scholarly journals Validation of the Reduced Vector Potential Formulation with the DtN Boundary Condition

2020 ◽  
Author(s):  
Anton Efremov ◽  
Lalita Udpa ◽  
Antonello Tamburrino
Keyword(s):  
Experimental Data ◽  
Boundary Condition ◽  
Nondestructive Testing ◽  
Vector Potential ◽  
Neumann Operator ◽  
Potential Formulation ◽  
Dirichlet To Neumann Operator

This work describes the validation against experimental data of a Reduced Vector Potential Formulation combined with a boundary condition given by the Dirichlet-to-Neumann operator. One of the classic nondestructive testing problems is investigated: the differential bobbin coil scan inside a tube with a defect. Several defects are simulated, and the results are compared to the experimental data acquired at four frequencies.

The impedance boundary condition in the boundary element-vector potential formulation

1988 ◽  
Vol 24 (6) ◽  
pp. 2503-2505 ◽  
Author(s):  
S. Subramaniam ◽  
S.R.H. Hoole
Keyword(s):  
Boundary Condition ◽  
Boundary Element ◽  
Vector Potential ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Potential Formulation

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 ¯ ) .

Poincaré duality angles and the Dirichlet-to-Neumann operator

2013 ◽  
Vol 29 (4) ◽  
pp. 045007 ◽  
Author(s):  
Clayton Shonkwiler
Keyword(s):  
Poincaré Duality ◽  
Poincare Duality ◽  
Neumann Operator ◽  
Dirichlet To Neumann Operator

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
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