A defect equation approach for the coupling of subdomains in domain decomposition methods

A defect equation for the coupling of nonlinear subproblems defined in nonoverlapped subdomains arise in domain decomposition methods is presented. Numerical solutions of defect equations by means of quasi-Newton methods are considered.

A new parameterization of Johnson's SB distribution with application to fitting forest tree diameter data

The SB distributional model of Johnson's 1949 paper was introduced by a transformation to normality, that is, z ~ N(0, 1), consisting of a linear scaling to the range (0, 1), a logit transformation, and an affine transformation, z = γ + δu. The model, in its original parameterization, has often been used in forest diameter distribution modelling. In this paper, we define the SB distribution in terms of the inverse transformation from normality, including an initial linear scaling transformation, u = γ′ + δ′z (δ′ = 1/δ and γ′ = �γ/δ). The SB model in terms of the new parameterization is derived, and maximum likelihood estimation schema are presented for both model parameterizations. The statistical properties of the two alternative parameterizations are compared empirically on 20 data sets of diameter distributions of Changbai larch (Larix olgensis Henry). The new parameterization is shown to be statistically better than Johnson's original parameterization for the data sets considered here.

On a parallel time-domain method for the nonlinear Black-Scholes equation

A parallel time-domain algorithm is described for the time-dependent nonlinear Black-Scholes equation, which may be used to build financial analysis tools to help traders making rapid and systematic evaluation of buy/sell contracts. The algorithm is particularly suitable for problems that do not require fine details at each intermediate time step, and hence the method applies well for the present problem.

A prognostic assessment method for power electronics modules

This paper describes a prognostic method which combines the physics of failure models with probability reasoning algorithm. The measured real time data (temperature vs. time) was used as the loading profile for the PoF simulations. The response surface equation of the accumulated plastic strain in the solder interconnect in terms of two variables (average temperature, and temperature amplitude) was constructed. This response surface equation was incorporated into the lifetime model of solder interconnect, and therefore the remaining life time of the solder component under current loading condition was predicted. The predictions from PoF models were also used to calculate the conditional probability table for a Bayesian Network, which was used to take into account of the impacts of the health observations of each product in lifetime prediction. The prognostic prediction in the end was expressed as the probability for the product to survive the expected future usage. As a demonstration, this method was applied to an IGBT power module used for aircraft applications.