1,721,051 research outputs found
Reliability of the time splitting Fourier method for singular solutions in quantum fluids
Full text linkWe study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross–Pitaevskii equation. In particular, we explore its capability of preserving a steady-state vortex solution, whose density profile is approximated by an accurate diagonal Padé expansion of degree [8,8], here explicitly derived for the first time. We show by several numerical experiments that the Fourier spectral method is only slightly more accurate than a time splitting finite difference scheme, while being reliable and efficient. Moreover, we notice that, at a post-processing stage, it allows an accurate evaluation of the solution outside grid points, thus becoming particularly appealing for applications where high resolution is needed, such as in the study of quantum vortex interactions
The ReLPM Exponential Integrator for FE Discretizations of Advection-Diffusion Equations
No full textBAMPHI: Matrix-free and transpose-free action of linear combinations of?-functions from exponential integrators
No full textThe time integration of stiff systems of Ordinary Differential Equations (ODEs), usually arising from the spatial discretization of Partial Differential Equations (PDEs), constitutes a hot topic in numerical analysis. In particular, exponential-type integrators have attracted much attention for their capacity to effectively handle the stiffness, allowing integration with large time steps. The efficiency of exponential-type integrators strongly relies on the fast computation of the action of the exponential of matrices which often change only slightly during the integration. The authors exploited this characteristic of exponential integrators to develop a backward stable algorithm, BAMPHI, which is designed to reuse the information gathered through the exponential integration steps, reaching unmatched levels of speed and accuracy on a variety of numerical experiments.(c) 2022 Elsevier B.V. All rights reserved
Approximation of the matrix exponential for matrices with a skinny field of values
No full textThe backward error analysis is a great tool which allows selecting in an effective way the scaling parameter s and the polynomial degree of approximation m when the action of the matrix exponential exp(A)v has to be approximated by (p(m)(s(-1)A)(s)v=exp(A+Delta A)v. We propose here a rigorous bound for the relative backward error Delta A(2)/A(2), which is of particular interest for matrices whose field of values is skinny, such as the discretization of the advection-diffusion or the Schrodinger operators. The numerical results confirm the superiority of the new approach with respect to methods based on the classical power series expansion of the backward error for the matrices of our interest, both in terms of computational cost and achieved accuracy
Hyperinterpolation in the cube
Full text linkWe construct an hyperinterpolation formula of degree n in the three-dimensional cube, by using the numerical cubature formula for the product Chebyshev measure given by the product of a (near) minimal formula in the square with Gauss–Chebyshev–Lobatto quadrature
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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