Masato Saitoh¹

CMES-Computer Modeling in Engineering & Sciences, Vol.67, No.3, pp. 211-238, 2010, DOI:10.3970/cmes.2010.067.211

Abstract This paper describes the transformation of impedance functions in general structural systems with non-classical damping into a one-dimensional spring-dashpot system (1DSD). A transformation procedure based on complex modal analysis is proposed, where the impedance function is transformed into a 1DSD comprising units arranged in series. Each unit is a parallel system composed of a spring, a dashpot, and a unit having a spring and a dashpot arranged in series. Three application examples are presented to verify the applicability of the proposed procedure and the accuracy of the 1DSDs. The results indicate that the 1DSDs accurately… More >

P. Bettini¹, M. Midrio², R. Specogna²

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.2, pp. 117-134, 2010, DOI:10.3970/cmes.2010.066.117

Abstract In this paper we propose a geometric formulation to solve 3D electromagnetic wave problems in unbounded regions in the frequency domain. An absorbing boundary condition (ABC) is introduced to limit the size of the computational domain by means of anisotropic Perfectly Matched Layers (PML) absorbing media in the outer layers of an unstructured mesh. The numerical results of 3D benchmark problems are presented and the effect of the PML parameters and scaling functions on PML effectiveness are discussed. More >

C.H. Tsai¹, D.L. Young², J. Kolibal³

CMES-Computer Modeling in Engineering & Sciences, Vol.66, No.1, pp. 53-72, 2010, DOI:10.3970/cmes.2010.066.053

Abstract The time evolution method of fundamental solutions (MFS) is proposed to solve backward heat conduction problems (BHCPs). The time evolution MFS belongs to one of the mesh-free numerical methods and is essentially composed of a sequence of diffusion fundamental solutions which exactly satisfy the heat conduction equations. Through correct treatment of temporal evolution, the resulting system of the time evolution MFS is smaller, and effectively decreases the possibility of ill-conditioning induced by such strongly ill-posed problems. Both one-dimensional and two-dimensional BHCPs are examined in this study, and the numerical results demonstrate the accuracy and stability More >

Montri Maleewong¹, Sirod Sirisup²

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 193-216, 2010, DOI:10.3970/cmes.2010.065.193

Abstract In this paper, we describe our investigation of an "on-line" POD-assisted projective integration method for solving a nonlinear PDE. Using the on-line method, we have computed the representative POD modes without assuming knowledge of the underlying slow manifold along the integration process. This approach is based on the "equation-free" framework where the governing PDE does not need to be projected onto the POD bases in order to build a reduced-order model. The main objectives of this study were to investigate the effectiveness of the method in reducing the computational time required for numerically solving a More >

Sunilkumar N¹, D Roy^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.65, No.2, pp. 107-154, 2010, DOI:10.3970/cmes.2010.065.107

Abstract The element-based piecewise smooth functional approximation in the conventional finite element method (FEM) results in discontinuous first and higher order derivatives across element boundaries. Despite the significant advantages of the FEM in modelling complicated geometries, a motivation in developing mesh-free methods has been the ease with which higher order globally smooth shape functions can be derived via the reproduction of polynomials. There is thus a case for combining these advantages in a so-called hybrid scheme or a 'smooth FEM' that, whilst retaining the popular mesh-based discretization, obtains shape functions with uniform C^p(p ≥ 1) continuity. One… More >

Bart Bergen¹, Bert Van Genechten¹, Dirk Vandepitte¹, Wim Desmet¹

CMES-Computer Modeling in Engineering & Sciences, Vol.61, No.2, pp. 155-176, 2010, DOI:10.3970/cmes.2010.061.155

Abstract The Wave Based Method (WBM) is a numerical prediction technique for Helmholtz problems. It is an indirect Trefftz method using wave functions, which satisfy the Helmholtz equation, for the description of the dynamic variables. In this way, it avoids both the large systems and the pollution errors that jeopardize accurate element-based predictions in the mid-frequency range. The enhanced computational efficiency of the WBM as compared to the element-based methods has been proven for the analysis of both three-dimensional bounded and two-dimensional unbounded problems. This paper presents an extension of the WBM to the application of More >

Chein-Shan Liu¹, Hong-Ki Hong¹, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.3, pp. 279-308, 2010, DOI:10.3970/cmes.2010.060.279

Abstract We propose novel algorithms to calculate the inverses of ill-conditioned matrices, which have broad engineering applications. The vector-form of the conjugate gradient method (CGM) is recast into a matrix-form, which is named as the matrix conjugate gradient method (MCGM). The MCGM is better than the CGM for finding the inverses of matrices. To treat the problems of inverting ill-conditioned matrices, we add a vector equation into the given matrix equation for obtaining the left-inversion of matrix (and a similar vector equation for the right-inversion) and thus we obtain an over-determined system. The resulting two modifications… More >

Daniel C. Moura¹, Jorge G. Barbosa¹, Ana M. Reis², João Manuel R. S. Tavares³

CMES-Computer Modeling in Engineering & Sciences, Vol.60, No.2, pp. 115-138, 2010, DOI:10.3970/cmes.2010.060.115

Abstract This paper presents a new method for the calibration of biplanar radiography that makes possible performing 3D reconstructions of the spine using conventional radiological systems. A novel approach is proposed in which a measuring device is used for determining focal distance and have a rough estimation of translation parameters. Using these data, 3D reconstructions of the spine with correct scale were successfully obtained without the need of calibration objects, something that was not previously achieved. For superior results, two optional steps may be executed that involve an optimisation of the geometrical parameters, followed by a… More >

Chein-Shan Liu¹, Weichung Yeih², Satya N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.3, pp. 301-324, 2010, DOI:10.3970/cmes.2010.059.301

Abstract When problems in engineering and science are discretized, algebraic equations appear naturally. In a recent paper by Liu and Atluri, non-linear algebraic equations (NAEs) were transformed into a nonlinear system of ODEs, which were then integrated by a method labelled as the Fictitious Time Integration Method (FTIM). In this paper, the FTIM is enhanced, by using the concept of arepellorin the theory ofnonlinear dynamical systems, to situations where multiple-solutions exist. We label this enhanced method as MSFTIM. MSFTIM is applied and illustrated in this paper through solving boundary-layer problems, boundary-value problems, and eigenvalue problems with More >

Chih-Wen Chang¹, Chein-Shan Liu²

CMES-Computer Modeling in Engineering & Sciences, Vol.59, No.3, pp. 239-274, 2010, DOI:10.3970/cmes.2010.059.239

Abstract In this article, we propose a backward group preserving scheme (BGPS) to tackle the multi-dimensional backward heat conduction problem (BHCP). The BHCP is well-known as severely ill-posed because the solution does not continuously depend on the given data. When eight numerical examples (including nonlinear and nonhomogeneous BHCP, and Neumann and Robin conditions of homogeneous BHCP) are examined, we find that the BGPS is applicable to the multi-dimensional BHCP. Even with noisy final data, the BGPS is also robust against disturbance. The one-step BGPS effectively reconstructs the initial data from the given final data, which with More >