An improved combined fine‐coarse mesh (CFCM) method for two transmission line models of diffusion is described. The method allows regular cells of different sizes to be connected and solved simultaneously. The CFCM method is applied to (a) a finite difference algorithm, (b) a conventional transmission line model and (c) a lossy transmission line model. The latter model is shown to be the most accurate. The proposed CFCM method is also compared with the graded mesh and the multigrid techniques.

ObjectiveSocial network plays a vital role in facilitating late‐life health and well‐being. The current research sought to examine the psychometric properties of the abbreviated Lubben Social Network Scale (LSNS‐6) among community‐dwelling Hong Kong Chinese older adults and to explore the association between social network and well‐being indicators such as life satisfaction, functional social support, loneliness and anxiety.MethodsWe administered the LSNS‐6 scale to 324 older adults (mean = 71.70, SD = 8.58, range: 58–95). We performed confirmatory factor analysis (CFA) to confirm the construct validity. Cronbach's alpha was chosen for internal consistency estimation. Correlational analysis was performed between LSNS‐6 scale and other measures to ascertain the convergent validity.ResultsThe two‐factor model of LSNS‐6 indicated an adequate fit. The goodness‐of‐fit index values for the model were χ2/df = 2.61, CFI = 0.98, RSMEA = 0.07, SRMR = 0.05. The internal consistency of the scale was α = 0.75. It also demonstrated good construct validity in measuring the social network and acceptable convergent validity to other measures.ConclusionsThe LSNS‐6, according to current findings, can be a valid reference to the social network of Hong Kong older adults, enabling researchers and clinicians to investigate and develop further corresponding remedies for those in need.

SUMMARYThe rnultigrid technique, which is mainly used in the finite difference method, is applied to the TLM (transrnission-line matrix or modelling) procedure. In the rnultigrid TLM, the field region is covered with sets of regular transrnission-line matrices of different mesh sizes. The finer grid pattern, which overlaps the coarser grid, fills the region with high field gradients. Data obtained in the coarser grid are transferred to the finer grid through an interpolation process and used as boundary conditions for the latter. The finer grid data are then transferred back to the coarser one, thus improving the coarse grid values. The method is applied to several diffusion problems and significant improvements in accuracy and efficiency are shown.

A new hybrid TLM-FDTD algorithm for solving di!usion problems is described. The method utilizes the transmission line model to de"ne the time step and the FDTD's leap-frog algorithm to determine the voltages and currents of the network analogue of the di!usion equation. Unlike the standard TLM method, the proposed one does not generate spurious oscillations. The method is explicit and can be used to solve highly non-linear problems without the need to solve non-linear equations. The implementation of a simple adaptive time-stepping algorithm is also described.

SUMMARYThe aim of this note is to point out that the boundary condition for the network modelling of thermal problems may have been incorrectly used in some previous studies. It is shown that the accuracy of the network analogue or the equivalent finite-difference method is on the par with the finite-element method for very fast transient thermal simulations. The electrical network analogue of the diffusion equation has been used for many years [1]. It is easy to implement and provides good accuracy. However, it has been reported that it is not suitable for the thermal modelling of power semiconductor devices that are subjected to short duration heat pulses. In a recent article [2], several thermal models for the electrothermal simulation of power semiconductor devices were compared. The authors concluded that the finite-difference model (FDM) or the electric network analogue of the diffusion equation was unacceptable because of accuracy problem. In this note, it is shown that the accuracy of this model is much better than the results described in [2], provided that the boundary is correctly terminated.A typical section of a one-dimensional thermal equivalent network is shown in Figure 1(a), which is identical to those used in References [2][3][4]. A commonly used boundary termination, which is also used in References [2][3][4], is shown in Figure 1(b). Simple node analysis shows thatwhere P in is the heat input, T 0 ; T 1 ; are the node temperatures and the RC (although Equation (1) does not include C) value represents the thermal properties of the medium. The equivalence between the thermal system and the network can be found in Reference [1] and will not be described here. The effect of the thermal capacitance has been ignored in Equation (1).