Dan Givoli

article

Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

Daniel Rabinovich, Dan Givoli, Jacobo Bielak, Eli Turkel

International Journal for Numerical and Analytical Methods in Geomechanics > 45 > 7 > 867 - 892

The problem of identifying an obstacle (scatterer) in the form of a cavity in a 2D geophysical medium is considered. This is posed as an inverse wave problem, where the location of the cavity is sought based on measurements of the elastic waves recorded by sensors located at certain points in the domain. The sensor measurements are noisy, and are generated synthetically as a first step. The inverse...

article

Obstacle identification using the TRAC algorithm with a second‐order ABC

Tomer Levin, Eli Turkel, Dan Givoli

International Journal for Numerical Methods in Engineering > 118 > 2 > 61 - 92

We consider obstacle identification using wave propagation. In such problems, one wants to find the location, shape, and size of an unknown obstacle from given measurements. We propose an algorithm for the identification task based on a time‐reversed absorbing condition (TRAC) technique. Here, we apply the TRAC method to time‐dependent linear acoustics, although our methodology can be applied to other...

article

LATIN: A new view and an extension to wave propagation in nonlinear media

Dan Givoli, Ritukesh Bharali, Lambertus J. Sluys

International Journal for Numerical Methods in Engineering > 112 > 2 > 125 - 156

The LATIN (acronym of LArge Time INcrement) method was originally devised as a non‐incremental procedure for the solution of quasi‐static problems in continuum mechanics with material nonlinearity. In contrast to standard incremental methods like Newton and modified Newton, LATIN is an iterative procedure applied to the entire loading path. In each LATIN iteration, two problems are solved: a local...

article

Computational Time Reversal for NDT Applications Using Experimental Data

Craig Lopatin, Daniel Rabinovich, Dan Givoli, Eli Turkel

Journal of Nondestructive Evaluation > 2017 > 36 > 3 > 1-18

A model-based non destructive testing (NDT) method is proposed for damage identification in elastic structures, incorporating computational time reversal (TR) analysis. Identification is performed by advancing elastic wave signals, measured at discrete sensor locations, backward in time. In contrast to a previous study, which was purely numerical and employed only synthesized data, here an experimental...

article

The Double Absorbing Boundary method for a class of anisotropic elastic media

Daniel Rabinovich, Dan Givoli, Jacobo Bielak, Thomas Hagstrom

Computer Methods in Applied Mechanics and Engineering > 2017 > 315 > C > 190-221

The Double Absorbing Boundary (DAB) method was recently introduced as a new approach for solving wave problems in unbounded domains. It has common features to local high-order Absorbing Boundary Conditions (ABC) on one hand, and to Perfectly Matched Layers (PML) on the other, and has relative advantages with respect to both. In the DAB method, the unbounded domain is truncated to produce a finite...

article

Combined arrival-time imaging and time reversal for scatterer identification

Eyal Amitt, Dan Givoli, Eli Turkel

Computer Methods in Applied Mechanics and Engineering > 2017 > 313 > C > 279-302

The computational inverse problem of identifying a scatterer in a time-dependent wave field is considered. The wave speed of the background medium and the wave source are assumed to be known. Wave measurements, possibly noisy, are given at chosen discrete points in space (sensor locations) and time. The goal is to find scatterer parameters such as location, size and shape. The computational solution...

chapter

Flaw Identification in Structures via Computationally Assisted NDT

Daniel Rabinovich, Dan Givoli, Shmuel Vigdergauz

Solid Mechanics and Its Applications > Advances in Mathematical Modeling and Experimental Methods for Materials and Structures > 223-235

The practice of Non-Destructive Testing (NDT) is applied in many different fields of engineering to detect the presence of flaws in structures without causing structural damage. Ultrasonic NDT is one such method: the tested specimen is subjected to an acoustic wave field and the reflected wave is measured and provides information on flaws contained in the specimen. A description of the physics involved...

