CMES-Vol. 40, No. 1, 2009

Open Access

ARTICLE

Solving the Inverse Problems of Laplace Equation to Determine the Robin Coefficient/Cracks' Position Inside a Disk
Chein-Shan Liu¹
CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 1-28, 2009, DOI:10.3970/cmes.2009.040.001
Abstract We consider an inverse problem of Laplace equation by recoverning boundary value on the inner circle of a two-dimensional annulus from the overdetermined data on the outer circle. The numerical results can be used to determine the Robin coefficient or crack's position inside a disk from the measurements of Cauchy data on the outer boundary. The Fourier series is used to formulate the first kind Fredholm integral equation for the unknown data f(θ) on the inner circle. Then we consider a Lavrentiev regularization, by adding an extra term αf(θ) to obtain the second kind Fredholm integral More >

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ARTICLE

A boundary element formulation for incremental nonlinear elastic deformation of compressible solids
Sergia Colli¹, Massimiliano Gei¹, Davide Bigoni^1,2
CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 29-62, 2009, DOI:10.3970/cmes.2009.040.029
Abstract Incremental plane strain deformations superimposed upon a uniformly stressed and deformed nonlinear elastic (compressible) body are treated by developing {\it ad hoc} boundary integral equations that, discretized, lead to a novel boundary element technique. The approach is a generalization to compressible elasticity of results obtained by Brun, Capuani, and Bigoni (2003, Comput. Methods Appl. Mech. Engrg. 192, 2461-2479), and is based on a Green's function here obtained through the plane-wave expansion method. New expressions for Green's tractions are determined, where singular terms are solved in closed form, a feature permitting the development of a optimized More >

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Large-Scale Full Wave Analysis of Electromagnetic Field by Hierarchical Domain Decomposition Method
A. Takei¹, S. Yoshimura¹, H. Kanayama²
CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 63-82, 2009, DOI:10.3970/cmes.2009.040.063
Abstract This paper describes a large-scale finite element analysis (FEA) for a high-frequency electromagnetic field of Maxwell equations including the displacement current. A stationary Helmholtz equation for the high-frequency electromagnetic field analysis is solved by considering an electric field and an electric scalar potential as unknown functions. To speed up the analysis, the hierarchical domain decomposition method (HDDM) is employed as a parallel solver. In this study, the Parent-Only type (Parallel processor mode: P-mode) of the HDDM is employed. In the P-mode, Parent processors perform the entire FEA. In this mode, all CPUs can be used More >

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Study of the Underfill Effect on the Thermal Fatigue Life of WLCSP-Experiments and Finite Element Simulations
Shaw-Jyh Shin¹, Chen-Hung Huang², Y.C. Shiah³
CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 83-104, 2009, DOI:10.3970/cmes.2009.040.083
Abstract Owing to the CTE (Coefficient of Thermal Expansion) mismatch among solder joints, IC (Integrated Circuit) chip, and PCB (Printed Circuit Board), electronic packages shall experience fatigue failure after going though a period of thermal cycling. As a major means to enhance the reliability of the solder joints, underfill is often dispensed to fill the gap between the die and the substrate. This study aims at investigating how the underfill may affect the thermal fatigue life of WLCSP (Wafer Level Chip Scale Package) by means of FEA (finite element analysis). In this study, the thermal fatigue More >

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