1,721,015 research outputs found
THE SCHWARZ ALGORITHM FOR SPECTRAL METHODS
No full textRecently, the Schwarz alternating method has been successfully coupled to spatial discretizations of spectral type, in order to solve boundary value, problems in complex, geometries with infinite order accuracy. In this paper, a simple version of the method is considered. A proof of its convergence is given in the energy norm, exploiting the properties of discrete-harmonic polynomials and a discrete maximum principle for spectral methods. More general situations can be handled theoretically in one space dimension
Spectral and pseudo-spectral methods for parabolic problems with non periodic boundary conditions
No full textThe advection-diffusion equation is approximated by Chebyshev and Legendre spectral and pseudo-spectral methods. Stability results in the energy norm and error estimates in terms of the discretization parameter and of the regularity of the solution in weighted Sobolev norms are presented.
© 1981 Instituto di Elaborazione della Informazione del CNR
Preconditioned minimal residual methods for chebyshev spectral calculations
No full textThe problem of preconditioning the pseudospectral Chebyshev approximation of an elliptic operator is considered. The numerical sensitivity to variations of the coefficients of the operator are investigated for two classes of preconditioning matrices: one arising from finite differences, the other from finite elements. The preconditioned system is solved by a conjugate gradient type method, and by a DuFort-Frankel method with dynamical parameters. The methods are compared on some test problems with the Richardson method [13] and with the minimal residual Richardson method [21].
© 1985
Combined finite element and spectral approximation of the Navier-Stokes equations
No full textWe present a method for the numerical approximation of Navier-Stokes equations with one direction of periodicity. In this direction a Fourier pseudospectral method is used, in the two others a standard F.E.M. is applied. We prove optimal rate of convergence where the two parameters of discretization intervene independently. © 1984 Springer-Verlag
Analysis of the combined finite element and Fourier interpolation
No full textWe consider Lagrange interpolation involving trigonometric polynomials of degree ≦N in one space direction, and piecewise polynomials over a finite element decomposition of mesh size ≦h in the other space directions. We provide error estimates in non-isotropic Sobolev norms, depending additively on the parameters h and N. An application to the convergence analysis of an elliptic problem, with some numerical results, is given. © 1982 Springer-Verlag
Adaptive Fourier-Galerkin Methods
No full textWe study the performance of adaptive Fourier-Galerkin methods in a periodic box in {R}^d with dimension d >= 1. These methods offer unlimited approximation power only restricted by solution and data regularity. They are of intrinsic interest but are also a first step towards understanding adaptivity for the hp-FEM. We examine two nonlinear approximation classes, one classical corresponding to algebraic decay of Fourier coefficients and another associated with exponential decay. We study the sparsity classes of the residual and show that they are the same as the solution for the algebraic class but not for the exponential one. This possible sparsity degradation for the exponential class can be compensated with coarsening, which we discuss in detail. We present several adaptive Fourier algorithms, and prove their contraction and optimal cardinality properties
CHEBYSHEV SPECTRAL METHOD FOR GAS TRANSIENTS IN PIPELINES
No full textA Chebyshev pseudospectral method is proposed for slow transients simulation of gas-transportation systems. The scheme is theoretically investigated. Comparisons with the Lax-Wendroff scheme prove that the Chebyshev method is more efficient in terms of storage and computer time. Infinite-order accuracy for smooth solutions is predicted by the theory and observed in the experiments
On the boundary treatment in spectral methods for hyperbolic systems
Full text linkSpectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions are clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100
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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