The dual reciprocity boundary element method for the eigenvalue analysis of Helmholtz problems

Kontoni, D.P.N.; Partridge, P. W.; Brebbia, C.A.

doi:10.1016/0961-3552(91)90040-b

Cited by 5 publications

(4 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The solution of the Helmholtz equation provides the natural or fundamental frequencies and vibration modes for a system [1,[16][17][18]. The Equation in its usual form is given by following equation:…”

Section: The Helmholtz Equationmentioning

confidence: 99%

“…In early numerical methods there were only two alternative solution procedures available to solve a problem [1]. Either internal cells had to be defined or *Corresponding Author Email: khodakarami@semnan.ac.ir (M. I.…”

Section: Introductionmentioning

confidence: 99%

“…Either internal cells had to be defined or *Corresponding Author Email: khodakarami@semnan.ac.ir (M. I. Khodakarami) fundamental solution had to be found which took into account all the terms in the governing equation [1][2][3]. After improvement of the numerical methods in recent decades some new methods were added to this type of analysis, any of these methods have advantageous and disadvantages [4,5].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of Decoupled Scaled Boundary Finite Element Method to Solve Eigenvalue Helmholtz Problems (Research Note)

Khodakarami

Hedayati

2020

IJE

View full text Add to dashboard Cite

A novel element with arbitrary domain shape by using decoupled scaled boundary finite element (DSBFEM) is proposed for eigenvalue analysis of 2D vibrating rods with different boundary conditions. Within the proposed element scheme, the mode shapes of vibrating rods with variable boundary conditions are modelled and results are plotted. All possible conditions for the rods ends are incorporated in analysis. The considered element stiffness and mass matrix are developed and extracrted. This element is able to model any curved or sharp edges without any aproximation and also the element is able to model any arbitrary domain shape as a single element without any meshing. The coefficient matrices for the element such as mass and stiffness matrices are diagonal symmetric and all equations are decoupled by using Gauss-Lobatto-Legendre (G.L.L) quadrature. The element is used in order to calculate modal parameters by Finite element method for some benchmark examples and comparing the answers with Helmholtz equation solution. The most important achievment of this element is solving matrix equations instead of differential equations where cause faster calculations speed. The boundaries for this element are solved with matrix calculation and the whole interior domain with solving governing equations numerically wich leads us to an exact answer in whole domain. The introduced element is applied to calculate some benchmark example which have exact solution. The results shows accuracy and high speed of calculation for this method in comparison with other common methods.

show abstract

Section: The Helmholtz Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of Decoupled Scaled Boundary Finite Element Method to Solve Eigenvalue Helmholtz Problems (Research Note)

Khodakarami

Hedayati

2020

IJE

View full text Add to dashboard Cite

show abstract

“…The volume integrals caused by the non‐homogeneous term can be transformed into boundary integrals with the help of various methods, such as the dual reciprocity method , the particular integral method , the multiple reciprocity method , and the radial integration method . Further developments and applications of these volume‐ or domain‐integral transform methods can be found, e.g., in References for acoustic eigenvalue problems and in Reference for fluid–structure interaction eigenvalue problems.…”

Section: Introductionmentioning

confidence: 99%

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

Zheng

Zhang

et al. 2016

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary For thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid–structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE–BE) method is developed for the numerical eigenanalysis of the fluid–structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton–Miller formulation is applied to tackle the fictitious eigenfrequency problem of the BEM, and the optimal choice of its coupling parameter is investigated for the coupled FE–BE method. Numerical examples are given and discussed to demonstrate the effectiveness and accuracy of the developed FE–BE method. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

A novel two-way coupling model for Euler-Lagrange simulations of multiphase flow

Verhnjak

Hriberšek

Steinmann

et al. 2020

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

The dual reciprocity boundary element method for the eigenvalue analysis of Helmholtz problems

Cited by 5 publications

References 1 publication

Application of Decoupled Scaled Boundary Finite Element Method to Solve Eigenvalue Helmholtz Problems (Research Note)

Application of Decoupled Scaled Boundary Finite Element Method to Solve Eigenvalue Helmholtz Problems (Research Note)

Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain

A novel two-way coupling model for Euler-Lagrange simulations of multiphase flow

Contact Info

Product

Resources

About