Convolution quadrature Galerkin boundary element method for the wave equation with reduced quadrature weight computation

2010 ◽  
Vol 31 (2) ◽  
pp. 640-666 ◽  
Author(s):  
D. J. Chappell
Keyword(s):  
Wave Equation ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Convolution Quadrature ◽  
Galerkin Boundary Element Method ◽  
Element Method

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.

A development of isogeometric Galerkin boundary element method for 2D periodic problem

2017 ◽  
Vol 2017.66 (0) ◽  
pp. 511
Author(s):  
Tetsuro HIRAI ◽  
Toru TAKAHASHI ◽  
Hiroshi ISAKARI ◽  
Toshiro MATSUMOTO
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Periodic Problem ◽  
Galerkin Boundary Element Method ◽  
Element Method
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