Hsiang-Wen Tang, Cha’o-Kung Chen¹, Chen-Yu Chiang

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.1, pp. 95-106, 2010, DOI:10.3970/cmes.2010.065.095

Abstract Up to now, solving some nonlinear differential equations is still a challenge to many scholars, by either numerical or theoretical methods. In this paper, the method of the maximum principle applied on differential equations incorporating the Residual Correction Method is brought up and utilized to obtain the upper and lower approximate solutions of nonlinear heat transfer problem of the non-Fourier fin. Under the fundamental of the maximum principle, the monotonic residual relations of the partial differential governing equation are established first. Then, the finite difference method is applied to discretize the equation, converting the differential equation into the mathematical programming… More >

P.H. Gaskell¹, Y.C. Lee², H.M. Thompson¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 77-112, 2010, DOI:10.3970/cmes.2010.062.077

Abstract The three-dimensional flow of a gravity-driven continuous thin liquid film on substrates containing micro-scale features is modelled using the long-wave lubrication approximation, encompassing cases when surface topography is either engulfed by the film or extends all the way though it. The discrete analogue of the time-dependent governing equations is solved accurately using a purpose designed multigrid strategy incorporating both automatic error-controlled adaptive time stepping and local mesh refinement/de-refinement. Central to the overall approach is a Newton globally convergent algorithm which greatly simplifies the inclusion of further physics via the solution of additional equations of the same form as the base… More >

D. Asprone¹, F. Auricchio², G. Manfredi¹, A. Prota¹, A. Reali², G. Sangalli³

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 1-22, 2010, DOI:10.3970/cmes.2010.062.001

Abstract Particle methods represent some of the most investigated meshless approaches, applied to numerical problems, ranging from solid mechanics to fluid-dynamics and thermo-dynamics. The objective of the present paper is to analyze some of the proposed particle formulations in one dimension, investigating in particular how the different approaches address second derivative approximation. With respect to this issue, a rigorous analysis of the error is conducted and a novel second-order accurate formulation is proposed. Hence, as a benchmark, three numerical experiments are carried out on the investigated formulations, dealing respectively with the approximation of the second derivative of given functions, as well… More >

Lorenzo Codecasa¹, Francesco Trevisan²

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.2, pp. 155-180, 2010, DOI:10.3970/cmes.2010.059.155

Abstract Electromagnetic problems spatially discretized by the so called Discrete Geometric Approach are considered, where Discrete Counterparts of Constitutive Relations are discretized within an Energetic Approach. Pairs of oriented dual grids are considered in which the primal grid is composed of (oblique) parallelepipeds, (oblique) triangular prisms and tetrahedra and the dual grid is obtained according to the barycentric subdivision. The focus of the work is the evaluation of the constants bounding the approximation error of the electromagnetic field; the novelty is that such constants will be expressed in terms of the geometrical details of oriented dual grids. A numerical analysis will… More >

B. Chandrasekhar¹

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.3, pp. 211-230, 2010, DOI:10.3970/cmes.2010.056.211

Abstract In this work, various basis functions used in the Method of Moments or Boundary Element (MoM/BEM) solution of acoustic scattering problems are compared with each other for their performance. Single layer formulation of the rigid bodies is considered in comparison of the solutions. Geometry of a scatterer is descritized using triangular patch modeling and basis functions are defined on triangular patches, edges and nodes for three different solutions. Far field scattering cross sections for different frequencies of incident acoustic wave are compared with the closed form solutions. Also, the errors of the solutions using these three types of basis functions… More >

M. A. Kelmanson¹ and M. C. Tenwick¹

CMES-Computer Modeling in Engineering & Sciences, Vol.55, No.2, pp. 191-210, 2010, DOI:10.3970/cmes.2010.055.191

Abstract A method is presented for improving the accuracy of the widely used Gauss-Legendre Nyström method for determining approximate solutions of Fredholm integral equations of the second kind on finite intervals. The authors' recent continuous-kernel approach is generalised in order to accommodate kernels that are either singular or of limited continuous differentiability at a finite number of points within the interval of integration. This is achieved by developing a Gauss-Jacobi Nyström method that moreover includes a mean-value estimate of the truncation error of the Hermite interpolation on which the quadrature rule is based, making it particularly accurate at low orders. A… More >

T. Starling¹, M. F. Daqaq¹, G. Li^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.45, No.3, pp. 207-226, 2009, DOI:10.3970/cmes.2009.045.207

Abstract Input-shaping is an open-loop control technique for dynamic control of electrostatic MEMS. In MEMS applications, open-loop control is attractive as it computes a priori the required system input to achieve desired dynamic behavior without using feedback. In this work, a 3-D computational electromechanical analysis is performed to preshape the voltage commands applied to electrostatically actuate a torsional micromirror to a desired tilt angle with minimal residual oscillations. The effect of higher vibration modes on the controlled response is also investigated. It is shown that, for some structural design parameters, the first bending mode of the micromirror can have a significant… More >

Jin Li¹, Ji-ming Wu², De-hao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.42, No.2, pp. 151-176, 2009, DOI:10.3970/cmes.2009.042.151

Abstract The trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods is discussed, and the asymptotic expansion of error function is obtained. A series to approach the singular point is constructed and the convergence rate is proved. Based on the asymptotic expansion of the error functional, algorithm with theoretical analysis of the generalized extrapolation are given. Some examples show that the numerical results coincide with the theoretic analysis very well. More >

Y.Y. Shan¹, C. Shu^1,2, Z.L. Lu³

CMES-Computer Modeling in Engineering & Sciences, Vol.25, No.2, pp. 99-114, 2008, DOI:10.3970/cmes.2008.025.099

Abstract The local multiquadric-based differential quadrature (MQ-DQ) method proposed by [Shu, Ding, and Yeo (2003)] is a natural mesh-free approach for derivative approximation, which is easy to be implemented to solve problems with curved boundary. Previously, it has been well tested for the two-dimensional (2D) case. In this work, this mesh-free method was extended to simulate fluid flow problems with curved boundary in three-dimensional (3D) space. The main concern of this work is to numerically study the performance of the 3D local MQ-DQ method and demonstrate its capability and flexibility for simulation of 3D incompressible fluid flows with curved boundary. Fractional… More >

Chany Lee¹, Chang-Hwan Im², Hyun-Kyo Jung³, Hong-Kyu Kim⁴, Do Wan Kim⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 35-42, 2007, DOI:10.3970/cmes.2007.020.035

Abstract In the present study, a residual-based a posteriori error estimation for a kind of meshless method, called fast moving least square reproducing kernel (FMLSRK) method is proposed. The proposed error estimation technique does not require any integration cells in evaluating error norm but recovers the exact solutions in a virtual area defined by a dilation parameter of FMLSRK and node density. The proposed technique was tested on typical electrostatic problems with gird or random node sets and the simulation results show that the proposed error estimation technique can be applied to adaptive node refinement process for more efficient meshless analysis… More >