Combined field integral equation formulation for inhomogeneous two- and three-dimensional bodies: the junction problem

1991 ◽  
Vol 39 (5) ◽  
pp. 667-672 ◽  
Author(s):  
J.M. Putnam ◽  
L.N. Medgyesi-Mitschang
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Field Integral

Combined field integral equation formulation for broad wall radiating slots of arbitrary shape

AFRICON 2009 ◽  
2009 ◽  
Author(s):  
Dominic B. Onyango Konditi ◽  
Vasant V Dharmadhikary ◽  
Edwin K. Koech ◽  
Josiah K. Makiche
Keyword(s):  
Integral Equation ◽  
Arbitrary Shape ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Field Integral

Application of Method of Moments to Acoustic Scattering From Fluid Filled Cylinders Using Three Different Formulations

1995 ◽  
Author(s):  
S. P. Sun ◽  
P. K. Raju ◽  
S. M. Rao
Keyword(s):  
Integral Equation ◽  
Cross Section ◽  
Method Of Moments ◽  
Acoustic Scattering ◽  
Arbitrary Cross Section ◽  
The Body ◽  
Equation Formulation ◽  
Integral Equation Formulation ◽  
Equivalent Problems ◽  
Field Integral

Abstract In this work, we present three different formulations Viz. The pressure field integral equation formulation (PFIE), the velocity field integral equation formulation (VFIE), and the combined field integral equation formulation (CEDE) for solving acoustic scattering problems associated with two dimensional fluid-filled bodies of arbitrary cross section. In particular using the boundary conditions on the surface of the body, two equivalent problems, each valid for the outside and inside regions of the scatterer, are derived. By properly selecting the associated equations for these equivalent problems, the three different formulations are derived. The PFIE, VFIE, and CFIE are then solved by approximating the cylindrical cross section by linear segments and employing the method of moments. Further, it is shown that the moment matrices generated by the PFIE and VFIE are ill-conditioned at resonant frequencies of the cylinder, whereas the CFIE generates a well-conditioned matrix at all frequencies. The solution techniques presented in this work are simple, efficient and applicable to truly arbitrary geometries. Numerical results are presented for certain canonical shapes and compared with other available data.

A well-posed integral equation formulation for three-dimensional rough surface scattering

2006 ◽  
Vol 462 (2076) ◽  
pp. 3683-3705 ◽  
Author(s):  
Simon N Chandler-Wilde ◽  
Eric Heinemeyer ◽  
Roland Potthast
Keyword(s):  
Integral Equation ◽  
Rough Surface ◽  
Double Layer ◽  
Inverse Operator ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Wave Number ◽  
Layer Potential ◽  
Equation Formulation ◽  
Integral Equation Formulation

We consider the problem of scattering of time-harmonic acoustic waves by an unbounded sound-soft rough surface. Recently, a Brakhage–Werner type integral equation formulation of this problem has been proposed, based on an ansatz as a combined single- and double-layer potential, but replacing the usual fundamental solution of the Helmholtz equation with an appropriate half-space Green's function. Moreover, it has been shown in the three-dimensional case that this integral equation is uniquely solvable in the space when the scattering surface does not differ too much from a plane. In this paper, we show that this integral equation is uniquely solvable with no restriction on the surface elevation or slope. Moreover, we construct explicit bounds on the inverse of the associated boundary integral operator, as a function of the wave number, the parameter coupling the single- and double-layer potentials, and the maximum surface slope. These bounds show that the norm of the inverse operator is bounded uniformly in the wave number, κ , for κ >0, if the coupling parameter η is chosen proportional to the wave number. In the case when is a plane, we show that the choice is nearly optimal in terms of minimizing the condition number.

Sign in / Sign up

Export Citation Format

Share Document