Iterative Solution of Boundary Integral Equations for Shallow Water Waves

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Gregory Baker ◽  
◽  
Edward Overman ◽  
Jing Yu
Keyword(s):  
Shallow Water ◽  
Integral Equations ◽  
Water Waves ◽  
Boundary Integral Equations ◽  
Iterative Solution ◽  
Boundary Integral ◽  
Shallow Water Waves

Iterative solutions of boundary integral equations in acoustics

1988 ◽  
Vol 417 (1852) ◽  
pp. 45-57 ◽  
Keyword(s):  
Helmholtz Equation ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Iterative Solution ◽  
Rates Of Convergence ◽  
Boundary Integral ◽  
Exterior Problems ◽  
Iterative Solutions ◽  
Boundary Integral Operators ◽  
Linear Operator Equations

It is shown that exterior problems for the Helmholtz equation may be solved iteratively for all frequencies. A general class of boundary-value problems for the Helmholtz equation is reduced to boundary integral equations. Using modified Green’s functions these boundary integral equations are known to be uniquely solvable. Even though the boundary integral operators are not self-adjoint they may be transformed into a form appropriate for iterative solution by a method developed for linear operator equations. Rates of convergence of the iteration are given and an example is presented to show the method.

RESPONSE CHARACTERISTICS OF GRAVEL BEACH FROM THE VIEWPOINT OF SHALLOW WATER WAVES AND MOVEMENT OF GRAVELS

2020 ◽  
Vol 76 (2) ◽  
pp. I_565-I_570
Author(s):  
Shin-ichi AOKI ◽  
Tomoki HAMANO ◽  
Taishi NAKAYAMA ◽  
Eiichi OKETANI ◽  
Takahiro HIRAMATSU ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Shallow Water Waves ◽  
Response Characteristics ◽  
Gravel Beach
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