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941.
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
942.
In this paper we formulate a theorem on the persistence of elliptic lower-dimensional invariant tori for nearly integrable analytic Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition, and give the measure estimates of parameters for the non-resonance conditions under Rüssmann’s non-degeneracy condition, which is essential for the proof of our result. 相似文献
943.
Sedimentation and erosion processes in sedimentary basins can be modeled by a parabolic equation with a limiter on the fluxes and a constraint on the time variation.This limiter happens to satisfy a stationary scalar hyperbolic inequality,within a constraint,for which the authors prove the existence and the uniqueness of the solution.Actually,this solution is shown to be the maximal element of a convenient convex set of functions.The existence proof is obtained thanks to the use of a numerical scheme. 相似文献
944.
Jing-na Li Xiao-feng Wang Zheng-an Yao 《应用数学学报(英文版)》2007,23(3):421-432
In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail. 相似文献
945.
Xi Nian FANG Jian Hua WANG 《数学学报(英文版)》2006,22(6):1819-1824
In this paper, we study the extension of isometries between the unit spheres of normed space E and C(Ω). We obtain that any surjective isometry between the unit spheres of normed space E and C(Ω) can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley's problem (where Ω be a compact metric space). 相似文献
946.
D Shaw 《The Journal of the Operational Research Society》2006,57(7):830-841
Problem-structuring group workshops can be used in organizations as a consulting tool and as a research tool. One example of the latter is using a problem-structuring method (PSM) to help a group tackle an organizational issue; meanwhile, researchers collect the participants’ initial views, discussion of divergent views, the negotiated agreement, and the reasoning for outcomes emerging. Technology can help by supporting participants in freely sharing their opinions and by logging data for post-workshop analyses. For example, computers let participants share views anonymously and without being influenced by others (as well as logging those views), and video-cameras can record discussions and intra-group dynamics. This paper evaluates whether technology-supported Journey Making workshops can be effective research tools that can capture quality research data when compared against theoretical performance benchmarks and other qualitative research tools. 相似文献
947.
Alexander Semenov Aurélia Charlot Rachel Auzély-Velty Marguerite Rinaudo 《Rheologica Acta》2007,46(5):541-568
Dynamics of associating polymer solutions above the reversible gelation point are studied. Each macromolecule consists of
a soluble backbone (B) and a small fraction of specific strongly interacting groups (A or C stickers) attached to B. A mixture
of B–A and B–C associating polymers with 1:1 stoichiometric ratio is considered. As a result of AC association, the polymers
reversibly gelate above the overlap concentration. It is shown that (1) the network strands are linear complexes (double chains)
of B–A and B–C; (2) “diffusion” of the network junction points is characterized by an apparent activation energy, which can
be significantly higher than the energy of one AC bond; (3) most importantly, the randomness of sticker distribution along
the chain can significantly slow down the network relaxation leading to a markedly non-Maxwellian viscoelastic behavior. The
theory elucidates the most essential features of rheological behavior of polysaccharide associating systems (with A = adamantyl
moiety, C = β-cyclodextrin, B = either chitosan or hyaluronan) including similar behavior of G
′ and G
″ in a wide frequency range, strong temperature dependence of the characteristic frequency ω
x
, and an extremely strong effect of added free stickers (fC) on the dynamics.
This paper was presented at Annual European Rheology Conference (AERC) held in Hersonisos, Crete, Greece, April 27–29, 2006. 相似文献
948.
Jing Ping YANG Shi Hong CHENG Xiao Qian WANG 《数学学报(英文版)》2007,23(3):467-478
This paper investigates bivariate recursive equations on excess-of-loss reinsurance. For an insurance portfolio, under the assumptions that the individual claim severity distribution has bounded continuous density and the number of claims belongs to R1 (a, b) family, bivariate recursive equations for the joint distribution of the cedent's aggregate claims and the reinsurer's aggregate claims are obtained. 相似文献
949.
Meghan Griffith 《Acta Analytica》2007,22(1):16-28
In this paper, I argue that trying is the locus of freedom and moral responsibility. Thus, any plausible view of free and
responsible action must accommodate and account for free tryings. I then consider a version of agent causation whereby the
agent directly causes her tryings. On this view, the agent is afforded direct control over her efforts and there is no need
to posit—as other agent-causal theorists do—an uncaused event. I discuss the potential advantages of this sort of view, and
its challenges. 相似文献
950.