Weichung Yeih^1,2, Cheng-Yu Ku^1,2,3, Chein-Shan Liu⁴, I-Yao Chan^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.4, pp. 255-282, 2013, DOI:10.3970/cmes.2013.090.255

Abstract In this paper, a scalar homotopy method with optimal hybrid search directions for solving nonlinear algebraic equations is proposed. To conduct the proposed method, we first convert the vector residual function to a scalar function by taking the square norm of the vector function and then, introduce a fictitious time variable to form a scalar homotopy function. To improve the convergence and the accuracy of the proposed method, a vector with multiple search directions and an iterative algorithm are introduced into the evolution dynamics of the solutions. Further, for obtaining the optimal search direction, linear and nonlinear optimization algorithms are… More >

Binbin Diao¹, Deli Gao^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.1, pp. 77-90, 2013, DOI:10.3970/cmes.2013.090.077

Abstract The measurement of the relative position of two adjacent wells is one of the key technologies in the directional drilling of twin parallel horizontal wells, and the downhole intersection of two adjacent wells. A new electromagnetic ranging system and a guidance method are introduced for determining the relative position of two adjacent wells. The system mainly consists of two solenoid assemblies, improved surveying instrument for measurement while drilling (MWD), and a computational procedure for guidance. Also, the distribution of the magnetic field of each energized solenoid assembly is discussed, by regarding the solenoid assembly as two independent oscillating magnetic dipoles.… More >

Zonglu Guo¹, Deli Gao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.1, pp. 65-76, 2013, DOI:10.3970/cmes.2013.090.065

Abstract The modeling of the bottomhole assembly (BHA) is an essential problem in directional drilling. Some basic equations for predicting the performance of the BHA are presented in this paper. These equations take into account the effects of the axial displacement. The method of weighted residuals and the Newton-Raphson iterations are used to compute the nonlinear effects of the deformation of the BHA. A computer program is developed for the analysis of the BHA in order to quantitatively predict the performance of the BHA in directional drilling. In addition, a case study is presented to evaluate the effect of the axial… More >

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

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.3, pp. 189-220, 2012, DOI:10.3970/cmes.2012.089.189

Abstract In this paper, the alternating direction implicit (ADI) method reported in [You(2006)] for the convection-diffusion equation is implemented in the context of compact integrated radial basis function (CIRBF) approximations. The CIRBF approximations are constructed over 3-point stencils, where extra information is incorporated via two forms: only nodal second-order derivative values (Scheme 1), and both nodal first- and second-order derivative values (Scheme 2). The resultant algebraic systems are sparse, especially for Scheme 2 (tridiagonal matrices). Several steady and non-steady problems are considered to verify the present schemes and to compare their accuracy with some other ADI schemes. Numerical results show that… More >

Annamaria Mazzia¹, Giorgio Pini¹, Flavio Sartoretto²

CMES-Computer Modeling in Engineering & Sciences, Vol.88, No.3, pp. 183-210, 2012, DOI:10.3970/cmes.2012.088.183

Abstract Pure meshless techniques are promising methods for solving Partial Differential Equations (PDE). They alleviate difficulties both in designing discretization meshes, and in refining/coarsening, a task which is demanded e.g. in adaptive strategies. Meshless Local Petrov Galerkin (MLPG) methods are pure meshless techniques that receive increasing attention. Very recently, new methods, called Direct MLPG (DMLPG), have been proposed. They rely upon approximating PDE via the Generalized Moving Least Square method. DMLPG methods alleviate some difficulties of MLPG, e.g. numerical integration of tricky, non-polynomial factors, in weak forms. DMLPG techniques require lower computational costs respect to their MLPG counterparts. In this paper… More >

H.B. Chen¹, Masa. Tanaka²

CMES-Computer Modeling in Engineering & Sciences, Vol.69, No.1, pp. 19-42, 2010, DOI:10.3970/cmes.2010.069.019

Abstract Highly accurate calculation of derivative values to the field variable is a key issue in numerical analysis of engineering problems. The boundary integral equations (BIEs) of potential second derivatives are of third order singularities and obviously the direct calculation of these high order singular integrals is rather cumbersome. The idea of the present paper is to use an indirect algorithm which is based on the regularized BIE formulations of the potential second derivatives, following the work of the present first author and his coworkers. The regularized formulations, numerical strategies and example tests are given for both potential first and second… More >

LiviuMarin ¹

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 203-242, 2008, DOI:10.3970/cmes.2008.037.203

Abstract In this paper, a meshless method for the stable solution of direct and inverse problems associated with the two-dimensional Laplace equation in the presence of boundary singularities and noisy boundary data is proposed. The governing equation and boundary conditions are discretized by the method of fundamental solutions (MFS), whilst the existence of the boundary singularity is taken into account by subtracting from the original MFS solution the corresponding singular solutions, as given by the asymptotic expansion of the solution near the singular point. However, even in the case when the boundary singularity is accounted for, the numerical solutions obtained by… More >

F. Reitich¹, K. K. Tamma²

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 287-294, 2004, DOI:10.3970/cmes.2004.005.287

Abstract This article has no abstract. More >

Roman Chapko¹, B. Tomas Johansson²

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 105-128, 2012, DOI:10.3970/cmes.2012.085.105

Abstract We consider a Cauchy problem for the Laplace equation in a 3-dimen -sional semi-infinite domain that contains a bounded inclusion. The canonical situation is the upper half-space in I\tmspace -.1667em R3 containing a bounded smooth domain. The function value of the solution is specified throughout the plane bounding the upper half-space, and the normal derivative is given only on a finite portion of this plane. The aim is to reconstruct the solution on the surface of the bounded inclusion. This is a generalisation of the situation in Chapko and Johansson (2008) to three-dimensions and with Cauchy data only partially given.… More >

L. Dong¹, S. N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 1-44, 2012, DOI:10.3970/cmes.2012.085.001

Abstract In this paper, a generalized Trefftz method in plane elasticity is developed, for solving problems in an arbitrary multiply connected domain. Firstly, the relations between Trefftz basis functions from different source points are discussed, by using the binomial theorem and the logarithmic binomial theorem. Based on these theorems, we clearly explain the relation between the T-Trefftz and the F-Trefftz methods, and why the traditional T-Trefftz method, which uses only one source point, cannot successfully solve problems in a multiply connected domain with genus larger than 1. Thereafter, a generalized Trefftz method is proposed, which uses logarithmic and negative power series… More >