The paper describes a multiple grid method for transonic flow calculations. The proposed scheme incorporates a generalized alternating direction method as the smoothing algorithm. Numerical experiments with this multigrid alternating direction (MAD) method indicate that it is both fast and reliable.

A thorough numerical assessment of Finite Difference Time Domain and Complex-Envelope Alternating-Direction-Implicit Finite-Difference-Time-Domain Methods has been carried out based on a basic single mode Plane Optical Waveguide structure. Simulation parameters for both methods were varied and the impact on the performance of both numerical methods is investigated.

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...

We present a sparse grid high-order alternating direction implicit (ADI) scheme for option pricing in stochastic volatility models. The scheme is second-order in time and fourth-order in space. Numerical experiments confirm the computational efficiency gains achieved by the sparse grid combination technique.

This paper suggests applying tools of analysis that had been used previously in the …eld of occupational segregation and horizontal inequity measurement to the study of intergenerational social immobility. The paper introduces the concept of “social immobility curve”and two indices of social immobility are proposed that are extensions of the Theil and Gini indices of inequality. The paper stres...

Direct Experimental Support for the Catalytic Effect of Iron-Group Metals on Electrodeposition of Rhenium Adi Naor, Noam Eliaz,* Larisa Burstein, and Eliezer Gileadi** Biomaterials and Corrosion Laboratory, The Materials and Nanotechnologies Program, Wolfson Applied Materials Research Center, and School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ra...

We investigate the factored ADI iteration for large and sparse Sylvester equations. A novel low-rank expression for the associated Sylvester residual is established which enables cheap computations of the residual norm along the iteration, and which yields a reformulated factored ADI iteration. The application to generalized Sylvester equations is considered as well. We also discuss the efficie...

Chinmay Khandekar,1 Weiliang Jin,1 Owen D. Miller,2 Adi Pick,3 and Alejandro W. Rodriguez1 1Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA 2Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 3Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA (Received 13 November 2015; r...

This paper shows how a well-balanced trade-off between a generic workstation and dumb but fast reconfigurable hardware can lead to a more efficient implementation of a cryptanalysis than a full hardware or a full software implementation. A realistic cryptanalysis of the A5/1 GSM stream cipher is presented as an illustration of such trade-off. We mention that our cryptanalysis requires only a mi...

1. Introduction. This note presents a few of the results which we have obtained by applying a classical and fundamental idea to the analysis of certain partial difference equations. The idea is that certain multidimensional problems can be solved by solving a few one-dimensional problems—it is the basis of the classical method of separation of variables of mathematical physics. In the case of p...