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Showing 1 to 20 of 121 for “"Eigenvalue Problem"”.
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Parallel symmetric eigenvalue problem solvers
<p>Sparse symmetric eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and spectral reordering, for example. Often, the large size of these problems requires the development of eigensolvers that scale well on parallel …
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Solving an eigenvalue problem in laser simulation
… is presented. This approach is based on an eigenvalue problem for singularly perturbed partial differential operators with complex coefficients; such operators have not been investigated in detail until now. The eigenvalue problem is discretized by finite elements, and convergence of the …
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Eigenvalue Problem for the 1-Laplace Operator
We consider the eigenvalue problem associated to the 1-Laplace operator. We define higher eigensolutions by means of weak slope and establish existence of a sequence of eigensolutions by using nonsmooth critical point theory. In addition, we deduce a new necessary condition for the first eigenvalue …
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On Solving the Large Sparse Generalized Eigenvalue Problem
… for solving the large sparse generalized eigenvalue problem Ax = (lamda)Bx. The matrices A and B are assumed to be symmetric, and haphazardly sparse, with B being positive definite. The problem is treated from a constrained optimization approach and an inverse iteration is developed which …
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Damage Detection Based on the Geometric Interpretation of the Eigenvalue Problem
… convexity of the geometric interpretation of the eigenvalue problem for undamped positive definite systems. The damage detection scheme establishes various damage scenarios which are used as failure sets. These scenarios are then compared to the structure's actual response by measuring the natural …
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Acceleration of convergence in solving the eigenvalue problem by matrix iteration using the power method
… Hotelling deflation, for the solution of the problem K.x = ω².M.x is here proposed. The problem can be written in the form D.x =λ.x, and the modification consists of raising the matrix D to an appropriate power p before carrying out the iteration process. The selection of a satisfactory value …
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Perturbation methods for slightly damped gyroscopic systems
… perturbation theory applicable to the algebraic eigenvalue problem. The objective is to express the perturbed eigenvalues and eigenvectors in terms of the unperturbed eigenvalues and eigenvectors and the perturbing matrices, without solving a new eigenvalue problem. If all of the unperturbed …
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An Sn Application of Homotopy Continuation in Neutral Particle Transport
… This occurs in higher dimensional heterogeneous problems [51]. We focus on utilizing homotopy continuation as a means of providing a better initial guess for difficult problems. We investigate various homotopy formulations for two primary diffcult problems: a thick-diffusive fixed internal …
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Multilevel solution procedures for structural dynamics eigenvalue problems
… that can solve the symmetric generalized eigenvalue problem encountered in structural dynamics. First, the multigrid algorithm for solving linear matrix equations is incorporated into the subspace iteration and block Lanczos methods to produce implicit subspace and Lanczos multigrid …
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Integrating matrix method for determining the natural vibrations of a rotating, unsymmetrical beam with application to twisted propeller blades
… equations is obtained in the form of an eigenvalue problem. The solutions to the eigenvalue problem are determined by an iteration method based upon a special orthogonality relationship which is derived. Numerical examples, including an application to a twisted propeller blade, are …
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Active control of distributed structures
… solution to the linear optimal control problem for the distributed structure. The optimal control forces are ideally distributed. If implementation of distributed control is not feasible, then the distributed control forces can be approximated by finite-dimensional control forces. The …
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Linear stability analysis of non-reacting and reacting elliptical jets
… basic flow. For the elliptical jet, an algebraic eigenvalue problem has been formulated by applying the Chebyshev and Fourier spectral collocation method to the disturbance equations of the flow expressed in a generalized cylindrical coordinate system. The resulting algebraic eigenvalue problem …
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Thermal Post-Buckling and Vibration Analysis of Thermally Buckled Antisymmetrically Laminated Beams Using a 20 DOF Finite Element
… and dynamic parts. For buckling analysis, the eigenvalue problem was solved for the critical temperature. The scaled first mode shape was used as the trial displacement vector for post-buckling deflection analysis, which employed a Newton-Raphson type iterative procedure. Once the final static …
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Application of wavelets in few-body problems.
… in light-front quantum field theory. Once the problem is stated in the form of an integral equation, a wavelet basis of a particular scale is used to discretize the problem into a dense matrix. Wavelets are a class of functions with special properties. Daubachies wavelets are a subset of …
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Sensitivity analysis and approximation methods for general eigenvalue problems
… reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method …
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Estudo teórico da estabilidade lateral de hastes submetidas a uma protensão externa
… of the characteristic equation obtained from the eigenvalue problem.
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Ab Initio Computation of Radiative Properties of Monatomic Hydrogen
… wave equation is cast as a discretized matrix eigenvalue problem which is solved using the ERAU parallel supercomputer. The numerical solutions for the wave functions are then integrated to determine the Einstein coefficients for emission and absorption, and hence the gas properties are …
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Numerical Study of Plasmon Resonances in Nanoparticles
… is presented. In this technique, the problem of determining the plasmon resonant frequencies is framed as an integral equation based eigenvalue problem, and the plasmon resonant frequencies can be directly found through the solution of this eigenvalue problem. For this reason, it is …
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The Transient Response of Flat Plates Using the Finite Element Method
… the former may be determined by solving a matrix eigenvalue problem followed by modal analysis. In contrast the equation of motion of a plate is derived as a fourth order partial differential equation. The finite element method is described with particular reference to plate bending by considering …
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