scholarly journals A Galerkin Boundary Element Method for High Frequency Scattering by Convex Polygons

2007 ◽  
Vol 45 (2) ◽  
pp. 610-640 ◽  
Author(s):  
S. N. Chandler‐Wilde ◽  
S. Langdon
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Frequency ◽  
Convex Polygons ◽  
Galerkin Boundary Element Method ◽  
Element Method

IMPROVEMENT OF A HIGH-FREQUENCY BROADBAND ENERGY-INTENSITY BOUNDARY ELEMENT METHOD TO INCLUDE HIGH RESOLUTION SPECULAR REFLECTION

2005 ◽  
Vol 13 (01) ◽  
pp. 99-125 ◽  
Author(s):  
JERRY ROUSE ◽  
LINDA FRANZONI
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
High Frequency ◽  
Fourier Expansion ◽  
Energy Intensity ◽  
Specular Reflection ◽  
Original Method ◽  
Energy Sources ◽  
Frequency Basis ◽  
Element Method

The prediction of the spatial mean-square pressure distribution within enclosed high-frequency broadband sound fields is computationally intensive if determined on a frequency-by-frequency basis. Recently an energy-intensity boundary element method (EIBEM) has been formally developed. This method employs uncorrelated broadband directional energy sources to expeditiously predict such pressure distributions. The source directivity accounts for local correlation effects and specular reflection. The method is applicable to high modal density fields, but not restricted to the usual low-absorption, diffuse, and quasi-uniform assumptions. The approach can accommodate fully specular reflection, or any combination of diffuse and specular reflection. This boundary element method differs from the classical version in that element size is large compared to an acoustic wavelength and equations are not solved on a frequency-by-frequency basis. In the earlier EIBEM, the source strength and directivity associated with the energy sources, distributed over enclosure boundaries, were determined in an iterative manner and the directivity was limited to three terms of a Fourier expansion. Here, the original method is improved by eliminating the iteration and allowing for an unlimited number of terms in the Fourier expansion of the directivity function. For verification, the improved EIBEM is compared to experimental measurements and exact analytical solutions; excellent agreement is obtained.

Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems

2020 ◽  
Vol 36 (6) ◽  
pp. 749-761
Author(s):  
Y. -Y. Ko
Keyword(s):  
Boundary Element Method ◽  
Rigid Body ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Neumann Problems ◽  
Galerkin Boundary Element Method ◽  
Element Method

ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

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