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The Method of Fundamental solutions for solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number

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Advances in Applied Mathematics and Mechanics 2013年第4期5卷 477-493页

作者： Wen chen Ji Lin c.s.chen college of Engineering Mechanics Hohai UniversityNanjing 210098JiangsuChina Department of Mathematics University of Southern MississippiHattiesburgMS 39406USA

In this paper,we investigate the method of fundamental solutions(MFs)for solving exterior Helmholtz problems with high wave-number in axisymmetric *** the coefficientmatrix in the linear system resulting fromtheMFs approximation has a block circulant structure,it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory *** numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains.

关键词： Method of fundamental solutions exterior Helmholtz problem circulant matrix fast Fourier transform axisymmetric domain

Geometric Design of Letters in Times Roman Font via RBF Meshless collocation Method

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Numerical Mathematics(Theory,Methods and Applications) 2023年第3期16卷 752-768页

作者： Lionel Amuzu c.s.chen Kwesi Acheampong Huiqing Zhu school of Mathematics and Natural sciences University of Southern MississippiHattiesburgMSUSA

Two mathematical models in the context of boundary value problems are proposed for the geometric design of letters in Times Roman *** adopt radial basis function meshless collocation method for numerically solving the two proposed mathematical models in 2D and *** this paper,B´ezier curves play an important role in the design of the *** examples with simply and multiply-connected domains in 2D and 3D are presented to demonstrate the visual effect of the letters in Times Roman font.

关键词： Kansa method Bezier curve implicit surface computer graphics image reconstruction meshless method radial basis functions

A Revisit on the Derivation of the Particular solution for the Differential Operator ∆^(2) ± λ^(2)

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Advances in Applied Mathematics and Mechanics 2009年第6期1卷 750-768页

作者： Guangming Yao c.s.chen chia cheng Tsai Department of Mathematics University of Southern MississippiHattiesburgMS 39406USA Department of Marine Environment Engineering National Kaohsiung Marine UniversityTaiwanChina

In this paper,we applied the polyharmonic splines as the basis functions to derive particular solutions for the differential operator ∆^(2) ± λ^(2).similar to the derivation of fundamental solutions,it is non-trivial to derive particular solutions for higher order differential *** this paper,we provide a simple algebraic factorization approach to derive particular solutions for these types of differential operators in 2D and *** main focus of this paper is its simplicity in the sense that minimal mathematical background is required for numerically solving higher order partial differential equations such as thin plate *** numerical examples in both 2D and 3D are given to validate particular solutions we derived.

关键词： The method of fundamental solutions radial basis functions meshless methods polyharmonic splines the method of particular solutions

The Method of Fundamental solutions for solving convection-Diffusion Equations with Variable coefficients

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Advances in Applied Mathematics and Mechanics 2009年第2期1卷 215-230页

作者： c.M.Fan c.s.chen J.Monroe Department of Mathematics University of Southern MississippiHattiesburgMS 39406USA Department of Mathematics Spring Hill CollegeMobileAL 36608USA

A meshless method based on the method of fundamental solutions(MFs)is proposed to solve the time-dependent partial differential equations with variable *** proposed method combines the time discretization and the onestage MFs for spatial *** contrast to the traditional two-stage process,the one-stage MFs approach is capable of solving a broad spectrum of partial differential *** numerical implementation is simple since both closed-form approximate particular solution and fundamental solution are easy to find than the traditional *** numerical results show that the one-stage approach is robust and stable.

关键词： Meshless method method of fundamental solutions particular solution singular value decomposition time-dependent partial differential equations

A Novel Method for solving Time-Dependent 2D Advection-Diffusion-Reaction Equations to Model Transfer in Nonlinear Anisotropic Media

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communications in computational Physics 2019年第6期26卷 233-264页

作者： Ji Lin sergiy Reutskiy c.s.chen Jun Lu state Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering International Center for Simulation Software in Engineering and SciencesCollege of Mechanics and MaterialsHohai UniversityNanjing 211100China state Institution"Institute of Technical Problems of Magnetism of the National Academy of sciences of Ukraine" Industrialnaya St.1961106KharkovUkraine Department of Mathematics University of Southern MississippiHattiesburgMS 39406USA Nanjing Hydraulic Research Institute Nanjing 210029China state Key Laboratory of Hydrology Water Resources and Hydraulic Engineering Nanjing 210098China

