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Author Graham, Ivan
Title Direct and Inverse Problems in Wave Propagation and Applications
Imprint Berlin/Boston : De Gruyter, Inc., 2013
©2013
book jacket
Descript 1 online resource (312 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
Series Radon Series on Computational and Applied Mathematics Ser. ; v.14
Radon Series on Computational and Applied Mathematics Ser
Note Intro -- Preface -- Differential electromagnetic imaging -- 1 Introduction -- 2 Basic theory of electromagnetic waves -- 2.1 The Helmholtz equation -- 2.2 The Maxwell equations -- 2.3 Fundamental solutions and radiation conditions -- 2.4 Transmission and boundary conditions -- 2.5 Dirichlet and Neumann functions and the Hodge decomposition -- 2.6 Trace theorems and first Green identity -- 2.7 Lippman-Schwinger representation formulas -- 2.8 The Helmholtz-Kirchhoff theorems -- 2.9 Limiting models -- 2.10 TheMaxwell equations with axis invariance -- 2.11 The Maxwell equations versus the Helmholtz equation -- 3 Electric and magnetic polarization tensors -- 4 small-volume expansions -- 4.1 The full Maxwell equations -- 4.2 The eddy currents model -- 4.3 The Helmholtz equation -- 4.4 The conductivity equation -- 4.5 Asymptotic formulas in the time domain -- 5 Imaging in the frequency domain -- 5.1 MUSIC-type imaging at a single frequency -- 5.2 Backpropagation type imaging at a single frequency -- 5.3 Imaging with a broad range of frequencies -- 6 Imaging in the time domain -- 6.1 Time-domain imaging with full viewmeasurements -- 6.2 Time-domain imaging in a cavity with limited-view data -- 6.3 Time-domain imaging in dissipative media -- 7 Numerical examples of MUSIC reconstructions for the full Maxwell equations -- 8 Shape representations -- 8.1 High-order polarization tensors -- 8.2 Frequency dependent high-order polarization tensors -- 9 Far-field imaging versus near-field imaging -- 10 Open problems -- Multitrace boundary integral equations -- 1 Introduction -- 1.1 Geometry -- 1.2 Transmission problems -- 2 Boundary integral operators -- 2.1 Trace spaces and operators -- 2.2 Potentials -- 2.3 Calderón projectors -- 3 Classical single-trace integral equations -- 3.1 Skeleton trace spaces -- 3.2 A first-kind boundary integral equation
3.3 Boundary element Galerkin discretization -- 4 Preconditioning -- 4.1 Operator products -- 4.2 Calderón identities -- 4.3 Operator preconditioning -- 4.4 Stable duality pairing for boundary elements -- 4.5 The challenge -- 5 Global multitrace formulation -- 5.1 Separated subdomains -- 5.2 The gap idea -- 5.3 Properties of global MTF -- 5.4 Galerkin discretization -- 6 Local multitrace formulation -- 6.1 Partial transmission conditions -- 6.2 Local MTF: variational formulation -- 6.3 Local MTF: Stability -- 6.4 Boundary element Galerkin discretization -- Direct and Inverse Elastic Scattering Problems for Diffraction Gratings -- 1 Introduction -- 2 Mathematical formulation of direct and inverse scattering problems -- 3 Solvability results for direct scattering problems: variational method -- 3.1 An equivalent variational formulation and its Fredholmproperty -- 3.2 Uniqueness and existence for direct scattering problems -- 3.3 Uniqueness and existence for transmission gratings -- 4 Uniqueness for inverse scattering problems -- 4.1 Inverse scattering of incident pressure waves -- 4.2 Inverse scattering of incident shear waves -- 5 Numerical solution of direct and inverse scattering problems -- 5.1 A discrete Galerkin method for (DP) -- 5.2 A two-step algorithm for (IP) -- Multigrid methods for Helmholtz problems: A convergent scheme in 1D using standard components -- 1 Introduction -- 2 Smoothing -- 2.1 Smoothing analysis -- 2.2 Jacobi smoothing -- 2.3 Two-step Jacobi smoothing -- 3 Coarse-grid correction -- 3.1 The Laplacian -- 3.2 The Helmholtz operator -- 4 Two-grid iteration -- 4.1 The Laplacian -- 4.2 The Helmholtz operator -- 5 Numerical examples -- 5.1 Two-grid experiments -- 5.2 Multigrid experiments, complexity -- 6 Conclusions -- Explicit local time-steppingmethods for time-dependent wave propagation -- 1 Introduction
2 Finite element discretizations for the wave equation -- 2.1 Continuous Galerkin formulation -- 2.2 Interior penalty discontinuous Galerkin formulation -- 2.3 Nodal discontinuous Galerkin formulation -- 3 Leap-frog-based LTS methods -- 3.1 Second-order method for undamped waves -- 3.2 Fourth-order method for undamped waves -- 3.3 Second-order leap-frog/Crank-Nicolson-basedmethod for damped waves -- 4 Adams-Bashforth-based LTS methods for damped waves -- 5 Numerical results -- 5.1 Stability -- 5.2 Convergence -- 5.3 Two-dimensional example -- 6 Concluding remarks -- Absorbing boundary conditions and perfectly matched layers in wave propagation problems -- 1 Introduction -- 2 ABC -- 2.1 Exact ABC -- 2.2 Approximation of the exact ABC -- 3 Plane waves analysis of an ABC -- 4 Perfectly matched layers -- 4.1 Helmholtz equation -- 4.2 The wave equation -- 5 Computation of the reflection coefficient of a PML -- 6 Conclusion -- Dynamic inverse scattering -- 1 Introduction -- 2 Reconstruction of time-dependent pulses by the point-source method -- 3 Time-domain probe method (TDPM) -- 4 Orthogonality sampling -- 5 Dynamic inversion via data assimilation techniques -- 5.1 Three-dimensional variational data assimilation -- 5.2 Cycled probing and samplingmethod -- 5.3 Partial reconstruction matching scheme -- 6 Numerical examples -- Boundary integral equations for Helmholtz boundary value and transmission problems -- 1 Introduction -- 2 Boundary integral equations -- 2.1 Boundary integral operators -- 2.2 Coercivity of boundary integral operators -- 2.3 Injectivity of boundary integral operators -- 2.4 Interior Robin boundary value problem -- 2.5 Boundary integral equations for exterior boundary value problems -- 3 Exterior Dirichlet boundary value problem -- 3.1 Direct boundary integral equations -- 3.2 Indirect boundary integral equations
3.3 Regularised combined boundary integral equations -- 4 Transmission problems -- 4.1 Steklov-Poincaré operator equations -- 4.2 Combined boundary integral equations -- 5 Conclusions -- Color plates -- Index
This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. The volume surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences. The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Link Print version: Graham, Ivan Direct and Inverse Problems in Wave Propagation and Applications Berlin/Boston : De Gruyter, Inc.,c2013 9783110282238
Subject Radio wave propagation.;Radio waves -- Diffraction.;Radio waves -- Scattering
Electronic books
Alt Author Langer, Ulrich
Melenk, Jens Markus
Sini, Mourad
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