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This paper illustrates how problems based on the Probabilistic Potential Method can be solved using a parallelized form of the Exodus Monte Carlo technique. The Exodus technique which does not use random number generation is shown to be more efficient for moderately large problems than the conventional fixed random walk method when programmed in both sequential and concurrent forms. The technique is illustrated for an electrostatic field problem by using as an example internal potential evaluation for a rectangular coaxial line. The problem geometry is torn into subsections which are then analysed independently using concurrent programming methods. The resulting algorithm is compared with the same problem executed using a conventional sequential algorithm. Computation is achieved by use of an array of transputers. The design of the concurrent algorithm is described in detail and typical results are compared with the fixed random walk Monte Carlo method and also with the finite difference relaxation method. Parallel Fortran is used throughout as the programming language. [ABSTRACT FROM AUTHOR]

SUMMARY Orthonormal vector fitting is a robust method for broadband macromodeling of frequency domain responses. The use of orthonormal rational basis functions makes the conditioning of the system equations less sensitive to the initial pole specification when compared with the classical Vector Fitting procedure. This paper presents a time domain generalization of the technique to compute broadband rational macromodels from transient input-output port responses. The efficacy of the approach is illustrated by two numerical examples. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

There is a class of material processing simulators which require solution of the diffusion equation over a surface which is evolving due to some physical or chemical process related to the concentration of the diffusing species. Because of its explicit and unconditionally stable nature, the transmission line matrix (TLM) method is well suited to efficiently solve the diffusion equation in these instances. However, the methodology for using TLM on a dynamic problem space is not well established. This paper describes the development of algorithms to handle the insertion, deletion and motion of TLM nodes along the one-dimensional surface of a two-dimensional thin film process simulator called GROFILMS. These routines are completely compatible with concurrent time scaling to increase computational efficiency. Central to this development is the use of an asymmetric TLM cell which provides more flexibility for representation and minimizes the disturbance effects of these nodal operations. The scaling routines apply conservation of charge and continuity of current into the affected region to recompute the scattered or the incident pulses as a result of the evolving network. Verification of these results through comparison with known analytic solutions is achieved where possible. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper introduces a simple model for solving a system of first-order rate equations using the TLM numerical method. A general algorithm is developed by setting up a matrix of discrete compartments. The rate constants provide the linkage between each compartment and the neighbouring ones. The method is demonstrated by some examples in which saturation conditions are considered. The TLM solution is compared with analytical solutions and the Rung-Kutta method of solving differential equations. [ABSTRACT FROM AUTHOR]

Series function expansion algorithms of the time-domain analysis of boundary value problems are discussed. Electromagnetic fields inside a structure under investigation are expanded into series of basis functions and the expansion coefficients are found by means of the Galerkin method. The numerical cost of algorithms is discussed and a cost efficient approach is proposed for formulations using sine and cosine expansion functions. Compared with conventional time-domain methods the algorithms described show the time evolution of the expansion coefficients rather than the samples of a physical continuum at discrete nodes. [ABSTRACT FROM AUTHOR]

A set of modified semiconductor equations is described together with novel algorithms for solving them. These ensure a well-behaved, guaranteed convergent solution for a steady-state semiconductor model. Examples results on the simulation of a GaAs Dual Gate MESFET are given to demonstrate the efficiency of the new scheme. [ABSTRACT FROM AUTHOR]

A novel procedure for the numerical modelling of current transport in semiconductor devices is presented. The method is based on high-order trigonometric expansions (Fourier series) of the solution. The expansion coefficients are calculated in a Galerkin-type algorithm. The method offers infinite-order accuracy regardless of the number of spatial dimensions of the model. Well-conditioning and diagonal dominance of the discrete equations render the numerical procedure stable and effective. Significant advantages are expected, particularly for the solution of strongly non-linear multidimensional device models. Properties of the algorithm are demonstrated on standard semiconductor devices. [ABSTRACT FROM AUTHOR]