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51.
In 1983, a preconditioner was proposed [J. Comput. Phys. 49 (1983) 443] based on the Laplace operator for solving the discrete Helmholtz equation efficiently with CGNR. The preconditioner is especially effective for low wavenumber cases where the linear system is slightly indefinite. Laird [Preconditioned iterative solution of the 2D Helmholtz equation, First Year's Report, St. Hugh's College, Oxford, 2001] proposed a preconditioner where an extra term is added to the Laplace operator. This term is similar to the zeroth order term in the Helmholtz equation but with reversed sign. In this paper, both approaches are further generalized to a new class of preconditioners, the so-called “shifted Laplace” preconditioners of the form Δφ−k2φ with
. Numerical experiments for various wavenumbers indicate the effectiveness of the preconditioner. The preconditioner is evaluated in combination with GMRES, Bi-CGSTAB, and CGNR. 相似文献
52.
53.
54.
A new grid‐free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non‐linear conservation equations are converted to linear convection equations with non‐linear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid‐free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid‐free scheme, solution‐based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid‐free scheme. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
55.
Y. A. Coutinho J. A. Martins Simões C. M. Porto 《Zeitschrift fur Physik C Particles and Fields》1997,73(4):705-709
In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e + e ? → W + W ?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin2 α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models. 相似文献
56.
L.-Q. Han S.-Y. Zhao Y.-D. Zhou P.-L. Zhang 《Applied physics. B, Lasers and optics》1997,65(3):399-402
Received: 18 June 1996/Revised version: 3 January 1997 相似文献
57.
Double-diffusive convection due to a cylindrical source submerged in a salt-stratified solution is numerically investigated
in this study. For proper simulation of the vortex generated around the cylinder, a computational domain with irregular shape
is employed. Flow conditions depend strongly on the thermal Rayleigh number, Ra
T
, and the buoyancy ratio, R
ρ. There are two types of onset of instability existing in the flow field. Both types are due to either the interaction of
the upward temperature gradient and downward salinity gradient or the interaction of the lateral temperature gradient and
downward salinity gradient. The onset of layer instability due to plume convection is due to the former, whereas, the onset
of layer instability of layers around the cylinder is due to the latter. Both types can be found in the flow field. The transport
mechanism of layers at the top of the basic plume belongs to former while that due to basic plume and layer around the cylinder
are the latter. The increase in Ra
T
reinforces the plume convection and reduces the layer numbers generated around the cylinder for the same buoyancy ratio.
For the same Ra
T
, the increase of R
ρ suppresses the plume convection but reinforces the layers generated around the cylinder. The profiles of local Nusselt number
reflects the heat transfer characteristics of plume convection and layered structure. The profiles of averaged Nusselt number
are between the pure conduction and natural convection modes and the variation is due to the evolution of layers.
Received on 13 September 1996 相似文献
58.
A technique for the characterization of an interior crack perpendicular to the surface of the plates is presented. A time-harmonic line load is applied on the upper surface of the plate. The scattered displacement field is calculated by using the strip element method. It is found that there are additional superimposed oscillations in the curve of the absolute values of the displacement in the region between the load and the crack. The mean value of the peaks of the additional oscillations increases with the crack length, and is less dependent on the distance from the load to the crack. The crack position is determined from the displacement distribution curve and the crack length is determined from the mean value of the peaks of the additional oscillations. Approximate polynomial formula of degree four for predicting the length of interior vertical cracks in isotropic homogeneous plates is also proposed. Numerical examples are given to demonstrate the present technique. 相似文献
59.
60.
We established that acetylacetone and acetone photolytically sensitize norbornene to undergo an efficient radical addition
of solvent (ranging from hexane, cyclic ethers, haloalkanes, acetone, alcohols and acetonitrile) across the double bond. In
view of its synthetic applicability, sensitized photoreactions of norbornene were reviewed and their mechanisms were compared.
Photolysis of acetylacetone in the presence of norbornene in hexane induced i) acetylacetone to cycloadd to norbornene giving
the expected 1,5-diketone, and ii) sensitization by triplet excited acetylacetone to generate reactive norbornene, which underwent
dimerization as well as the addition of a solvent molecule by radical chain processes. In other solvents, the radical chain
addition of solvent dominated the photoreaction, and superseded the cycloaddition, to give excellent to good yields of adducts
to norbornene. While the excited species of acetylacetone for the sensitization was deduced to be its spectroscopic triplet
excited state, that for the cycloaddition should involve a different one which may be a twisted triplet acetylacetone; sensitization
experiments showed that the cycloaddition did not occur from the spectroscopic triplet state. Triplet excited acetone sensitized
norbornene to undergo the same solvent addition more efficiently and cleanly than acetylacetone did. In view of various conflicts
existing in the proposed energy transfer mechanism, the sensitized norbornene reactions were rationalized with electron transfer
and a cation radical chain mechanism. 相似文献