scholarly journals Fast numerical calculation of UHF propagation over two dimensional dielectric irregular terrain using an integral equation method

2002 ◽  
Author(s):  
E.M. Kenny ◽  
P.J. Cullen
Keyword(s):  
Integral Equation ◽  
Numerical Calculation ◽  
Integral Equation Method ◽  
Equation Method ◽  
Two Dimensional ◽  
Irregular Terrain

Parallel Volume Integral Equation Method for Two-Dimensional Elastodynamic Analysis

2019 ◽  
Vol 16 (06) ◽  
pp. 1840025
Author(s):  
Jungki Lee ◽  
Hogwan Jeong
Keyword(s):  
Integral Equation ◽  
Wave Scattering ◽  
Integral Equation Method ◽  
Equation Method ◽  
Two Dimensional ◽  
Volume Integral ◽  
Scattering Problems ◽  
Volume Integral Equation ◽  
Parallel Volume ◽  
Volume Integral Equation Method

The parallel volume integral equation method (PVIEM) is applied for the analysis of two-dimensional elastic wave scattering problems in an unbounded isotropic solid containing various types of multiple multilayered anisotropic inclusions. It should be noted that the volume integral equation method (VIEM) does not require the use of the Green’s function for the anisotropic inclusion — only the Green’s function for the unbounded isotropic matrix is needed. A detailed analysis of the SH wave scattering problem is presented for various types of multiple multilayered orthotropic inclusions. Numerical results are presented for the elastic fields at the interfaces for square and hexagonal packing arrays of various types of multilayered orthotropic inclusions in a broad frequency range of practical interest. Standard parallel programming was used to speed up computation in the VIEM. The PVIEM enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shapes and geometry, isotropy/anisotropy, and softness/hardness of various types of multiple multilayered anisotropic inclusions on displacements and stresses at the interfaces of the inclusions and far-field scattering patterns. Also, powerful capabilities of the PVIEM for the analysis of general two-dimensional multiple scattering problems are investigated.

The Evaluation of an Integral Equation Method for Two-Dimensional Shock-Free Flows

1975 ◽  
Vol 26 (1) ◽  
pp. 59-70 ◽  
Author(s):  
D Nixon ◽  
J Patel
Keyword(s):  
Integral Equation ◽  
Integral Equation Method ◽  
Free Flow ◽  
Equation Method ◽  
Computational Time ◽  
Test Cases ◽  
Two Dimensional ◽  
Exact Methods ◽  
Wide Range ◽  
Steady Shock

SummaryThe numerical aspects of the integral equation method developed by Nixon and Hancock for two-dimensional steady shock-free flow have been rationalised; this numerically refined method is evaluated by calculating the pressure distribution around a wide range of aerofoils. These test cases include aerofoils in supercritical shock-free flow as well as subcritical flow and exact solutions are available for comparison. The computational time in the present method is significantly less than that required by the exact methods. The present results compare satisfactorily with the exact results.

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