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
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Article
Open AccessEnergy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media
The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and st...
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Article
Open AccessOn the Maxwell-wave equation coupling problem and its explicit finite-element solution
It is well known that in the case of constant dielectric permittivity and magnetic permeability, the electric field solving the Maxwell’s equations is also a solution to the wave equation. The converse is also...
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Book and Conference Proceedings
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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...
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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...
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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...
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Article
Open AccessReconstruction of annular bi-layered media in cylindrical waveguide section
We consider a radial transverse resonance model for a circular cylindrical waveguide composed into two layers with different frequency dependent complex dielectric constants. An inverse problem with four unkno...
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Book
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Chapter
Erratum to: Numerical Linear Algebra: Theory and Applications
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Chapter
Elements of Perturbation Theory
In this chapter we study the influence of perturbations of matrices on the solutions of such basic problems of linear algebra as calculating eigenvalues and singular values of operators, constructing the inver...
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Chapter
Numerical Solution of Linear Least Squares Problems
In this chapter we present methods for numerical solution of linear least squares problems. These problems arise in many real-life applications such that curve fitting, statistical modelling and different inve...
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Chapter
Algorithms for the Nonsymmetric Eigenvalue Problem
In chapter, we will present the main algorithms for solving the nonsymmetric eigenvalue problem using direct methods. Direct methods are usually applied to dense matrices, and iterative methods such as the R...
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Chapter
Introduction to Iterative Methods for the Solution of Linear Systems
In this chapter we will discuss iterative for the solution of linear systems of equations (LSE) \(Ax=b\) . These algorithms are used when direct methods take a lot of time and computer space to solve this s...
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Chapter
Vector Spaces
In courses on analytic geometry, basic operations with vectors in three-dimensional Euclidean space are studied. If some basis in the space is fixed, then a one-to-one correspondence between geometric vectors ...
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Chapter
Linear Operators
In this chapter we introduce the concept of a linear operator defined on a linear space. We study basic properties of linear operators acting on finite-dimensional linear spaces. We give a detailed investigati...
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Chapter
Vector and Matrix Norms
In this chapter the concept of a norm on the vector space \({\mathbb {C}}^n\) is introduced. We investigate relationships between differe...
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Chapter
Solving Systems of Linear Equations
In this chapter we present algorithms and error analysis of numerical methods for solving linear systems \(Ax=b\) with nonsingular square...
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Chapter
Algorithms for Solution of Symmetric Eigenvalue Problems
In this chapter we will discuss algorithms that can solve only symmetric eigenvalue using direct noniterative methods.
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Chapter
Preliminaries
In this chapter we provide the necessary background from the theory of complex numbers. Then we describe the basic properties of polynomials and their roots. We introduce the concept of determinants, establish...
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Chapter
Inner Product Spaces
As discussed in the previous chapter, vector spaces are analogous to three-dimensional Euclidean space \(\mathbf {V}_3\) of geometric vec...