chapter

Non-Reflecting Boundaries: High-Order Treatment

Dan Givoli

A Celebration of Mathematical Modeling > 53-72

A class of numerical methods to solve wave problems in unbounded domains is based on truncating the infinite domain via an artificial boundary B and applying an appropriate boundary condition on B. The latter is called a Non-Reflecting Boundary Condition (NRBC). In this paper we (a) briefly recount the history of NRBC development and related issues, (b) explain the notion of high-order local NRBCs,...

book

A Celebration of Mathematical Modeling

Dan Givoli, Marcus J. Grote, George C. Papanicolaou, Springer Netherlands

ThisvolumecelebratestheeightiethbirthdayofJosephB. Keller. The authors who contributed to this volume belong to what can be called the “Keller school of applied mathematics. ” They are former students, postdoctoral fellows and visiting scientists who have collaborated with Joe (some of them still do) during his long career. They all look at Joe as their ultimate (role) model. JoeKeller’sdistinguishedcareerhasbeendividedbetweentheCourant...

article

DtN-based mixed-dimensional coupling using a Boundary Stress Recovery technique

Yoav Ofir, Dan Givoli

Computer Methods in Applied Mechanics and Engineering > 2015 > 287 > C > 31-53

A new computational approach for the mixed-dimensional modeling of time-harmonic waves in elastic structures is proposed. A two-dimensional (2D) structure is considered, which includes a part that is assumed to behave in a one-dimensional (1D) way. The 2D and 1D structural regions are discretized by using 2D and 1D Finite Element (FE) formulations. The hybrid model, if designed properly, is much more...

article

The double absorbing boundary method for elastodynamics in homogeneous and layered media

Daniel Rabinovich, Dan Givoli, Jacobo Bielak, Thomas Hagstrom

Advanced Modeling and Simulation in Engineering Sciences > 2015 > 2 > 1 > 1-27

Background Recently the Double Absorbing Boundary (DAB) method was introduced as a new approach for solving wave problems in unbounded domains. It has common features to each of two types of existing techniques: local high-order Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML). However, it is different from both and enjoys relative advantages with respect to both. Methods The...

article

The Nitsche method applied to a class of mixed-dimensional coupling problems

Daniel Rabinovich, Yoav Ofir, Dan Givoli

Computer Methods in Applied Mechanics and Engineering > 2014 > 274 > Complete > 125-147

A computational approach for the mixed-dimensional modeling of time-harmonic waves in elastic structures is proposed. A two-dimensional (2D) structure is considered, that includes a part which is assumed to behave in a one-dimensional (1D) way. The 2D and 1D structural regions are discretized using 2D and 1D finite element formulations. The coupling of the 2D and 1D regions is performed weakly, by...

article

The Double Absorbing Boundary method

Thomas Hagstrom, Dan Givoli, Daniel Rabinovich, Jacobo Bielak

Journal of Computational Physics > 2014 > 259 > Complete > 220-241

A new approach is devised for solving wave problems in unbounded domains. It has common features to each of two types of existing techniques: local high-order Absorbing Boundary Conditions (ABC) and Perfectly Matched Layers (PML). However, it is different from both and enjoys relative advantages with respect to both. The new method, called the Double Absorbing Boundary (DAB) method, is based on truncating...

article

Time reversal for crack identification

Eyal Amitt, Dan Givoli, Eli Turkel

Computational Mechanics > 2014 > 54 > 2 > 443-459

A general computational methodology is proposed for identifying cracks in structures. It is based on a time reversal (TR) technique and on the notion of refocusing. In the proposed procedure, a known source generates waves in the structure, and the time-varying response of the structure is measured only at certain points and times. In an industrial application this step is performed experimentally,...

article

Special issue on Advanced Modelling of Wave Propagation in Solids

Jüri Engelbrecht, Dan Givoli, Thomas Hagstrom, Gerard Maugin

Wave Motion > 2013 > 50 > 7 > 1061-1062

article

Time reversal with partial information for wave refocusing and scatterer identification

