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Direct and inverse problems in wave propagation and applications / edited by Ivan Graham, Ulrich Langer, Jens Markus Melenk, Mourad Sini. — 1 online resource. — <URL:http://elib.fa.ru/ebsco/661697.pdf>.

Дата создания записи: 11.11.2013

Тематика: Radio wave propagation.; Radio waves — Scattering.; Radio waves — Diffraction.; TECHNOLOGY & ENGINEERING / Mechanical

Коллекции: EBSCO

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Оглавление

  • 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

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