A New Approach To Inverse Problems Of Wave Equations

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HAL Id: hal-00602335 https://hal.archives-ouvertes.fr/hal-00602335 Submitted on 22 Jun 2011 HAL is a multi-disciplinary open access archive for the deposit and

INVERSE SOURCE PROBLEMS FOR MAXWELL S EQUATIONS AND THE

new inversion formula. Windowed Fourier transform techniques have previously been applied to scalar inverse source problems in [4, 5], but no connection to exponential ray transforms (or similar integral transforms) has been exploited in these works. For further recent contributions to inverse source problems for Maxwell s equations we refer

Numerical performance of layer stripping algorithms for two

Figure 1. The w inverse scattering problem. and wave speed C(Z,Z) are smooth functions of depth z and lateral position z. The medium is bounded by a free (pressure-release) surface z = 0. The density po and wave speed co for z < 0 and z -+ M are known. The medium is probed

Differential and integral methods for three-dimensional

Marchenko integral equations by Newton [ 1-31, These integral equations are generali- sations of similar equations derived for the one-dimensional inverse scattering problems. Alternative derivations have been given for the generalised Marchenko equation in [4-81 and for the generalised Gel fand-Levitan equation in [8].

SOLVING INVERSE PROBLEMS OF IDENTIFICATION TYPE BY OPTIMAL

This type of inverse problem corresponds to parameter identification in a model with known struc- ture involving some unknown data.6 Other inverse problems corresponding to: (i) model identifica- tion, (ii) reconstructions from projections, or (iii) integral equations of the first type, etc. are not included in our approach.

The inverse water wave problem of bathymetry detection

The inverse water wave problem of bathymetry detection is the problem of deducing the bottom topography of the seabed from measurements of the water wave surface. In this paper, we present a fully nonlinear method to address this problem. The method starts from the Euler water wave equations for inviscid irrotational uid ow, without any

A Mathematical Framework for Inverse Wave Problems in

certain infeasible-model methods for inverse problems in wave propagation. Another useful by-product of the theory is the nite speed of propagation property for hyperbolic systems with bounded, measurable coe cients, a result which so far as we can tell is new.

The subelliptic oblique derivative problem. University of

Dispersive Partial Di erential Equations, Oberwolfach, August 12{16, 2013. Plenary Lecturer, Conference on Inverse Problems in Honor of Gunther Uhlmann, UC Irvine, June 18{22, 2012. Plenary Lecturer, Hangzhou Conference on Harmonic Analysis and PDE, Hangzhou, China, June 6{10, 2011. Invited Lecture, Workshop on Inverse Problems: Theory and

A NEW APPROACH FOR SOLITON SOLUTIONS OF RLW EQUATION AND (1+2

of a method of solution to two class of nonlinear wave equations termed the reg-ularized long-wave (RLW) equation and the nonlinear Schr odinger s equation (NLSE). The RLW equation arises in the study of shallow-water waves. The generalized version of the RLW equation is known as the R(m;n) equation.

Water waves and Korteweg-de Vries equations

Armed with a new approach, it is then possible to seek equations which can be solved and which, it is to be hoped, will also prove to be useful. Here, we are particularly interested in the various Korteweg-de Vries equa- tions that arise from the classical water-wave problem. By deriving all the equations -

TABLE OF INVERSE LAPLACE TRANSFORMS

differential equations, and for that reason I have tried to exploit the reader's physical and geometric intuition. At one extreme, it is possible to approach the subject on a highly rigorous lemma-theoremcorollary level, which, for a course like differential equations, squeezes out the lifeblood of the

A FAST DIRECT IMAGING METHOD FOR THE INVERSE OBSTACLE

resolution, one approach is simply to use an incident wave with shorter wavelength or higher frequency as an illumination. A topical review can be found in [8] on computational approaches and mathematical analysis for solving inverse scattering problems by multi-frequencies.

The analysis of fractional-order Helmholtz equations via a

Mar 05, 2021 The Helmholtz equation or reduced wave equation is an elliptical partial differential equation (PDE) derived directly from the wave model. Helmholtz equation is a PDE that signifies time-independent mechanical growth in the universe. The Helmholtz equation is one of the essential applied mathematics and physics equations.

