We study accuracy of alternating direction implicit (ADI) methods for parabolic equations. The original ADI method applied to parabolic equations is a perturbation of the Crank-Nicolson di erence equation and has second-order accuracy both in space and time. The perturbation error is on the same order as the discretization error, in terms of mathematical description. However, we often observe i...

Near Net Shape (NNS) manufacturing produces the engineering components closer to its final specification in single stage or minimum number of stages. ADI process technology is one of the NNS manufacturing technologies, currently being followed by the industries for manufacturing of engineering components at competitive price. Austempered Ductile Iron is a new class of engineering material which...

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence (CDI) FDTD method. In this paper, formulations from time-collocated to fundamental are presented ADI CDI methods. For implemented using E-E E-H update procedures, which comprise simple concise right-hand sides...

1. introduction a drought is a prolonged period of water deficit and usually occurs when an area does not receive significant precipitation for a sustained period of time, say several months (chen, kuo, & yu, 2009; linsely, kohlerm, & paulhus, 1959). the effects of drought often accumulate slowly over a considerable period of time that may linger for several years even after the termination of dr...

This paper describes a new unconditionally stable numerical method for the full-wave physical modeling of semiconductor devices by a combination of the finite-difference Laguerre time-domain (FDLTD) and alternative direction implicit finite-difference time-domain (ADI-FDTD) approaches. The unconditionally stable method by using FDLTD scheme for the electromagnetic model and semi-implicit ADI-FD...

The ADI iteration is closely related to the rational Krylov projection methods for constructing low rank approximations to the solution of Sylvester equation. In this paper we show that the ADI and rational Krylov approximations are in fact equivalent when a special choice of shifts are employed in both methods. We will call these shifts pseudo H2-optimal shifts. These shifts are also optimal i...

The numerical solution of the time-dependent neutron transport problem in 2-D Cartesian geometry is considered. The problem is described by a coupled system of hyperbolic partial differential equations with the parameters of multiple groups. The system, for given group parameter, is discretized by a discrete ordinate method (SN) in angular direction and adaptive spline wavelet method with alter...