We present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dial grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points xi. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that sp...

The complex-step method for calculating sensitivities and its use in numerical algorithms is presented. A general procedure for the implementation of this method is described in detail and a script is developed that automates its implementation. The numerical examples include the automatic conversion of a structural finite element and a two-dimensional computational fluid dynamics code. In both...

Maximum likelihood (ML) estimation maximizes the likelihood function and is a celebrated principle in linear regression analysis. Asymptotically, the Cramér-Rao lower bound for the covariance matrix of unbiased estimated parameters is reached by the maximum likelihood estimator. With asymptotic arguments, it has been proved that this principle can also be applied to autoregression and to the mo...

Partial differential equations are used to describe physical phenomena in many science and engineering fields. Finite differencing methods map these continuous equations into discrete space so that they may be solved on computers. Co-Array Fortran provides the means for implementing such solution methods in parallel processing computing environments. In this report we describe our experiences w...