We provide an overview of our work to date on the parallelization of implicit time domain methods, in particular the alternating direction implicit finite-difference time-domain method (ADI-FDTD). First we describe a domain decomposition scheme for parallel ADI-FDTD in three dimensions that is suitable for implementation on widely available high performance computer architectures such as symmet...

There is currently a regain of interest in the Alternating Direction Implicit (ADI) algorithms as preconditioners for iterative methods for solving large sparse linear systems, because of their suitability for parallel computing. However, the classical ADI iteration is not directly applicable to Finite Element (FE) matrices, tends to converge too slowly for 3-D problems, and the selection of ad...

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is furthe...

(2014). Fundamental locally one-dimensional method for 3-D thermal simulation. IEICE transactions on electronics, E97.C(7), 636-644. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification o...

The lumped network alternating direction implicit finite difference time domain (LN-ADI-FDTD) technique is proposed as an extension of the conventional ADI-FDTD method in this paper, which allows the lumped networks to be inserted into some ADI-FDTD cells. Based on the piecewise linear recursive convolution (PLRC) technique, the current expression of the loaded place can be obtained. Then, subs...

We consider new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer [12]. Different numerical discretizations which lead to schemes which are fourth-order accurate in space and sec...

sex in evolution Adi Livnat∗† ‡, Christos Papadimitriou ‡ , Jonathan Dushoff § and Marcus W. Feldman ¶ †Miller Institute for Basic Research in Science, University of California, Berkeley, CA 94720 USA,‡Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720 USA,§Department of Biology, McMaster University, Hamilton, ON L8S 4K1 CANADA, and ¶Departme...