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Articles 1 - 16 of 16
Full-Text Articles in Physical Sciences and Mathematics
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
Michigan Tech Publications
In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s − 1) is obtained if the corresponding eigenvector u ∈ Hs − 1(Ω) and ∇ × u ∈ Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation.
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
A Priori And A Posteriori Error Estimates For The Quad-Curl Eigenvalue Problem, Lixiu Wang, Qian Zhang, Jiguang Sun, Zhimin Zhang
Michigan Tech Publications
In this paper, we consider a priori and a posteriori error estimates of the H(curl2)-conforming finite element when solving the quad-curl eigenvalue problem. An a priori estimate of eigenvalues with convergence order 2(s 1) is obtained if the corresponding eigenvector u a Hs 1(Ω) and-u a Hs(Ω). For the a posteriori estimate, by analyzing the associated source problem, we obtain lower and upper bounds for the errors of eigenvectors in the energy norm and upper bounds for the errors of eigenvalues. Numerical examples are presented for validation.
(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, Md. Fayz-Al-Asad, Md. Al-Rumman, Md. Nur Alam, Salma Parvin, Cemil Tunç
(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, Md. Fayz-Al-Asad, Md. Al-Rumman, Md. Nur Alam, Salma Parvin, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped -dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs …
Eigenvalue Problems On Atypical Domains - The Finite Element Method, Toufiic Ayoub
Eigenvalue Problems On Atypical Domains - The Finite Element Method, Toufiic Ayoub
Undergraduate Student Research Internships Conference
Why do we care about eigenvalues and eigenvectors? What's the big deal? For many people enrolled in entry level linear algebra courses, these concepts seem like far fetched abstractions that become pointless exercises in computation. But in reality, these fundamental ideas are vital to how we live our lives every single day. But how?
Inexact And Nonlinear Extensions Of The Feast Eigenvalue Algorithm, Brendan E. Gavin
Inexact And Nonlinear Extensions Of The Feast Eigenvalue Algorithm, Brendan E. Gavin
Doctoral Dissertations
Eigenvalue problems are a basic element of linear algebra that have a wide variety of applications. Common examples include determining the stability of dynamical systems, performing dimensionality reduction on large data sets, and predicting the physical properties of nanoscopic objects. Many applications require solving large dimensional eigenvalue problems, which can be very challenging when the required number of eigenvalues and eigenvectors is also large. The FEAST algorithm is a method of solving eigenvalue problems that allows one to calculate large numbers of eigenvalue/eigenvector pairs by using contour integration in the complex plane to divide the large number of desired pairs …
Generalized Problem Of Thermal Bending Analysis In The Cartesian Domain, V. S. Kulkarni, Vinayaki Parab
Generalized Problem Of Thermal Bending Analysis In The Cartesian Domain, V. S. Kulkarni, Vinayaki Parab
Applications and Applied Mathematics: An International Journal (AAM)
This is an attempt for mathematical formulation and general analytical solution of the most generalized thermal bending problem in the Cartesian domain. The problem has been formulated in the context of non-homogeneous transient heat equation subjected to Robin’s boundary conditions. The general solution of the generalized thermoelastic problem has been discussed for temperature change, displacements, thermal stresses, deflection, and deformation. The most important feature of this work is any special case of practical interest may be readily obtained by this most generalized mathematical formulation and its analytical solution. There are 729 such combinations of possible boundary conditions prescribed on parallelepiped …
Sparse Sums With Bases Of Chebyshev Polynomials Of The Third And Fourth Kind, Maryam Shams Solary
Sparse Sums With Bases Of Chebyshev Polynomials Of The Third And Fourth Kind, Maryam Shams Solary
Turkish Journal of Mathematics
We derive a generalization for the reconstruction of $M$-sparse sums in Chebyshev bases of the third and fourth kind. This work is used for a polynomial with Chebyshev sparsity and samples on a Chebyshev grid of $[-1,1]$. Further, fundamental reconstruction algorithms can be a way for getting M-sparse expansions of Chebyshev polynomials of the third and fourth kind. The numerical results for these algorithms are designed to compare the time effects of doing them.
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.
Localized Meshless Methods With Radial Basis Functions For Eigenvalue Problems, Amy M. Kern
Localized Meshless Methods With Radial Basis Functions For Eigenvalue Problems, Amy M. Kern
Honors Theses
Two localized meshless methods with radial basis functions are considered for solving eigenvalue problems on two different domains, i.e., a L-shaped domain and an irregular domain. The irregular domain used in this study comes from an application of the eigenvalue problem as it plays a role in the reconstruction of velocity vector fields. This study finds that both localized Kansa’s method and the Localized Method of Approximate Particular Solutions provide a good numerical approximation to the solution of the eigenvalue problem. Through numerical experiments, a good value for the shape parameter can be determined for each domain for each method …
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
William F. Trench
Let $R=P \diag(\gamma_{0}I_{m_{0}}, \gamma_{1}I_{m_{1}}, \dots, \gamma_{k-1}I_{m_{k-1}})P^{-1}\in\mathbb{C}^{m\times m}$ and $S_{\sigma}=Q\diag(\gamma_{\sigma(0)}I_{n_{0}},\gamma_{\sigma(1)}I_{n_{1}}, \dots,\gamma_{\sigma(k-1)}I_{n_{k-1}})Q^{-1}\in\mathbb{C}^{n\times n}$, where $m_{0}+m_{1}+\cdots +m_{k-1}=m$, $n_{0}+n_{1}+\cdots+n_{k-1}=n$, $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$ are distinct complex numbers, and $\sigma :\mathbb{Z}_{k}\to\mathbb{Z}_{k}= \{0,1, \dots, k-1\}$. We say that $A\in\mathbb{C}^{m\times n}$ is $(R,S_{\sigma})$-commutative if $RA=AS_{\sigma}$. We characterize the class of $(R,S_{\sigma})$-commutative matrrices and extend results obtained previously for the case where $\gamma_{\ell}=e^{2\pi i\ell/k}$ and $\sigma(\ell)=\alpha\ell+\mu \pmod{k}$, $0 \le \ell \le k-1$, with $\alpha$, $\mu\in\mathbb{Z}_{k}$. Our results are independent of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$, so long as they are distinct; i.e., if $RA=AS_{\sigma}$ for some choice of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{_{k-1}}$ (all distinct), then $RA=AS_{\sigma}$ for arbitrary of …
Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, William F. Trench
Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, William F. Trench
William F. Trench
No abstract provided.
Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench
Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench
William F. Trench
No abstract provided.
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
Characterization And Properties Of Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
William F. Trench
No abstract provided.
An Oscillation Theorem For Discrete Eigenvalue Problems, Martin Bohner, Ondřej Došlý, Werner Kratz
An Oscillation Theorem For Discrete Eigenvalue Problems, Martin Bohner, Ondřej Došlý, Werner Kratz
Mathematics and Statistics Faculty Research & Creative Works
In this paper we consider problems that consist of symplectic difference systems depending on an eigenvalue parameter, together with self-adjoint boundary conditions. Such symplectic difference systems contain as important cases linear Hamiltonian difference systems and also Sturm-Liouville difference equations of second and of higher order. The main result of this paper is an oscillation theorem that relates the number of eigenvalues to the number of generalized zeros of solutions.