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Wei CHOON TAY Eng LEONG TAN Ding YU HEH
This paper presents a fundamental locally one-dimensional (FLOD) method for 3-D thermal simulation. We first propose a locally one-dimensional (LOD) method for heat transfer equation within general inhomogeneous media. The proposed LOD method is then cast into compact form and formulated into the FLOD method with operator-free right-hand-side (RHS), which leads to computationally efficient update equations. Memory storage requirements and boundary conditions for both FLOD and LOD methods are detailed and compared. Stability analysis by means of analyzing the eigenvalues of amplification matrix substantiates the stability of the FLOD method. Additionally, the potential instability of the Douglas Gunn (DG) alternating-direction-implicit (ADI) method for inhomogeneous media is demonstrated. Numerical experiments justify the gain achieved in the overall efficiency for FLOD over LOD, DG-ADI and explicit methods. Furthermore, the relative maximum error of the FLOD method illustrates good trade-off between accuracy and efficiency.
Junji YAMAUCHI Jun SHIBAYAMA Shu NAKAMURA Hisamatsu NAKANO
The field profile and effective index of a rib waveguide are calculated using an improved semivectorial beam-propagation method using the imaginary-distance procedure. Convergence behavior of the effective index is compared with that obtained by the conventional Crank-Nicholson scheme and with that derived from a Bierwirth-type formula, demonstrating the effectiveness of the present method. Field discontinuities at the interface between different materials are clearly displayed.
Junji YAMAUCHI Takashi ANDO Morihiko IKEGAYA Hisamatsu NAKANO
Pure bend loss of a fiber with a trench section is calculated by the alternating-direction implicit finite-difference method. The dependence of the loss on the trench location is evaluated. The mechanism of the oscillatory behavior of the loss is discussed in terms of a modal approach in a dielectric slab waveguide.