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1.
2.
Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial
differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences.
By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via
a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast.
Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized
matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant
matrix.
By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the
block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method.
A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse
GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are
preserved.
AMS subject classification (2000) 43A30, 65T99, 20B25 相似文献
3.
J rgen Rosenqvist Kristina Axe Staffan Sj berg Per Persson 《Colloids and surfaces. A, Physicochemical and engineering aspects》2003,220(1-3):91-104
The adsorption of the dicarboxylates o-phthalate, maleate, fumarate, malonate, and oxalate (representing ligands with the general composition −O2C---Cn---CO2−; n=0, 1, or 2) on gibbsite were studied by means of quantitative batch adsorption experiments and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. The interpretations of ATR-FTIR spectra were aided by comparison with IR spectra of solution species and by results from theoretical frequency calculations. The main objectives of the study were to identify the molecular level bonding mechanisms of the dicarboxylates to gibbsite, and to investigate how these were influenced by the composition and structure of the ligands. Carboxylates with n=2 formed predominantly outer sphere complexes, whereas the importance of inner sphere complexes progressively increased for n=1 and 0. The inner sphere structures were identified as mononuclear chelates with one oxygen from each carboxylate group bonded to Al(III) at the surface. This showed the importance of chelate ring structure for the formation of inner sphere surface complexes, with stabilities of the complexes increasing in the order seven-membered ring less than six-membered ring less than five-membered ring. For ligands with n=2 only small variations in surface speciation were observed as a function of steric factors; irrespective of the relative positions of the carboxylate groups and bulkiness of the ligands outer sphere bonding is the dominating adsorption mode. Adsorption experiments were also conducted with gibbsite particles exhibiting differences in shape and surface roughness. These experiments showed that inner sphere complexes were favored on the less well-developed and more irregular gibbsite particles. 相似文献
4.
5.
During irradiation of liquid samples of 1-vinylimidazole, 2-vinylnaphthalene, 2-vinylpyridine, 4-vinylpyridine and 1,1-diphenylethene
with positive muons, radicals of the type MuCH2ĊHAr (Ar=the appropriate aromatic group), and the MuCH2ĊPh2 radical were observed by transverse field μSR; the muon hyperfine couplings are considered in the context of the effectiveness
of the aryl groups in delocalising the unpaired electron. 相似文献
6.
Gašper Jaklič Jernej Kozak Marjeta Krajnc Vito Vitrih Emil Žagar 《Numerical Algorithms》2007,45(1-4):49-60
In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric
coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries
over to triangulations in a natural way. The construction is based upon group action of S
3 on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.
相似文献
7.
Juan Pablo Trelles Emil Pfender Joachim Heberlein 《Plasma Chemistry and Plasma Processing》2006,26(6):557-575
The dynamics of the electric arc inside a direct current non-transferred arc plasma torch are simulated using a three-dimensional, transient, equilibrium model. The fluid and electromagnetic equations are solved numerically in a fully coupled approach by a multiscale finite element method. Simulations of a torch operating with argon and argon–hydrogen under different operating conditions are presented. The model is able to predict the operation of the torch in steady and takeover modes without any further assumption on the reattachment process except for the use of an artificially high electrical conductivity near the electrodes, needed because of the equilibrium assumption. The results obtained indicate that the reattachment process in these operating modes may be driven by the movement of the arc rather than by a breakdown-like process. It is also found that, for a torch operating in these modes and using straight gas injection, the arc will tend to re-attach to the opposite side of its original attachment. This phenomenon seems to be produced by a net angular momentum on the arc due to the imbalance between magnetic and fluid drag forces. 相似文献
8.
A necessary and sufficient condition for regularity of the
-Neumann operator on (0,q)-forms in a smooth bounded pseudoconvex domain in Cn is that the orthogonal projections onto
-closed forms of degrees (0,q−1), (0,q), and (0,q+1) all be regular.
The first author partially supported by NSF Grant DMS-8701038 相似文献
9.
10.
Kolman David Heberlein Joachim Pfender Emil 《Plasma Chemistry and Plasma Processing》1998,18(1):73-89
In this paper, a comprehensive model for thermal plasma chemical vapor deposition (TPCVD) with liquid feedstock injection is documented. The gas flow is assumed to be steady, of a single temperature. Radiation and charged species contributions are excluded, but extensive homogeneous and heterogeneous chemistry is included. The liquid phase is traced by considering individual droplets. Discussion on the model's application to diamond production from acetone in a hydrogen–argon plasma is included. The major conclusions are: (1) Liquid injection possesses a capability to deliver the hydrocarbon precursor directly onto the deposition target. (2) For the case of complete evaporation of the droplet before reaching the substrate, the deposition rate is similar to that obtained with gaseous precursors. (3) The computational results compare well with experimental data. The modeling results can be used to optimize the injection parameters with regard to the deposition rate. 相似文献