This paper presents a new numerical technique for solving initial and bound-ary value problems with unsteady strongly nonlinear advection diffusion reaction(ADR)*** method is based on the use of the radial basis functions(RBF)for the approximation space of the *** crank-Nicolson scheme is used for approximation in *** results in a sequence of stationary nonlinear ADR *** equations are solved sequentially at each time step using the proposed semi-analytical technique based on the *** approximate solution is sought in the form of the analytical expansion over basis functions and contains free *** basis functions are constructed in such a way that the expansion satisfies the boundary conditions of the problem for any choice of the free *** free parameters are determined by substitution of the expansion in the equation and collocation in the solution *** the case of a nonlinear equation,we use the well-known procedure of *** transforms the original equation into a sequence of the linear ones on each time *** numerical examples confirm the high accuracy and robustness of the proposed numerical scheme.

关键词： Advection diffusion reaction time-dependent fully nonlinear anisotropic media crank-Nicolson scheme meshless method

A Boundary Meshless Method for solving Heat Transfer Problems Using the Fourier Transform

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Advances in Applied Mathematics and Mechanics 2011年第5期3卷 572-585页

作者： A.Tadeu c.s.chen J.Antonio Nuno simoes Department of civil Engineering Faculty of Sciences and TechnologyUniversity of CoimbraPolo II-Pinhal de Marrocos3030-290 CoimbraPortugal Department of Mathematics University of Southern MississippiHattiesburgMS 39406USA

Fourier transform is applied to remove the time-dependent variable in the diffusion *** non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation,which is solved by the method of fundamental solutions and the method of particular *** particular solution of Helmholtz equation is available as shown in[4,15].The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform *** frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static *** numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.

关键词： Transient heat transfer meshless methods method of particular solutions method of fundamental solutions frequency domain Fourier transform

The Recursive Formulation of Particular solutions for some Elliptic PDEs with Polynomial source Functions

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communications in computational Physics 2009年第5期5卷 942-958页

作者： J.Ding H.Y.Tian c.s.chen Department of Mathematics University of Southern MississippiHattiesburgMS 39406USA

In this paper we develop an efficient meshless method for solving inhomogeneous elliptic partial differential *** first approximate the source function by chebyshev *** then focus on how to find a polynomial particular solution when the source function is a *** the principle of the method of undetermined coefficients and a proper arrangement of the terms for the polynomial particular solution to be determined,the coefficients of the particular solution satisfy a triangular system of linear algebraic *** recursive formulas for the coefficients of the particular solutions are derived for different types of elliptic *** method is further incorporated into the method of fundamental solutions for solving inhomogeneous elliptic *** results show that our approach is efficient and accurate.

关键词： The method of fundamental solutions particular solution Helmholtz equation chebyshev polynomial Laplace-Helmholtz equation convection-reaction equation

THE·cLIMATE OF cHEKIANG

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地理学报 1943年 177-179页

作者： c.s.chen National central Universiiy

chekiang, the smallest province of china, is situated in the eastern part of the country, Facing east to the sea, it lies between the latitudes 27°-3Ⅰ°N, and the longitudes Ⅱ8;Ⅰ23°E. With the exception of the lo... 详细信息

关键词： THE than In cLIMATE OF cHEKIANG

Preface special Issue for scPDE08: Numerical Methods and Analysis for PDEs and Inverse Problems

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Advances in Applied Mathematics and Mechanics 2009年第6期1卷 I0001-I0002页

作者： c.s.chen Ming-chih Lai Leevan Ling Jichun Li Masahiro Yamamoto Department of Mathematics University of southern Mississippi Department of Applied Mathematics National chiao Tung University Department of Mathematics Hong Kong Baptist University Hong KongChina Department of Mathematical sciences University of Nevada Las Vegas Department of Mathematical sciences University of Tokyo

The Third International conference on scientific computing and Partial Differential Equations(scPDE)was held from December 8 to December 12,2008 at china Hong Kong Baptist *** was a sequel to similar conferences held in Hong Kong region(2002 and 2005).The conference aims to promote research interests in scientific *** scPDE 2008,there were 118 participants from seventeen countries and regions participated in the *** Programme included seventeen plenary addresses,thirty invited talks,twenty five contributed talks and seven poster presentations.

关键词： computation Inverse Issue