Page
%P
17 Result(s)
within
Larisa Beilina
Numerical Analysis
-
Book
-
Chapter
Approximately Globally Convergent Numerical Method
In this chapter, we present our approximately globally convergent numerical method for a multidimensional CIP for a hyperbolic PDE. This method also works for a similar CIP for a parabolic PDE. The numerical m...
-
Chapter
The Adaptive Finite Element Technique and Its Synthesis with the Approximately Globally Convergent Numerical Method
In Chap. 2, we have described our approximately globally convergent numerical method for a CIP for the hyperbolic \( c\,(x)\,{u_{tt}}=\triangle u.\) ...
-
Chapter
Backscattering Data
In Sects. 6.1–6.8 we describe results of [115]. As to the numerical results of Sect. 6.8, Figs. 6.2a, b were published inMethods and Applications of Analysis [116] and are reprinted with permission. Other figures...
-
Chapter
Two Central Questions of This Book and an Introduction to the Theories of Ill-posed and Coefficient Inverse Problems
This is an introductory chapter. In Sect. 1.1, we outline two central questions discussed in this book. Sections 1.2–1.9 are introductory ones to the theory of illposed problems. In Sects. 1.10 and 1.11, we pr...
-
Chapter
Numerical Implementation of the Approximately Globally Convergent Method
In this chapter, we describe our computational implementation of the approximately globally convergent numerical method of Chap. 2. We use the algorithm of Sect. 2.6.1. Theorems 2.8.2 and 2.9.4 ensure the appr...
-
Chapter
Blind Experimental Data
All tables and figures of this chapter were published in Inverse Problems either in [109] or in [28]. All of them are reprinted with permission. In particular, Tables 5.1– 5.5 and 5.6 were published in [109]. Tab...
-
Book and Conference Proceedings
-
Chapter and Conference Paper
Reconstruction of Dielectric Constants in a Cylindrical Waveguide
We present the model of reconstruction of two constant complex dielectrics in a cylindrical waveguide using frequency domain measurements at the one point of a waveguide. We formulate two gradient-like methods...
-
Chapter and Conference Paper
The Layer-Strip** Algorithm for Reconstruction of Dielectrics in an Optical Fiber
We present a new model of an approximate globally convergent method in a frequency domain for reconstruction of dielectric permittivity of a weakly guiding optical fiber. We consider data which are given only ...
-
Chapter and Conference Paper
Determination of Permittivity from Propagation Constant Measurements in Optical Fibers
We present a new method for determination of dielectric permittivity constant using measurements of fundamental mode of propagation constant in optical fiber’s. We first solve the forward spectral problem to c...
-
Chapter and Conference Paper
Time-adaptive FEM for distributed parameter identification in mathematical model of HIV infection with drug therapy
We propose a time-adaptive finite element method for the solution of a parameter identification problem for ODE system which describes dynamics of primary HIV infection with drug therapy. We present framework ...
-
Chapter and Conference Paper
Methods of Quantitative Reconstruction of Shapes and Refractive Indices from Experimental data
In this chapter we summarize results of [5, 6, 14] and present new results of reconstruction of refractive indices and shapes of objects placed in the air from blind backscattered experimental data using two-s...
-
Chapter and Conference Paper
Convergence of Stabilized P1 Finite Element Scheme for Time Harmonic Maxwell’s Equations
The paper considers the convergence study of the stabilized P1 finite element method for the time harmonic Maxwell’s equations. The model problem is for the particular case of the dielectric permittivity funct...
-
Chapter and Conference Paper
Convergence of Explicit \(P_1\) Finite-Element Solutions to Maxwell’s Equations
This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell’s equations in terms of the sole electric field. The space discretization is per...
-
Chapter and Conference Paper
The Finite Element Method and Balancing Principle for Magnetic Resonance Imaging
This work considers a finite element method in combination with balancing principle for a posteriori choice of the regularization parameter for image reconstruction problem appearing in magnetic resonance imag...
-
Book and Conference Proceedings
Gas Dynamics with Applications in Industry and Life Sciences
On Gas Kinetic/Dynamics and Life Science Seminar, March 25–26, 2021 and March 17–18, 2022
