Solution of the time-harmonic viscoelastic inverse problem with interior data in two dimensions

2012 ◽  
Vol 92 (13) ◽  
pp. 1100-1116 ◽  
Author(s):  
Yixiao Zhang ◽  
Assad A Oberai ◽  
Paul E Barbone ◽  
Isaac Harari
Keyword(s):  
Inverse Problem ◽  
Two Dimensions ◽  
Interior Data ◽  
Time Harmonic

Framework for Flaw Detection: Application to Dynamic Crack Detection in Flat Membranes

2008 ◽  
Author(s):  
Daniel Rabinovich ◽  
Dan Givoli ◽  
Shmuel Vigdergauz
Keyword(s):  
Inverse Problem ◽  
Crack Detection ◽  
Flexible Structures ◽  
Flaw Detection ◽  
Forward Problem ◽  
Dynamic Crack ◽  
Computational Framework ◽  
Time Harmonic ◽  
Present Context ◽  
Flat Membranes

A computational framework is developed for the detection of flaws in flexible structures. The framework is based on posing the detection problem as an inverse problem, which requires the solution of many forward problems. Each forward problem is associated with a known flaw; an appropriate cost functional evaluates the quality of each candidate flaw based on the solution of the corresponding forward problem. On the higher level, the inverse problem is solved by a global optimization algorithm. The performance of the computational framework is evaluated by considering the detectability of various types of flaws. In the present context detectability is defined by introducing a measure of the distance between the sought flaw and trial flaws in the space of the parameters characterizing the configuration of the flaw. The framework is applied to crack detection in flat membranes subjected to time-harmonic and transient excitations. The detectability of cracks is compared for these two cases.

scholarly journals Integral equation methods in inverse obstacle scattering

2000 ◽  
Vol 42 (1) ◽  
pp. 65-78 ◽  
Author(s):  
Rainer Kress
Keyword(s):  
Boundary Integral Equations ◽  
Plane Waves ◽  
Research Work ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Field Pattern ◽  
Integral Equation Methods ◽  
Time Harmonic ◽  
Domain With A Corner ◽  
Far Field Pattern

AbstractIn this survey we consider a regularized Newton method for the approximate solution of the inverse problem to determine the shape of an obstacle from a knowledge of the far field pattern for the scattering of time-harmonic acoustic or electromagnetic plane waves. Our analysis is in two dimensions and the numerical scheme is based on the solution of boundary integral equations by a Nyström method. We include an example of the reconstruction of a planar domain with a corner both to illustrate the feasibility of the use of radial basis functions for the reconstruction of boundary curves with local features and to connect the presentation to some of the research work of Professor David Elliott.

scholarly journals A Hölder-logarithmic stability estimate for an inverse problem in two dimensions

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Matteo Santacesaria
Keyword(s):  
Inverse Problem ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stability Estimate ◽  
Two Dimensions ◽  
Positive Energy ◽  
Two Dimensional ◽  
Ill Posed ◽  
Dirichlet To Neumann Map ◽  
Logarithmic Stability

AbstractThe problem of the recovery of a real-valued potential in the two-dimensional Schrödinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction of the potential is only logarithmic stable in general. In this paper a new stability estimate is proved, which is explicitly dependent on the regularity of the potentials and on the energy. Its main feature is an efficient

The boundary inverse problem for the Laplace equation in two dimensions

1996 ◽  
Vol 12 (5) ◽  
pp. 565-577 ◽  
Author(s):  
N D Aparicio ◽  
M K Pidcock
Keyword(s):  
Inverse Problem ◽  
Laplace Equation ◽  
Two Dimensions

MATHEMATICAL ANALYSIS OF THE ACOUSTIC DIFFRACTION BY A MUFFLER CONTAINING PERFORATED DUCTS

2005 ◽  
Vol 15 (07) ◽  
pp. 1059-1090 ◽  
Author(s):  
A. S. BONNET-BEN DHIA ◽  
D. DRISSI ◽  
N. GMATI
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Scalar Problem ◽  
Fredholm Type ◽  
Numerical Examples ◽  
Time Harmonic ◽  
Impedance Condition ◽  
Absorbing Material ◽  
Acoustic Diffraction ◽  
Theoretical Results

We consider the three-dimensional scalar problem of acoustic propagation in a muffler. We develop and analyze a Fredholm-type formulation for a stationary fluid in the time-harmonic setting. We prove a homogenization result for a muffler containing periodically perforated ducts. Essentially, the perforated boundaries become completely transparent when the period of perforations, which is assumed to be of the same order as the size of perforations, tends to zero. We also derive a homogenized impedance condition when the perforated duct is coated by an absorbing material. We present numerical examples in two dimensions, obtained from coupling finite elements in the muffler with modal decompositions in the inlet and outlet ducts, which demonstrate the limiting validity of the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document