Parallel numerical methods for analysing optical devices with the BPM

In this work, some developments in the theory of modelling integrated optical devices are discussed. The theory of the Beam Propagation Method (BPM) to analyse longitudinal optical waveguides is established. The BPM is then formulated and implemented numerically to study both two and three-dimensional optical waveguides using several Finite-Difference (FD) techniques. For the 2-D analysis, comparisons between the performance of the implicit Crank Nicholson (CN), the explicit Real Space (RS) and the Explicit Finite-Difference (EFD) are made through systematic tests on slab waveguide geometries. For three-dimensional applications, two explicit highly-parallel three-dimensional FD-BPMs (the RS and the EFD) have been implemented on two different parallel computers, namely a transputer array (MIMD type) and a Connection Machine (SIMD type). To assess the performance of parallel computers in this context, serial computer codes for the two methods have been implemented and a comparison between the speed of the serial and parallel codes has been made. Large gains in the speed of the parallel FD-BPMs have been obtained compared to the serial implementations; both methods, in their parallel form, can execute, per propagational step, a large problem containing 106 discretisation points in a few seconds. In addition, a comparison between the performance of the transputer array and the Connection Machine in executing the two FD-BPMs has been discussed. To assess and compare the two methods, three different rib waveguides and three different directional couplers have been analysed and the results compared with published results. It has been concluded from testing these methods that the parallel EFD-BPM is more efficient than the parallel RS-BPM. Then, the linear parallel EFD-BPM was extended to model nonlinear second harmonic generation process in three-dimensional waveguides, where the source field is allowed to deplete, using the transputer array and the Connection Machine

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Parallel processing for nonlinear dynamics simulations of structures including rotating bladed-disk assemblies

The principal objective of this research is to develop, test, and implement coarse-grained, parallel-processing strategies for nonlinear dynamic simulations of practical structural problems. There are contributions to four main areas: finite element modeling and analysis of rotational dynamics, numerical algorithms for parallel nonlinear solutions, automatic partitioning techniques to effect load-balancing among processors, and an integrated parallel analysis system

Field simulation of axisymmetric plasma screw pinches by alternating-direction-implicit methods

An axisymmetric plasma screw pinch is an axisymmetric column of ionized gaseous plasma radially confined by forces from axial and azimuthal currents driven in the plasma and its surroundings. This dissertation is a contribution to detailed, high resolution computer simulation of dynamic plasma screw pinches in 2-d {ital rz}-coordinates. The simulation algorithm combines electron fluid and particle-in-cell (PIC) ion models to represent the plasma in a hybrid fashion. The plasma is assumed to be quasineutral; along with the Darwin approximation to the Maxwell equations, this implies application of Ampere`s law without displacement current. Electron inertia is assumed negligible so that advective terms in the electron momentum equation are ignored. Electrons and ions have separate scalar temperatures, and a scalar plasma electrical resistivity is assumed. Altemating-direction-implicit (ADI) methods are used to advance the electron fluid drift velocity and the magnetic fields in the simulation. The ADI methods allow time steps larger than allowed by explicit methods. Spatial regions where vacuum field equations have validity are determined by a cutoff density that invokes the quasineutral vacuum Maxwell equations (Darwin approximation). In this dissertation, the algorithm was first checked against ideal MM stability theory, and agreement was nicely demonstrated. However, such agreement is not a new contribution to the research field. Contributions to the research field include new treatments of the fields in vacuum regions of the pinch simulation. The new treatments predict a level of magnetohydrodynamic turbulence near the bulk plasma surface that is higher than predicted by other methods

Finite elements software and applications

The contents of this thesis are a detailed study of the software for the finite element method. In the text, the finite element method is introduced from both the engineering and mathematical points of view. The computer implementation of the method is explained with samples of mainframe, mini- and micro-computer implementations. A solution is presented for the problem of limited stack size for both mini- and micro-computers which possess stack architecture. Several finite element programs are presented. Special purpose programs to solve problems in structural analysis and groundwater flow are discussed. However, an efficient easy-to-use finite element program for general two-dimensional problems is presented. Several problems in groundwater flow are considered that include steady, unsteady flows in different types of aquifers. Different cases of sinks and sources in the flow domain are also considered. The performance of finite element methods is studied for the chosen problems by comparing the numerical solutions of test problems with analytical solutions (if they exist) or with solutions obtained by other numerical methods. The polynomial refinement of the finite elements is studied for the presented problems in order to offer some evidence as to which finite element simulation is best to use under a variety of circumstances