Time Domain Wave-Splittings and Inverse Problems

7.2 The dynamical equations for the split components for the wave and telegraph equations 303 7.3 Inverse problem: the Green's function approach 307 7.4 Inverse problem: the continuation method 317 7.5 Non-planar wave-splitting for the wave equation 326 7.6 Present and future research 330 Exercises for Chapter 7 331 Wave-splitting of Maxwell's

Nonreflecting Boundary Conditions for the Time-Dependent Wave

The scalar wave equation and Maxwell s equations govern problems in such diverse application areas as ultrasonics, seismics, underwater acoustics, antenna design, and mi-croelectronics [1, 6, 9, 13, 17, 28, 30, 36]. In many cases, the governing equations are posed as exterior problems, and the infinite physical domain must be reduced to a

EFFECTIVE APPROACHES USING COMBINATORICS TO SOLVE INVERSE

2-D distributed systems, inverse problems, identification of field sources, Fibonacci sequence Abstract In this paper, new, effective approaches to solve third and second order difference equations are introduced. These approaches consist in the use of new computational tools constructed by

Inverse problems in random media: a kinetic approach

Inverse problems in random media: a kinetic approach Guillaume Bal Department of Applied Physics and Applied Mathematics, Columbia University, New York NY, 10027, U.S.A. E-mail: [email protected] Abstract. We consider the validity and accuracy of kinetic equations to model the propagation of high frequency waves in highly heterogeneous media.

The boundary control approach to inverse spectral theory

1.2. Simon approach. In [21] Barry Simon proposed a new approach to in-verse spectral theory which has got a further development in the paper by Gesztesy and Simon [18] (see also an excellent survey paper [17]). The inverse data in this approach is the Titchmarsh{Weyl m-function which is equivalent to the knowledge of the spectral measure.

One-dimensional inverse scattering and spectral problems

9) Some new inverse problems for the heat and wave equations are studied. 10) A study of inverse scattering problem for an inhomogeneous Schr odinger equation; 1Key words: property C forODE, inversespectral and scattering problems, problems PDE and ODE, spectral and scattering theory. 2Math subject classi cation: 35R30, 34B25, 34A55, 81F05

A Modification of Gradient Descent Method for Solving

Numerical methods, suitable for solving the coefficient inverse problems for hyperbolic systems and equations, are usually divided into direct ones and iterative ones. Direct methods are based on the Gelfand Levitan Krein approach [25 30] and boundary control method [31,32]. It was shown that the discrete coefficients inverse problems

WORKSHOP ON INVERSE PROBLEMS IN SCATTERING AND IMAGING

Inverse Problems for Non-Linear Hyperbolic Equations Gunther Uhlmann Department of Mathematics, University of Washington We consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold. We formulate the concept of active mea-surements for relativistic models.

BAYESIAN APPROACH TO INVERSE PROBLEMS FOR FUNCTIONS WITH A

equations (e.g., sound velocity in the acoustic wave equation). Inverse problems aim to reconstruct the coe cients from some measurements of the solutions of the partial di erential equations. The forward model described using partial di eren-tial equations usually has a unique solution, while the inverse problem does not [40]. In order to

SPECTRAL ESTIMATION AND INVERSE INITIAL BOUNDARY VALUE PROBLEMS

ary spectral and dynamical inverse problems for partial differential equations (see, e.g., [2, 10, 14, 15]). Proposed originally for solving the boundary inverse problem for the multi-dimensional wave equation, it was successfully extended to the heat, Schrodinger, and other fundamental equations of mathematical physics (see, e.g.,

DEEP NEURAL NETWORK APPROACH TO FORWARD-INVERSE PROBLEMS

inverse problems to implement them. This calls for simplistic methods that unify two steps in solving forward-inverse problems. The contributions of this paper are three-fold. First, the DNN architecture pre-sented in this paper highlights its simplistic approach to handling forward-inverse problems simultaneously.

A Neural Network Approach for Solving Inverse Problems in NDE

A NEURAL NETWORK APPROACH FOR SOLVING INVERSE PROBLEMS IN NDE I. Elshafiey, L. Udpa, and S. S. Udpa Department of Electrical Engineering and Computer Engineering and Center for NDE Iowa State University Ames, IA 50010 INTRODUCTION Solution to inverse problems is of interest in many fields of science ancl engineering.

