Dispersion Analysis Of The Meshless Local
Boundary Integral Equation (LBIE) Method For
The Helmholtz Equation
Author(s)
H. Dogan & V. Popov
Abstract
Numerical solutions of the Helmholtz equation suffer from numerical pollution
especially for the case of high wavenumbers. The major component of the
numerical pollution is, as has been reported in the literature, the dispersion error
which is defined as the phase difference between the numerical and the exact
wave. The dispersion error for the meshless methods can be a priori determined
at an interior source node assuming that the potential field obeys a harmonic
evolution of the numerical wavenumber.
In this work the meshless local boundary integral equation (LBIE) in 2D is
investigated with respect to the dispersion effect. Radial basis functions, with
second order polynomials and frequency dependent polynomial basis vectors, are
used for the interpolation of the potential field. The results have been found to be
of comparable accuracy with other meshless approaches.
Keywords: meshless methods, dispersion, local boundary integral equation,
radial basis functions, Helmholtz equation.
1 Introduction
Accurate solution of the Helmholtz equation is of importance for many
applications in acoustics such as ultrasonics, microfluidics, aeroacoustics, etc.
The simulations involving the high frequency oscillations and large scale
industrial setups get cumbersome to solve due to immense computational storage
and time requirements.
It is well known that numerical solutions of the Helmholtz equation encounter
the pollution affect especially for high wavenumbers. The major component of
the numerical pollution is the dispersion error which is defined as the relative
Keywords
meshless methods, dispersion, local boundary integral equation,
radial basis functions, Helmholtz equation.
Related Book
Other papers in this volume
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