Integral equation solution method of two-dimensional electromagnetic fields—a method to employ the transverse field components

1991 ◽  
Vol 74 (11) ◽  
pp. 32-38
Author(s):  
Masanori Matsuhara ◽  
Keishi Nakamura
Keyword(s):  
Integral Equation ◽  
Electromagnetic Fields ◽  
Solution Method ◽  
Transverse Field ◽  
Two Dimensional ◽  
Equation Solution

An improved integral equation for the numerical solution of two-dimensional diffraction problems

1970 ◽  
Vol 48 (8) ◽  
pp. 954-963 ◽  
Author(s):  
Lotfollah Shafai
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Integral Equations ◽  
Electromagnetic Fields ◽  
Current Distribution ◽  
Conformal Transformation ◽  
Sharp Edge ◽  
Two Dimensional ◽  
Square Prism

Using a conformal transformation, the singularities of electromagnetic fields near a sharp edge are related to the geometry of the scatterer. The results are then used to treat the singularities of the current in the integral equations for the current distribution. The properties of the improved integral equations and the procedure for their evaluation is discussed by considering two-dimensional scattering by a conducting square prism.

Lifting Surface Theory for the Problem of an Arbitrarily Yawed Sinusoidal Gust Incident on a Thin Aerofoil in Incompressible Flow

1970 ◽  
Vol 21 (2) ◽  
pp. 182-198 ◽  
Author(s):  
J. M. R. Graham
Keyword(s):  
Integral Equation ◽  
Kernel Function ◽  
Incompressible Flow ◽  
Velocity Component ◽  
Normal Velocity ◽  
Two Dimensional ◽  
Surface Theory ◽  
Equation Solution ◽  
Chebyshev Expansion ◽  
Dimensional Integral

SummaryThe solution to the problem of the loading generated on a two-dimensional thin aerofoil by an incompressible flow whose normal velocity component is of the general form exp [i(λx+/μy — ωt)] is calculated. The method used extends the two-dimensional integral equation solution for the induced vorticity by means of a Chebyshev expansion of part of the kernel function. Thin aerofoil approximations are made throughout, but no collocation procedure, as such, is required.

FINITE-DIFFERENCE MODELING IN MEDIA WITH MANY SMALL-SCALE CRACKS

2001 ◽  
Vol 09 (03) ◽  
pp. 815-831
Author(s):  
GERBEN B. VAN BAREN ◽  
GERARD C. HERMAN ◽  
WIM A. MULDER
Keyword(s):  
Integral Equation ◽  
Wave Propagation ◽  
Finite Difference ◽  
Point Sources ◽  
Small Scale ◽  
Two Dimensional ◽  
Equation Solution ◽  
Finite Difference Technique ◽  
Embedding Medium ◽  
Dimensional Wave

We discuss a finite-difference modeling technique for scalar, two-dimensional wave propagation in a medium containing a large number of small-scale cracks. The embedding medium can be heterogeneous. The boundaries of the cracks are not represented in the finite-difference mesh but the cracks are incorporated as distributed point sources. This enables the use of grid cells that are considerably larger than the crack sizes. We compare our method to an accurate integral-equation solution for the case of a homogeneous embedding and conclude that the finite-difference technique is accurate and computationally fast.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

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