Control and Inverse Problems for Partial Difierential

for the wave equation can be applied for solving control and inverse problems for the heat and Schr˜odinger equations. The talk is partly based on a joint work with M. Belishev, on the paper (M.I. Belishev, Inverse Problems, 20 (2004), 647{672) and on Chapter VII 1

Inverse random source scattering for the Helmholtz equation

Aug 16, 2017 In this work, we propose a new approach for solving the stochastic inverse source scatter-ing problem in inhomogeneous media. We study both the direct and inverse source scattering problems for the stochastic Helmholtz equation in an inhomogeneous medium. By construct-

Spatiotemporal Kalman Filtering: a new approach to solving

a new approach to solving dynamical inverse problems Andreas Galkay;z, Okito Yamashitaz and Tohru Ozakiz y Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany z Institute of Statistical Mathematics (ISM), Minami-Azabu 4-6-7, Tokyo 106-8569, Japan Email: [email protected] Abstract This paper discusses a new

A Direct Solution Approach to the Inverse Shallow-Water Problem

2.1. Discretization of the Governing Equations of the Forward Problem The discretization of the governing equations is one of the most important steps in the numerical solution of partial differential equations in engineering and science. Many discretization techniques have been developed to suit specific problems. In the context

Partial Uniqueness and Obstruction to Uniqueness in Inverse

order. Our main tool, a new approach in inverse problems for elastic media, is the representation of the equations of motion in a covariant form (following Marsden and Hughes, 1983) that preserves the underlying physics. In the case of classical linear elastodynamics we then investigate how the type

Special Section on Photonic Crystals and Their Device

model problems, which provide a deeper insight into the structure of the optimal design problems. key words: inverse problems, optimal design, photonic crystals, wave problems, Maxwell equations, helmholtz equations 1. Introduction A new paradigm has emerged, in which the band structure concepts of solid state physics are applied (cf.[1],[2]) to

arXiv:math/9201261v1 [math.AP] 1 Jan 1992

FOR OSCILLATORY RIEMANN-HILBERT PROBLEMS P. Deift and X. Zhou In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in par-ticular, in evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method.

Two-Step Enhanced Deep Learning Approach for Electromagnetic

YAO et al.: TWO-STEP ENHANCED DEEP LEARNING APPROACH FOR ELECTROMAGNETIC INVERSE SCATTERING PROBLEMS 2255 Fig. 1. Schematic of scattering of TMz wave from a dielectric region Dobj. described. The next section discusses the process of employ-ing the proposed DL method to solve EMIS. In Section III, numerical benchmarks are provided to show the

A.G.Ramm, One-dimensional inverse scattering and spectral

9) Some new inverse problems for the heat and wave equations are studied. 10) A study of inverse scattering problem for an inhomogeneous Schr¨odinger equation; Contents

INVERSE TIME-HARMONIC ELECTROMAGNETIC SCATTERING FROM COATED

INVERSE TIME-HARMONIC ELECTROMAGNETIC SCATTERING FROM COATED POLYHEDRAL SCATTERERS WITH A SINGLE FAR-FIELD PATTERN GUANG-HUI HUy, MANMOHAN VASHISTHzAND JIAQING YANG Abstract. It i

A new approach to hyperbolic inverse problems

May 07, 2020 A new approach to hyperbolic inverse problems II: global step G Eskin-An inverse problem for a wave equation with arbitrary initial values and a finite time of observations Rolci Cipolatti and Masahiro Yamamoto-Topical Review Masahiro Yamamoto-Recent citations Determining the time-dependent matrix potential in a wave equation from partial

arXiv:2001.07599v2 [math.AP] 21 Feb 2020

results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems. Contents 1. Introduction and main results 1 2.

An integral equation approach to the prediction of indoor

to a sparse form. The resulting sparse system of linear equations is efficiently solved using a conjugate gradient algorithm. The entire solution technique is applied to the simulation of indoor wave propagation problems and is illustrated by two examples. 1. Introduction In anticipation of the introduction of a new gen-