Acoustic scattering in nonhomogeneous media and the problem of discontinuous gradients: Analysis and inf‐sup stability in the method of finite spheres

2021 ◽  
Author(s):  
Williams L. Nicomedes ◽  
Klaus‐Jürgen Bathe ◽  
Fernando J. S. Moreira ◽  
Renato C. Mesquita
Keyword(s):  
Acoustic Scattering ◽  
Nonhomogeneous Media ◽  
Finite Spheres

scholarly journals The method of finite spheres in acoustic wave propagation through nonhomogeneous media: Inf-sup stability conditions

2020 ◽  
Vol 42 (3) ◽  
pp. 209-237
Author(s):  
Williams L. Nicomedes ◽  
Klaus-Jürgen Bathe ◽  
Fernando J. S. Moreira ◽  
Renato C. Mesquita
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Acoustic Wave Propagation ◽  
Nonhomogeneous Media ◽  
Finite Dimensional ◽  
Pressure Fields ◽  
Time Harmonic ◽  
The Stability ◽  
Finite Spheres ◽  
Well Posed

When the method of finite spheres is used for the solution of time-harmonic acoustic wave propagation problems in nonhomogeneous media, a mixed (or saddle-point) formulation is obtained in which the unknowns are the pressure fields and the Lagrange multiplier fields defined at the interfaces between the regions with distinct material properties. Then certain inf-sup conditions must be satisfied by the discretized spaces in order for the finite-dimensional problems to be well-posed. We discuss in this paper the analysis and use of these conditions. Since the conditions  involve norms of functionals in fractional Sobolev spaces, we derive ‘stronger’ conditions that are simpler in form. These new conditions pave the way for the inf-sup testing, a tool for assessing the stability of the discretized problems.

Acoustic Scattering from Heterogeneous Rough Seabeds

2002 ◽  
Author(s):  
Anatoliy N. Ivakin ◽  
Darrell R. Jackson ◽  
Timothy K. Stanton
Keyword(s):  
Acoustic Scattering
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