The numerical solution of a non-linear boundary integral equation on smooth surfaces

1994 ◽  
Vol 14 (4) ◽  
pp. 461-483 ◽  
Author(s):  
KENDALL E. ATKINSON
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Smooth Surfaces ◽  
Linear Boundary ◽  
Non Linear

scholarly journals LIMIT WAVES ON HORIZONTAL SEA FLOOR

1986 ◽  
Vol 1 (20) ◽  
pp. 41
Author(s):  
Chia-Chi Lu ◽  
John D. Wang ◽  
Bernard Le Mehaute
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Integral Equation ◽  
Gravity Waves ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Wave Crest ◽  
Solution Technique ◽  
Sea Floor ◽  
Surface Gravity Waves

A numerical solution to periodic nonlinear irrotational surface gravity waves on a horizontal sea floor is developed using an iterative Boundary Integral Equation Method (BIEM). This solution technique is subsequently applied to determine the characteristics of limit waves for which the wave crest theoretically ceases to be rounded and become angled with an included angle of 120 degrees.

scholarly journals Numerical Solution of the Kirchhoff Plate Bending Problem with BEM

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
V. V. Zozulya
Keyword(s):  
Integral Equation ◽  
Numerical Solution ◽  
Boundary Integral ◽  
Kirchhoff Plate ◽  
Reciprocal Theorem ◽  
Plate Bending ◽  
Linear Boundary ◽  
Analytical Formulas ◽  
Bending Problems ◽  
Plate Bending Problem

Direct approach based on Betty's reciprocal theorem is employed to obtain a general formulation of Kirchhoff plate bending problems in terms of the boundary integral equation (BIE) method. For spatial discretization a collocation method with linear boundary elements (BEs) is adopted. Analytical formulas for regular and divergent integrals calculation are presented. Numerical calculations that illustrate effectiveness of the proposed approach have been done.

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