R. Itza Balam^1,2, M. Uh Zapata^1,2, J. Montalvo-Urquizo³

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, Vol.39, No.4, pp. 1-12, 2023, DOI:10.23967/j.rimni.2023.12.002 - 28 December 2023

Abstract This paper introduces a sixth-order Immersed Interface Method (IIM) for addressing 2D Poisson problems characterized by a discontinuous forcing function with straight interfaces. In the presence of this discontinuity, the problem exhibits a non-smooth solution at the interface that divides the domain into two regions. Here, the IIM is employed to compute the solution on a fixed Cartesian grid. This method integrates necessary jump conditions resulting from the interface into the numerical schemes. In order to achieve a sixth-order method, the proposed approach combines implicit finite differences with the IIM. The proposed scheme is efficient More >

A. Arulmary^1,*, V. Rajamani², T. Kavitha²

Computer Systems Science and Engineering, Vol.46, No.2, pp. 1617-1630, 2023, DOI:10.32604/csse.2023.034681 - 09 February 2023

Abstract The method opted for accuracy, and no existing studies are based on this method. A design and characteristic survey of a new small band gap semiconducting Single Wall Carbon Nano Tube (SWCNT) Field Effect Transistor as a photodetector is carried out. In the proposed device, better performance is achieved by increasing the diameter and introducing a new single halo (SH) doping in the channel length of the CNTFET device. This paper is a study and analysis of the performance of a Carbon Nano Tube Field Effect Transistor (CNTFET) as a photodetector using the self-consistent Poisson… More >

Luciano Pereira da Silva^1,*, Bruno Benato Rutyna¹, Aline Roberta Santos Righi², Marcio Augusto Villela Pinto³

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 699-715, 2021, DOI:10.32604/cmes.2021.014239 - 22 July 2021

Abstract In this article, we improve the order of precision of the two-dimensional Poisson equation by combining extrapolation techniques with high order schemes. The high order solutions obtained traditionally generate non-sparse matrices and the calculation time is very high. We can obtain sparse matrices by applying compact schemes. In this article, we compare compact and exponential finite difference schemes of fourth order. The numerical solutions are calculated in quadruple precision (Real * 16 or extended precision) in FORTRAN language, and iteratively obtained until reaching the round-off error magnitude around 1.0E −32. This procedure is performed to ensure More >

Chunglun Kuo*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.22, No.4, pp. 173-173, 2019, DOI:10.32604/icces.2019.05272

Abstract In this article, a directional method of particular solution (DMPS) is derived to solve the 3D Poisson equation in an arbitrary domain. The proposed DMPS for the 3D problems are based on the 2D particular solution. Together with the directional technique we can construct the 3D particular solution easily by introducing a series of planar directors into the 2D particular solution. The intensities of the basis functions are determined by imposing the boundary condition on the boundary collocation points. Besides, the inverse Cauchy problems are also addressed in this article. The inverse problems are highly More >

Cheinshan Liu^1,2, Fajie Wang^1,3,*, Wenzheng Qu^4,*

CMES-Computer Modeling in Engineering & Sciences, Vol.114, No.3, pp. 351-380, 2018, DOI:10.3970/cmes.2018.114.351

Abstract In this paper we propose a novel two-stage method to solve the three-dimensional Poisson equation in an arbitrary bounded domain enclosed by a smooth boundary. The solution is decomposed into a particular solution and a homogeneous solution. In the first stage a multiple-scale polynomial method (MSPM) is used to approximate the forcing term and then the formula of Tsai et al. [Tsai, Cheng, and Chen (2009)] is used to obtain the corresponding closed-form solution for each polynomial term. Then in the second stage we use a multiple/scale/direction Trefftz method (MSDTM) to find the solution of More >

Xiaojing Liu^1,2, Jizeng Wang¹, Youhe Zhou¹

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 433-446, 2015, DOI:10.3970/cmes.2015.107.433

Abstract Based on the approximation scheme for a L²-function defined on a three-dimensional bounded space by combining techniques of boundary extension and Coiflet-type wavelet expansion, a modified wavelet Galerkin method is proposed for solving three-dimensional Poisson problems with various boundary conditions. Such a wavelet-based solution procedure has been justified by solving five test examples. Numerical results demonstrate that the present wavelet method has an excellent numerical accuracy, a fast convergence rate, and a very good capability in handling complex boundary conditions. More >

C.M.T. Tien¹, N. Thai-Quang¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.105, No.4, pp. 301-340, 2015, DOI:10.3970/cmes.2015.105.301

Abstract In this study, we present a numerical discretisation scheme, based on a direct fully coupled approach and compact integrated radial basis function (CIRBF) approximations, to simulate viscous flows in regular/irregular domains. The governing equations are taken in the primitive form where the velocity and pressure fields are solved in a direct fully coupled approach. Compact local approximations, based on integrated radial basis functions, over 3-node stencils are introduced into the direct fully coupled approach to represent the field variables. The present scheme is verified through the solutions of several problems including Poisson equations, Taylor-Green vortices More >

C.M.T. Tien¹, N. Thai-Quang¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.6, pp. 425-469, 2015, DOI:10.3970/cmes.2015.104.425

Abstract In this paper, we propose a three-point coupled compact integrated radial basis function (CCIRBF) approximation scheme for the discretisation of second-order differential problems in one and two dimensions. The CCIRBF employs integrated radial basis functions (IRBFs) to construct the approximations for its first and second derivatives over a three-point stencil in each direction. Nodal values of the first and second derivatives (i.e. extra information), incorporated into approximations by means of the constants of integration, are simultaneously employed to compute the first and second derivatives. The essence of the CCIRBF scheme is to couple the extra… More >

C.M.T. Tien¹, N. Pham-Sy¹, N. Mai-Duy¹, C.-D. Tran¹, T. Tran-Cong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.104, No.4, pp. 251-304, 2015, DOI:10.3970/cmes.2015.104.251

Abstract This paper presents a high-order coupled compact integrated RBF (CC IRBF) approximation based domain decomposition (DD) algorithm for the discretisation of second-order differential problems. Several Schwarz DD algorithms, including one-level additive/ multiplicative and two-level additive/ multiplicative/ hybrid, are employed. The CCIRBF based DD algorithms are analysed with different mesh sizes, numbers of subdomains and overlap sizes for Poisson problems. Our convergence analysis shows that the CCIRBF two-level multiplicative version is the most effective algorithm among various schemes employed here. Especially, the present CCIRBF two-level method converges quite rapidly even when the domain is divided into… More >

Chih-Wen Chang^1,2, Chein-Shan Liu³

CMC-Computers, Materials & Continua, Vol.34, No.2, pp. 143-175, 2013, DOI:10.3970/cmc.2013.034.143

Abstract The nonlinear Poisson problems in heat diffusion governed by elliptic type partial differential equations are solved by a modified globally optimal iterative algorithm (MGOIA). The MGOIA is a purely iterative method for searching the solution vector x without using the invert of the Jacobian matrix D. Moreover, we reveal the weighting parameter αc in the best descent vector w = αcE + DTE and derive the convergence rate and find a criterion of the parameter γ. When utilizing αc and γ, we can further accelerate the convergence speed several times. Several numerical experiments are carefully More >