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Let A = A* ∈ Mn and ${\cal L} = \{ (U_k, \lambda_k)|\; U_k \in {\mathbb{C}}^n, ||U_k|| = 1$ and λk ∈ ℝ } for k = 1,⋯,n be the set of eigenpairs of A. In this paper we develop a modified Newton method that converges to a point in starting from any point in a compact subset ...
A new mesh smoothing algorithm that can improve quadrilateral mesh quality is presented. Poor quality meshes can produce inaccurate finite element analysis; their improvement is important. The algorithm improves mesh quality by adjusting the position of the mesh’s internal nodes based on optimization of a torsion spring system using a Gauss-Newton-based approach. The approach obtains a reasonably...
The work presented here is an experimental study of four iterative algorithms for solving the Inverse Additive Singular Value Problem (IASVP). The algorithms are analyzed and evaluated with respect to different points of view: memory requirements, convergence, accuracy and execution time, in order to observe their behaviour with different problem sizes and to identify those capable to solve the problem...
A method for computing orthogonal URV/ULV decompositions of block tridiagonal (or banded) matrices is presented. The method discussed transforms the matrix into structured triangular form and has several attractive properties: The block tridiagonal structure is fully exploited; high data locality is achieved, which is important for high efficiency on modern computer systems; very little fill-in occurs,...
Computing a few eigenpairs of large-scale matrices is a significant problem in science and engineering applications and a very active area of research. In this paper, two methods that compute extreme eigenpairs of positive-definite matrix pencils are combined into a hybrid scheme that inherits the advantages of both constituents. The hybrid algorithm is developed and analyzed in the framework of model-based...
In the paper we design an adaptive numerical method to solve stiff ordinary differential equations with any reasonable accuracy set by the user. It is a two-step second order method possessing the A-stability property on any nonuniform grid [3]. This method is also implemented with the local-global step size control developed earlier in [8] to construct the appropriate grid automatically. It is shown...
The Continuation of Invariant Subspaces (CIS) algorithm produces a smoothly varying basis for an invariant subspace $\mathcal{R}(s)$ of a parameter-dependent matrix A(s). In the case when A(s) is the Jacobian matrix for a system that comes from a spatial discretization of a partial differential equation, it will typically be large and sparse. Cl_matcont is a user-friendly matlab package for the...
In this paper, we present a new approach to simulate time-dependent initial value differential equations which solutions have a common property of blowing-up in a finite time. For that purpose, we introduce the concept of “sliced-time computations”, whereby, a sequence of time intervals (slices) {[Tn − 1, Tn]| n ≥ 1} is defined on the basis...
Modeling unsaturated flow using numerical techniques such as the finite element method can be especially difficult because of the highly nonlinear nature of the governing equations. This problem is even more challenging when a steady-state solution is needed. This paper describes the implementation of a pseudo-transient technique to drive the solution to steady-state and gives results for a real-world...
Spherical Harmonic Transforms (SHTs) which are essentially Fourier transforms on the sphere are critical in global geopotential and related applications. Discrete SHTs are more complex to optimize computationally than Fourier transforms in the sense of the well-known Fast Fourier Transforms (FFTs). Furthermore, for analysis purposes, discrete SHTs are difficult to formulate for an optimal discretization...
The Newton-Krylov method is used to solve the incompressible Navier-Stokes equations. In the present study, two numerical schemes are considered for the method: employing the predictor-corrector method as preconditioner, and solving the equations without the preconditioner. The standard driven cavity flow is selected as the test problem to demonstrate the efficiency and the reliability of the present...
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