On a parallel time-domain method for the nonlinear Black-Scholes equation

A parallel time-domain algorithm is described for the time-dependent nonlinear Black-Scholes equation, which may be used to build financial analysis tools to help traders making rapid and systematic evaluation of buy/sell contracts. The algorithm is particularly suitable for problems that do not require fine details at each intermediate time step, and hence the method applies well for the present problem.

Simulating the evacuation of very large populations in large domains using a parallel implementation of the buildingEXODUS evacuation model

Computer egress simulation has potential to be used in large scale incidents to provide live advice to incident commanders. While there are many considerations which must be taken into account when applying such models to live incidents, one of the first concerns the computational speed of simulations. No matter how important the insight provided by the simulation, numerical hindsight will not prove useful to an incident commander. Thus for this type of application to be useful, it is essential that the simulation can be run many times faster than real time. Parallel processing is a method of reducing run times for very large computational simulations by distributing the workload amongst a number of CPUs. In this paper we examine the development of a parallel version of the buildingEXODUS software. The parallel strategy implemented is based on a systematic partitioning of the problem domain onto an arbitrary number of sub-domains. Each sub-domain is computed on a separate processor and runs its own copy of the EXODUS code. The software has been designed to work on typical office based networked PCs but will also function on a Windows based cluster. Two evaluation scenarios using the parallel implementation of EXODUS are described; a large open area and a 50 story high-rise building scenario. Speed-ups of up to 3.7 are achieved using up to six computers, with high-rise building evacuation simulation achieving run times of 6.4 times faster than real time.

Predicting toxic species concentrations in a full-scale vitiated fire

A toxicity model on dividing the computational domain into two parts, a control region (CR) and a transport region (TR), for species calculation was recently developed. The model can be incorporated with either the heat source approach or the eddy dissipation model (EDM). The work described in this paper is a further application of the toxicity model with modifications of the EDM for vitiated fires. In the modified EDM, chemical reaction only occurs within the CR. This is consistent with the approach used in the species concentration calculations within the toxicity model in which yields of combustion products only change within the CR. A vitiated large room-corridor fire, in which the carbon monoxide (CM) concentrations are very high and the temperatures are relatively low at locations distant from the original fire source, is simulated using the modified EDM coupled with the toxicity model. Compared with the EDM, the modified EDM provide significant improvements in the predictions of temperatures at remote locations. Predictions of species concentrations at various locations follow the measured trends. Good agreements between the measured and predicted species concentrations are obtained at the vitiated fire stage.

A hybrid Laplace transform/finite difference boundary element method for diffusion problems

The solution process for diffusion problems usually involves the time development separately from the space solution. A finite difference algorithm in time requires a sequential time development in which all previous values must be determined prior to the current value. The Stehfest Laplace transform algorithm, however, allows time solutions without the knowledge of prior values. It is of interest to be able to develop a time-domain decomposition suitable for implementation in a parallel environment. One such possibility is to use the Laplace transform to develop coarse-grained solutions which act as the initial values for a set of fine-grained solutions. The independence of the Laplace transform solutions means that we do indeed have a time-domain decomposition process. Any suitable time solver can be used for the fine-grained solution. To illustrate the technique we shall use an Euler solver in time together with the dual reciprocity boundary element method for the space solution

Discourse and soul: Jung, literature, science and tragedy as mythical writing

This paper will propose that literature and science, far from being discrete spheres of cultural activity, are, in fact, the cultural expressions of interlocking myths. They therefore overlap and even take each other’s places, as examination of the ‘science’ of C.G. Jung and the ‘art’ of a writer such as John Cowper Powys, will show. ‘Dis-course’, I argue, is the material aspect of the mythical structuring of psychic experience. In the work of Jung and Powys, discourse is the articulation of the soul in the world that spans personal, social, natural and cosmic space. [From the Author]