Singularity of scattering and Dirichlet-to-Neumann operator symbols in elliptic wave propagation models

2014 ◽  
Vol 80 (3) ◽  
pp. 651-675
Author(s):  
J.-H. Yoon ◽  
J.-H. Kim ◽  
J. Jo
Keyword(s):  
Wave Propagation ◽  
Propagation Models ◽  
Neumann Operator ◽  
Dirichlet To Neumann Operator ◽  
Operator Symbols

scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

scholarly journals The Dirichlet-to-Neumann operator on rough domains

2011 ◽  
Vol 251 (8) ◽  
pp. 2100-2124 ◽  
Author(s):  
W. Arendt ◽  
A.F.M. ter Elst
Keyword(s):  
Neumann Operator ◽  
Dirichlet To Neumann Operator

scholarly journals VERIFICATION OF NUMERICAL WAVE PROPAGATION MODELS IN TIDAL INLETS

1988 ◽  
Vol 1 (21) ◽  
pp. 30 ◽  
Author(s):  
J.A. Vogel ◽  
A.C. Radder ◽  
J.H. De Reus
Keyword(s):  
Wave Propagation ◽  
Numerical Models ◽  
River Estuary ◽  
Regular Grid ◽  
Local Wind ◽  
Tidal Inlets ◽  
Propagation Models ◽  
Dutch Coast ◽  
Model Based ◽  
Numerical Wave

The performance of two numerical wave propagation models has been investigated by comparison with field data. The first model is a refractiondiffraction model based on the parabolic equation method. The second is a refraction model based on the wave action equation, using a regular grid. Two field situations, viz. a tidal inlet and a river estuary along the Dutch coast, were used to determine the influence of the local wind on waves behind an island and a breaker zone. It may be concluded from the results of the computations and measurements that a much better agreement is obtained when wave growth due to wind is properly accounted for in the numerical models. In complicated coastal areas the models perform well for both engineering and research purposes.

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