Intro; Preface; Contents; Optimization Analysis of a 2D Magnetic Cloaking Problem for Bilayer Structure; 1 Introduction; 2 Statement of Direct Magnetic Scattering Problem; 3 Formulation of the Inverse Problem. Applying the Optimization Method. Derivation of the Optimality System; 4 Uniqueness and Stability of Optimal Solutions; References; Synthesis Problem and Mathematical Modeling of Multilayered Absorbing Coating; 1 Introduction; 2 Synthesis Problem; 3 Mathematical Statement of the Inverse Problem; 3.1 A Perfect Conductor. Two-Sectional Diaphragm

3.2 A ``Good'' Conductor. Two-Sectional Diaphragm4 Synthesis Problem; 5 Numerical Results; 6 Conclusion; References; Reconstruction of Inhomogeneity Parameters by Measurements of Near Field Outside the Body; 1 Introduction; 2 Statement of the Direct Problem; 3 Discretization of the Direct Problem; 4 Inverse Problem; 5 Numerical Results; 6 Conclusion; 7 Funding; References; Diffraction of TE Polarized Electromagnetic Waves by a Layer with a Nonlinear Medium; 1 Introduction; 2 Statement of the Problem; 3 Saturated Nonlinearity; 4 Kerr Nonlinearity; 5 Numerical Results; References

A Nonlinear Multiparameter EV Problem1 Introduction; 2 Statement of the Problem; 3 Nonlinear Integral Equations; 4 Investigation of the Operator Equation; 5 Existence of Eigentuples; 5.1 The Linear Problem; 5.2 The Nonlinear Problem; 6 Conclusion; References; Numerical Study of the Azimuthal Symmetric Hybrid Waves in a Nonlinear Cylindrical Waveguide; 1 Introduction; 2 Statement of the Problem; 3 Numerical Method; 4 Numerical Results; 5 Conclusion and Discussion; References; Two-Step Method for Solving Inverse Problem of Diffraction by an Inhomogenous Body; 1 Introduction

2 Theoretical Investigation of the Problem2.1 Quasi-Classical Formulation of the Direct Scattering Problem; 2.2 The Lippmann-Schwinger Integral Equation; 2.3 Statement of the Inverse Problem; 2.4 The Two-Step Method for Solving the Inverse Diffraction Problem; 2.5 On Uniqueness of a Solution to the Integral Equation of the First Kind; 3 Numeric Study of the Inverse Problem; References; Numerical Studies of the Lagrangian Approach for Reconstruction of the Conductivity in a Waveguide; 1 Introduction; 2 Statement of the Forward and Inverse Problems; 3 Tikhonov Functional; 4 Lagrangian Approach

5 Finite Element Method for the Solution of an Optimization Problem5.1 Finite Element Discretization; 5.2 Fully Discrete Scheme; 5.3 The Algorithm; 6 Numerical Studies; 6.1 Test Case (i); 6.2 Test Case (ii); 6.3 Test Case (iii); 6.4 Test Case (iv); 7 Discussion and Conclusion; References; On Finite Element Method for Magnetic Resonance Imaging; 1 Introduction; 2 Statement of the Forward and Inverse Problem; 3 The Finite Element Method for Minimization of the Tikhonov Functional; 4 The Adaptive Algorithm; 5 Numerical Experiment; 5.1 MR Data Acquisition