Mixed-dimensional consistent coupling by multi-point constraint equations for efficient multi-scale modeling

Finding an appropriate linking method to connect different dimensional element types in a single finite element model is a key issue in the multi-scale modeling. This paper presents a mixed dimensional coupling method using multi-point constraint equations derived by equating the work done on either side of interface connecting beam elements and shell elements for constructing a finite element multiscale model. A typical steel truss frame structure is selected as case example and the reduced scale specimen of this truss section is then studied in the laboratory to measure its dynamic and static behavior in global truss and local welded details while the different analytical models are developed for numerical simulation. Comparison of dynamic and static response of the calculated results among different numerical models as well as the good agreement with those from experimental results indicates that the proposed multi-scale model is efficient and accurate.

Deriving a preference-based measure for cancer using the EORTC QLQ-C30 : a confirmatory versus exploratory approach

Background: To derive preference-based measures from various condition-specific descriptive health-related quality of life (HRQOL) measures. A general 2-stage method is evolved: 1) an item from each domain of the HRQOL measure is selected to form a health state classification system (HSCS); 2) a sample of health states is valued and an algorithm derived for estimating the utility of all possible health states. The aim of this analysis was to determine whether confirmatory or exploratory factor analysis (CFA, EFA) should be used to derive a cancer-specific utility measure from the EORTC QLQ-C30. Methods: Data were collected with the QLQ-C30v3 from 356 patients receiving palliative radiotherapy for recurrent or metastatic cancer (various primary sites). The dimensional structure of the QLQ-C30 was tested with EFA and CFA, the latter based on a conceptual model (the established domain structure of the QLQ-C30: physical, role, emotional, social and cognitive functioning, plus several symptoms) and clinical considerations (views of both patients and clinicians about issues relevant to HRQOL in cancer). The dimensions determined by each method were then subjected to item response theory, including Rasch analysis. Results: CFA results generally supported the proposed conceptual model, with residual correlations requiring only minor adjustments (namely, introduction of two cross-loadings) to improve model fit (increment χ2(2) = 77.78, p < .001). Although EFA revealed a structure similar to the CFA, some items had loadings that were difficult to interpret. Further assessment of dimensionality with Rasch analysis aligned the EFA dimensions more closely with the CFA dimensions. Three items exhibited floor effects (>75% observation at lowest score), 6 exhibited misfit to the Rasch model (fit residual > 2.5), none exhibited disordered item response thresholds, 4 exhibited DIF by gender or cancer site. Upon inspection of the remaining items, three were considered relatively less clinically important than the remaining nine. Conclusions: CFA appears more appropriate than EFA, given the well-established structure of the QLQ-C30 and its clinical relevance. Further, the confirmatory approach produced more interpretable results than the exploratory approach. Other aspects of the general method remain largely the same. The revised method will be applied to a large number of data sets as part of the international and interdisciplinary project to develop a multi-attribute utility instrument for cancer (MAUCa).

Unbiased estimating equations from working correlation models for irregularly timed repeated measures

The method of generalized estimating equation-, (GEEs) has been criticized recently for a failure to protect against misspecification of working correlation models, which in some cases leads to loss of efficiency or infeasibility of solutions. However, the feasibility and efficiency of GEE methods can be enhanced considerably by using flexible families of working correlation models. We propose two ways of constructing unbiased estimating equations from general correlation models for irregularly timed repeated measures to supplement and enhance GEE. The supplementary estimating equations are obtained by differentiation of the Cholesky decomposition of the working correlation, or as score equations for decoupled Gaussian pseudolikelihood. The estimating equations are solved with computational effort equivalent to that required for a first-order GEE. Full details and analytic expressions are developed for a generalized Markovian model that was evaluated through simulation. Large-sample ".sandwich" standard errors for working correlation parameter estimates are derived and shown to have good performance. The proposed estimating functions are further illustrated in an analysis of repeated measures of pulmonary function in children.

Effective Cell-Centred Time-Domain Maxwell's Equations Numerical Solvers

This research work analyses techniques for implementing a cell-centred finite-volume time-domain (ccFV-TD) computational methodology for the purpose of studying microwave heating. Various state-of-the-art spatial and temporal discretisation methods employed to solve Maxwell's equations on multidimensional structured grid networks are investigated, and the dispersive and dissipative errors inherent in those techniques examined. Both staggered and unstaggered grid approaches are considered. Upwind schemes using a Riemann solver and intensity vector splitting are studied and evaluated. Staggered and unstaggered Leapfrog and Runge-Kutta time integration methods are analysed in terms of phase and amplitude error to identify which method is the most accurate and efficient for simulating microwave heating processes. The implementation and migration of typical electromagnetic boundary conditions. from staggered in space to cell-centred approaches also is deliberated. In particular, an existing perfectly matched layer absorbing boundary methodology is adapted to formulate a new cell-centred boundary implementation for the ccFV-TD solvers. Finally for microwave heating purposes, a comparison of analytical and numerical results for standard case studies in rectangular waveguides allows the accuracy of the developed methods to be assessed.

Some Remarks on the Approximation of Transitional Density in Stochastic Differential Equations

Aijt-Sahalia (2002) introduced a method to estimate transitional probability densities of di®usion processes by means of Hermite expansions with coe±cients determined by means of Taylor series. This note describes a numerical procedure to ¯nd these coe±cients based on the calculation of moments. One advantage of this procedure is that it can be used e®ectively when the mathematical operations required to ¯nd closed-form expressions for these coe±cients are otherwise infeasible.