Multi-physics modelling of materials processes on high performance parallel computers

Abstract not available

Multi-physics modelling for design optimization and manufacturing on high-performance parallel systems

Abstract not available

Time domain decomposition for European options in financial modelling

Finance is one of the fastest growing areas in modern applied mathematics with real world applications. The interest of this branch of applied mathematics is best described by an example involving shares. Shareholders of a company receive dividends which come from the profit made by the company. The proceeds of the company, once it is taken over or wound up, will also be distributed to shareholders. Therefore shares have a value that reflects the views of investors about the likely dividend payments and capital growth of the company. Obviously such value will be quantified by the share price on stock exchanges. Therefore financial modelling serves to understand the correlations between asset and movements of buy/sell in order to reduce risk. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and systematic evaluation of buy/sell contracts. There are other financial activities and it is not an intention of this paper to discuss all of these activities. The main concern of this paper is to propose a parallel algorithm for the numerical solution of an European option. This paper is organised as follows. First, a brief introduction is given of a simple mathematical model for European options and possible numerical schemes of solving such mathematical model. Second, Laplace transform is applied to the mathematical model which leads to a set of parametric equations where solutions of different parametric equations may be found concurrently. Numerical inverse Laplace transform is done by means of an inversion algorithm developed by Stehfast. The scalability of the algorithm in a distributed environment is demonstrated. Third, a performance analysis of the present algorithm is compared with a spatial domain decomposition developed particularly for time-dependent heat equation. Finally, a number of issues are discussed and future work suggested.

Multi-physics modelling - A vital component of virtual manufacturing

One of the core tasks of the virtual-manufacturing environment is to characterise the transformation of the state of material during each of the unit processes. This transformation in shape, material properties, etc. can only be reliably achieved through the use of models in a simulation context. Unfortunately, many manufacturing processes involve the material being treated in both the liquid and solid state, the trans-formation of which may be achieved by heat transfer and/or electro-magnetic fields. The computational modelling of such processes, involving the interactions amongst various interacting phenomena, is a consider-able challenge. However, it must be addressed effectively if Virtual Manufacturing Environments are to become a reality! This contribution focuses upon one attempt to develop such a multi-physics computational toolkit. The approach uses a single discretisation procedure and provides for direct interaction amongst the component phenomena. The need to exploit parallel high performance hardware is addressed so that simulation elapsed times can be brought within the realms of practicality. Examples of Multiphysics modelling in relation to shape casting, and solder joint formation reinforce the motivation for this work.

Dynamic load balancing of distributed memory parallel computational mechanics using unstructured meshes for multi-physical modelling

As the complexity of parallel applications increase, the performance limitations resulting from computational load imbalance become dominant. Mapping the problem space to the processors in a parallel machine in a manner that balances the workload of each processors will typically reduce the run-time. In many cases the computation time required for a given calculation cannot be predetermined even at run-time and so static partition of the problem returns poor performance. For problems in which the computational load across the discretisation is dynamic and inhomogeneous, for example multi-physics problems involving fluid and solid mechanics with phase changes, the workload for a static subdomain will change over the course of a computation and cannot be estimated beforehand. For such applications the mapping of loads to process is required to change dynamically, at run-time in order to maintain reasonable efficiency. The issue of dynamic load balancing are examined in the context of PHYSICA, a three dimensional unstructured mesh multi-physics continuum mechanics computational modelling code.

Enhancing the numerical performance of fire field models (CMS Paper)

This paper describes two new techniques designed to enhance the performance of fire field modelling software. The two techniques are "group solvers" and automated dynamic control of the solution process, both of which are currently under development within the SMARTFIRE Computational Fluid Dynamics environment. The "group solver" is a derivation of common solver techniques used to obtain numerical solutions to the algebraic equations associated with fire field modelling. The purpose of "group solvers" is to reduce the computational overheads associated with traditional numerical solvers typically used in fire field modelling applications. In an example, discussed in this paper, the group solver is shown to provide a 37% saving in computational time compared with a traditional solver. The second technique is the automated dynamic control of the solution process, which is achieved through the use of artificial intelligence techniques. This is designed to improve the convergence capabilities of the software while further decreasing the computational overheads. The technique automatically controls solver relaxation using an integrated production rule engine with a blackboard to monitor and implement the required control changes during solution processing. Initial results for a two-dimensional fire simulation are presented that demonstrate the potential for considerable savings in simulation run-times when compared with control sets from various sources. Furthermore, the results demonstrate the potential for enhanced solution reliability due to obtaining acceptable convergence within each time step, unlike some of the comparison simulations.