Exterior boundary‐value problems for the Helmholtz equation with a generalized impedance boundary condition

1986 ◽  
Vol 80 (S1) ◽  
pp. S104-S104
Author(s):  
Allan G. Dallas
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Exterior Boundary

A METHOD FOR THE TREATMENT OF A SLOPING SEA BOTTOM IN THE PARABOLIC APPROXIMATION

1996 ◽  
Vol 04 (01) ◽  
pp. 89-100 ◽  
Author(s):  
J. S. PAPADAKIS ◽  
B. PELLONI
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Pressure Field ◽  
Impedance Boundary Condition ◽  
Parabolic Approximation ◽  
Impedance Boundary ◽  
Local Boundary ◽  
Sea Bottom ◽  
Local Boundary Condition ◽  
Non Local

The impedance boundary condition for the parabolic approximation is derived in the case of a sea bottom profile sloping at a constant angle, as a non-local boundary condition imposed exactly at the interface. This condition is integrated into the IFD code for the numerical computation of the pressure field and implemented to test its accuracy in some benchmark cases, for which the backscattered field is negligible. It is shown that by avoiding the sloping interface, the results obtained are closer to the benchmark results given by normal mode codes solving the full Helmholtz equation, such as the 2-way COUPLE code, than those of the standard IFD or other 1-way codes, at least for problems that do not have significant backscattering effects.

scholarly journals Numerical solution to the Complex 2D Helmholtz Equation based on Finite Volume Method with Impedance Boundary Conditions

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 436-443 ◽  
Author(s):  
Angela Handlovičová ◽  
Izabela Riečanová
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Robin Boundary Condition ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Volume Method ◽  
Robin Boundary

AbstractIn this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.

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