
H. Riou ◽  
X. Bohineust
Keyword(s):  
Frequency Range ◽  
Variational Theory ◽  
Elastic Structures ◽  
Medium Frequency ◽  
New Approach ◽  
Numerical Examples ◽  
Vibrational Response ◽  
Complex Rays ◽  
Medium Frequency Range

A new approach called the ''Variational Theory of Complex Rays'' (VTCR) is being developed in order to calculate the vibrations of slightly damped elastic structures in the medium-frequency range. Here, the emphasis is put on the extension of this theory to analysis across a range of frequencies. Numerical examples show the capability of the VTCR to predict the vibrational response of a structure in a frequency range.

scholarly journals THE VARIATIONAL THEORY OF COMPLEX RAYS FOR THREE-DIMENSIONAL HELMHOLTZ PROBLEMS

2012 ◽  
Vol 20 (04) ◽  
pp. 1250021 ◽  
Author(s):  
LOUIS KOVALEVSKY ◽  
PIERRE LADEVÈZE ◽  
HERVÉ RIOU ◽  
MARC BONNET
Keyword(s):  
Spherical Harmonics ◽  
A Priori ◽  
Three Dimensional ◽  
Variational Theory ◽  
Actual Case ◽  
Analytical Properties ◽  
And Performance ◽  
Definition Of ◽  
Complex Rays

This paper proposes an extension of the variational theory of complex rays (VTCR) to three-dimensional linear acoustics, The VTCR is a Trefftz-type approach designed for mid-frequency range problems and has been previously investigated for structural dynamics and 2D acoustics. The proposed 3D formulation is based on a discretization of the amplitude portrait using spherical harmonics expansions. This choice of discretization allows to substantially reduce the numerical integration work by taking advantage of well-known analytical properties of the spherical harmonics. It also permits (like with the previous 2D Fourier version) an effective a priori selection method for the discretization parameter in each sub-region, and allows to estimate the directivity of the pressure field by means of a natural definition of rescaled amplitude portraits. The accuracy and performance of the proposed formulation are demonstrated on a set of numerical examples that include results on an actual case study from the automotive industry.

scholarly journals The variational theory of complex rays for the calculation of medium‐frequency vibrations

2001 ◽  
Vol 18 (1/2) ◽  
pp. 193-214 ◽  
Author(s):  
P. Ladevèze ◽  
L. Arnaud ◽  
P. Rouch ◽  
C. Blanzé
Keyword(s):  
Variational Theory ◽  
Medium Frequency ◽  
Complex Rays
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