Dan Givoli, Eli Turkel

Computer Methods in Applied Mechanics and Engineering > 2012 > 213-216 > Complete > 223-242

Time reversal is a well-known procedure in application fields involving wave propagation. Among other uses, it can be applied as a computational tool for solving certain inverse problems. The procedure is based on advancing the solution of the relevant wave problem “backward in time”. One important use of numerical time-reversal is that of refocusing, where a reverse run is performed to recover the...

article

Combined asymptotic finite-element modeling of thin layers for scalar elliptic problems

Clara Sussmann, Dan Givoli, Yakov Benveniste

Computer Methods in Applied Mechanics and Engineering > 2011 > 200 > 47-48 > 3255-3269

Thin layers with material properties which differ significantly from those of the adjacent media appear in a variety of applications, as in the form of fiber coatings in composite materials. Fully modeling of such thin layers by standard finite element (FE) analysis is often associated with difficult meshing and high computational cost. Asymptotic procedures which model such thin domains by an interface...

article

A finite element scheme with a high order absorbing boundary condition for elastodynamics

Daniel Rabinovich, Dan Givoli, Jacobo Bielak, Thomas Hagstrom

Computer Methods in Applied Mechanics and Engineering > 2011 > 200 > 23-24 > 2048-2066

A high-order absorbing boundary condition (ABC) is devised on an artificial boundary for time-dependent elastic waves in unbounded domains. The configuration considered is that of a two-dimensional elastic waveguide. In the exterior domain, the unbounded elastic medium is assumed to be isotropic and homogeneous. The proposed ABC is an extension of the Hagstrom–Warburton ABC which was originally designed...

article

On the stability of the high-order Higdon Absorbing Boundary Conditions

Daniel Baffet, Dan Givoli

Applied Numerical Mathematics > 2011 > 61 > 6 > 768-784

The Higdon sequence of Absorbing Boundary Conditions (ABCs) for the linear wave equation is considered. Building on a previous work of Ha-Duong and Joly, which related to other forms of boundary conditions, the Higdon ABCs are proved to be energy-stable (on the continuous level) up to any order. This type of stability is stronger than the more standard notion of stability of initial boundary value...

article

Optimal modal reduction of dynamic subsystems: Extensions and improvements

Shaul Tayeb, Dan Givoli

International Journal for Numerical Methods in Engineering > 85 > 1 > 1 - 30

The problem of optimal reduction of a linear dynamic subsystem is revisited. The subsystem may represent, for example, a complex but minor part of a large elastic structure. The goal is to drastically reduce the number of degrees of freedom of a subsystem attached through an interface to a main system in such a way as to affect the dynamic behavior of the main system in the least possible way. In...

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Search results for: Dan Givoli

Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

Obstacle identification using the TRAC algorithm with a second‐order ABC

LATIN: A new view and an extension to wave propagation in nonlinear media

Computational Time Reversal for NDT Applications Using Experimental Data

The Double Absorbing Boundary method for a class of anisotropic elastic media

Combined arrival-time imaging and time reversal for scatterer identification

Flaw Identification in Structures via Computationally Assisted NDT

Non-Reflecting Boundaries: High-Order Treatment

A Celebration of Mathematical Modeling

DtN-based mixed-dimensional coupling using a Boundary Stress Recovery technique

The double absorbing boundary method for elastodynamics in homogeneous and layered media

The Nitsche method applied to a class of mixed-dimensional coupling problems

The Double Absorbing Boundary method

Time reversal for crack identification

Special issue on Advanced Modelling of Wave Propagation in Solids

Time reversal with partial information for wave refocusing and scatterer identification

Combined asymptotic finite-element modeling of thin layers for scalar elliptic problems

A finite element scheme with a high order absorbing boundary condition for elastodynamics

On the stability of the high-order Higdon Absorbing Boundary Conditions

Optimal modal reduction of dynamic subsystems: Extensions and improvements

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