In this paper,the time-dependent Maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are *** and uniqueness of the modeling equations are *** fully discrete finite element sch...
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In this paper,the time-dependent Maxwell’s equations used to modeling wave propagation in dispersive lossy bi-isotropic media are *** and uniqueness of the modeling equations are *** fully discrete finite element schemes are proposed,and their practical implementation and stability are discussed.
We first derive the asymptotic expansion of the bilinear finite volume element for the linear parabolic problem by employing the energy-embedded method on uniform grids, and then obtain a high accuracy combination poi...
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We first derive the asymptotic expansion of the bilinear finite volume element for the linear parabolic problem by employing the energy-embedded method on uniform grids, and then obtain a high accuracy combination pointwise formula of the derivatives for the finite volume element approximation based on the above asymptotic expansion. Furthermore, we prove that the approximate derivatives have the convergence rate of order two. Numerical experiments confirm the theoretical results.
In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then,...
In this paper, combining some special eigenvalue inequalities of matrix’s product and sum with the equivalent form of the continuous coupled algebraic Riccati equation (CCARE), we construct linear inequalities. Then, in terms of the properties of M-matrix and its inverse matrix, through solving the derived linear inequalities, we offer new upper matrix bounds for the solution of the CCARE, which improve some of the recent results. Finally, we present a corresponding numerical example to show the effectiveness of the given results.
Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl -operato...
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Two-level additive preconditioners are presented for edge element discretizations of time-harmonic Maxwell equations. The key is to construct a special “coarse mesh” space, which adds the kernel of the curl -operator in a fine space to a coarse mesh space, to solve the original problem, and then uses the fine mesh space to solve the H ( curl ) -elliptic problem. It is shown that the generalized minimal residual (GMRES) method applied to the preconditioned system converges uniformly provided that the coarsest mesh size is reasonably small (but independent of the fine mesh size) and the parameter for the “coarse mesh” space solver is sufficiently large. Numerical experiments show the efficiency of the proposed approach.
This paper summarizes significant progress in quantifying organic substituent effects in the last 20 years. The main content is as follows: (1) The principle of electronegativity equalization has gained wide acceptanc...
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This paper summarizes significant progress in quantifying organic substituent effects in the last 20 years. The main content is as follows: (1) The principle of electronegativity equalization has gained wide acceptance, and has been used to calculate the intramolecular charge distribution and inductive effect of groups. A valence electrons equalization method was proposed to compute the molecular electronegativity on the basis of geometric mean method, harmonic mean method, and weighted mean method. This new calculation method further extended the application of the principle of electronegativity equalization. (2) A scale method was established for experimentally determining the electrophilic and nucleophilic ability of reagents, in which benzhydryliumions and quinone methides were taken as the reference compounds, and the research field was extended to the gas phase conditions, organometallic reaction and radicals system. Moreover, the nucleophilicity parameters N and electrophilicity parameters E for a series of reagents were obtained. The definition and quantitative expression of electrophilicity index ω and nucleophilicity index ω - were proposed theoretically, and the correlation between the parameters from experimental determination and the indexes from theoretical calculation was also investigated. (3) The polarizability effect parameter was initially calculated by empirical method and further developed by quantum chemistry method. Recently, the polarizability effect index of alkyl (PEI) and groups (PEIX) were proposed by statistical method, and got wide applications in explaining and estimating gas-phase acidity and basicity, ionization energy, enthalpy of formation, bond energy, reaction rate, water solubility and chromatographic retention for organic compounds. (4) The excited-state substituent constant σ ccex obtained directly from the UV absorption energy data of substituted benzenes, is different from the polar constants in molecular ground state and th
We discuss the cubic spline collocation method with two parameters for solving the initial value problems (IVPs) of fractional differential equations (FDEs). Some results of the local truncation error, the convergence...
In this paper,a new numerical algorithm for solving the time fractional Fokker-Planck equation is *** analysis of local truncation error and the stability of this method are *** analysis and numerical experiments show...
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In this paper,a new numerical algorithm for solving the time fractional Fokker-Planck equation is *** analysis of local truncation error and the stability of this method are *** analysis and numerical experiments show that the proposed method has higher order of accuracy for solving the time fractional Fokker-Planck equation.
We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averag...
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We propose some new weighted averaging methods for gradient recovery,and present analytical and numerical investigation on the performance of these weighted averaging *** is shown analytically that the harmonic averaging yields a superconvergent gradient for any mesh in one-dimension and the rectangular mesh in *** results indicate that these new weighted averaging methods are better recovered gradient approaches than the simple averaging and geometry averaging methods under triangular mesh.
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