A multidomain integrated‐radial‐basis‐function collocation method for elliptic problems

This article is concerned with the use of integrated radial‐basis‐function networks (IRBFNs) and nonoverlapping domain decompositions (DDs) for numerically solving one‐ and two‐dimensional elliptic problems. A substructuring technique is adopted, where subproblems are discretized by means of one‐dimensional IRBFNs. A distinguishing feature of the present DD technique is that the continuity of the RBF solution across the interfaces is enforced with one order higher than with conventional DD techniques. Several test problems governed by second‐ and fourth‐order differential equations are considered to investigate the accuracy of the proposed technique. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008     

ON THE RADIAL GROUND STATE OF P-LAPLACIAN EQUATION WITH GRADIENT TERM PERTURBATION

1IntroductionInthispaper,weconsidertheexistence,uniqueuessandnonexistenceoftheradialgroundstatetothefollowingp-Laplacianequation:whereApu=div(IDttl)Du),n>p22,qissubcriticalexponents,i.e.,qo.Bydefinition,afunctionu(x)issaidtobetheradialgroundstateto(1.1),ifu(x)=u(r)satisfies:1)u(r),Iu'Ip-'U'eC'([o, oo));2)u(r)isthesolutionofthefollowingCauchyproblem:3)u(r)satisfiesIn0urf0rmerpaper[1],westlldiedtheexistenceanduniqueness0fradialgroundstatetoproblem(1-1)inthecasewhereq…     

Ability of the radial basis function approach to extrapolate nuclear mass

The ability of the radial basis function(RBF) approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31), Hartree–Fock-Bogoliubov(HFB27), finite-range droplet model(FRDM12) and Weizs?cker-Skyrme(WS4) mass models. It is found that when the RBF approach is employed with a simple linear basis function, different mass models have different performances in extrapolating nuclear masses in the same region, and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions. The WS4 and FRDM12 models(two macroscopic–microscopic mass models), combined with the RBF approach, may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.     

二氧化碳探测仪典型透镜支撑结构的设计及分析(英文)

为了降低外界载荷和温度变化对二氧化碳探测仪光学系统透镜面形及共轴的影响,根据系统的特点和技术要求,对其典型透镜的支撑结构进行了研究,设计了一种径向挠性支撑结构并建立了3D实体模型。运用工程CAD分析软件,采用非线性有限元分析方法对其进行了动静刚度特性和热特性仿真分析,验证了支撑结构设计的合理性。分析结果表明,透镜结构组件的一阶固有频率为1 301 Hz;利用面型拟合,得到了各工况下镜面面形误差值为PV≤λ/10,RMS≤λ/50,偏转误差≤1″。该径向支撑结构能很好地保持透镜共轴精度,减小了温度变化对镜面变形的影响,各项结果满足设计要求,证明了结构设计的合理性。     

三维不规则区域热传导问题无网格方法的数值模拟

配点型无网格法是纯无网格法,它不需要任何背景网格,效率高。本文用加权最小二乘配点方法(Weighted Least-Squares Collocation Method-WLSCM)计算不规则区域热传导问题,形函数采用径向基函数近似。通过二维具有分析解的实例表明WLSCM方法精度高,稳定性好且具有较高的计算效率。此外,将WLSCM方法应用于工程中常见的三维不规则区域热传导问题,结果表明:WLSCM方法的计算结果与FLUENT的计算结果符合很好。     

SOLUTIONS OF A SYSTEM OF FORCED BURGERS EQUATION IN TERMS OF GENERALIZED LAGUERRE POLYNOMIALS

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|n-1eβ|x|2/2,β≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

Solutions of a system of forced burgers equation in terms of generalized laguerre polynomials

In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|ⁿ⁻¹eβ|x|²/2,${\left|x\right|}^{n-1}{e}^{\beta {\left|x\right|}^2}/2,$, β≥0, x ∈?n$\beta \ge 0,\hspace{0.17em}x\hspace{0.17em}\in {?}^n$. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation.     

A compact 9 point stencil based on integrated RBFs for the convection–diffusion equation

In this paper, a high-order compact stencil for solving the convection–diffusion equation in two dimensions is proposed. The convection and diffusion terms are both approximated by means of radial basis functions (RBFs) that are constructed over 3×3$3\times 3$ rectangular stencils. Salient features here are that (i) integration is employed to construct local RBF approximations; and (ii) through the constants of integration, values of the convection–diffusion equation at several selected nodes on the stencil are also enforced. Numerical results indicate that (i) the inclusion of the governing equation into the stencil leads to a significant improvement in accuracy; (ii) when the convection dominates, accurate solutions are obtained at a regime of the RBF width which makes the RBFs peaked; and (iii) high levels of accuracy are achieved using relatively coarse grids.     

A new multiobjective allocator of capacitor banks and distributed generations using a new investigated differential evolution

This article has investigated a new multiobjective allocation of optimal sizing and sitting of distributed generation (DG) units and capacitor banks in simultaneous mode to improve reliability and reduce energy losses. The proposed method consists of four objectives, that is, cost of energy not supplied, system average interruption duration index, costs of energy loss and investment. A novel structure differential evolution has been suggested to solve this nonlinear complex problem and its results are compared with related values of genetic algorithm and simple differential evolutionary algorithm. In addition to the novel objective function, the other contribution of this article is proposing a new model for load and energy cost. Three types of DGs, that is, wind turbine, solar cell, and diesel generator have been used in placement process. To verify the comprehensiveness of the proposed function, three scenarios have been introduced: scenario i: first, placement of DGs, then capacitor banks, scenario ii: first, placement of capacitor banks, and then DGs, and scenario iii: simultaneous placement of DGs and capacitor banks. Simulations have been carried out on one part of practical distribution network in Metropolitan Tabriz in North West of Iran. The results of simulations have been discussed and analyzed using the five novel indices. The obtained simulation results using proposed function shows that the simultaneous placement of DGs and capacitor banks results in more reduction of the energy losses and increase improvements of reliability indices as well as voltage profile. © 2013 Wiley Periodicals, Inc. Complexity 19: 40–54, 2014     

复线性微分方程解的导数的Julia集的径向分布

本文主要研究一类复线性微分方程的整函数解的导数的Julia集的径向分布.在适当条件下,本文证明这类复微分方程的整函数解及其导数的Julia集具有相似的径向分布,并找到了它们的下界,从而改进了最近的一些相关结果.