A domain decomposition algorithm for viscous/inviscid coupling

In fluid mechanics, it is well accepted that the Euler equation is one of the reduced forms of the Navier-Stokes equation by truncating the viscous effect. There are other truncation techniques currently being used in order to truncate the Navier-Stokes equation to a reduced form. This paper describes one such technique, suitable for adaptive domain decomposition methods for the solution of viscous flow problems. The physical domain of a viscous flow problem is partitioned into viscous and inviscid subdomains without overlapping regions, and the technique is embedded into a finite volume method. Some numerical results are provided for a flat plate and the NACA0012 aerofoil. Issues related to distributed computing are discussed.

A defect equation approach for the coupling of subdomains in domain decomposition methods

A defect equation for the coupling of nonlinear subproblems defined in nonoverlapped subdomains arise in domain decomposition methods is presented. Numerical solutions of defect equations by means of quasi-Newton methods are considered.

Domain decomposition using a 2-level correction scheme

The PHYSICA software was developed to enable multiphysics modelling allowing for interaction between Computational Fluid Dynamics (CFD) and Computational Solid Mechanics (CSM) and Computational Aeroacoustics (CAA). PHYSICA uses the finite volume method with 3-D unstructured meshes to enable the modelling of complex geometries. Many engineering applications involve significant computational time which needs to be reduced by means of a faster solution method or parallel and high performance algorithms. It is well known that multigrid methods serve as a fast iterative scheme for linear and nonlinear diffusion problems. This papers attempts to address two major issues of this iterative solver, including parallelisation of multigrid methods and their applications to time dependent multiscale problems.

Feller transition functions, Resolvent Decomposition Theorems, and their application in unstable denumerable Markov processes

This paper surveys the recent progresses made in the field of unstable denumerable Markov processes. Emphases are laid upon methodology and applications. The important tools of Feller transition functions and Resolvent Decomposition Theorems are highlighted. Their applications particularly in unstable denumerable Markov processes with a single instantaneous state and Markov branching processes are illustrated.

A domain decomposition algorithm for inverse welding problems

A mathematical model and a numerical scheme for the inverse determination of heat sources generated by means of a welding process is presented in this paper. The accuracy of the heat source retrieval is discussed.

Domain decomposition methods for welding problems

This paper, a 2-D non-linear electric arc-welding problem is considered. It is assumed that the moving arc generates an unknown quantity of energy which makes the problem an inverse problem with an unknown source. Robust algorithms to solve such problems e#ciently, and in certain circumstances in real-time, are of great technological and industrial interest. There are other types of inverse problems which involve inverse determination of heat conductivity or material properties [CDJ63][TE98], inverse problems in material cutting [ILPP98], and retrieval of parameters containing discontinuities [IK90]. As in the metal cutting problem, the temperature of a very hot surface is required and it relies on the use of thermocouples. Here, the solution scheme requires temperature measurements lied in the neighbourhood of the weld line in order to retrieve the unknown heat source. The size of this neighbourhood is not considered in this paper, but rather a domain decomposition concept is presented and an examination of the accuracy of the retrieved source are presented. This paper is organised as follows. The inverse problem is formulated and a method for the source retrieval is presented in the second section. The source retrieval method is based on an extension of the 1-D source retrieval method as proposed in [ILP].

Electronic packaging and reduction in modelling time using domain decomposition

The domain decomposition method is directed to electronic packaging simulation in this article. The objective is to address the entire simulation process chain, to alleviate user interactions where they are heavy to mechanization by component approach to streamline the model simulation process.

Domain decomposition methods for some aerodynamic noise problems

Abstract not available

A domain decomposition based algorithm for non-linear 2D inverse heat conduction problems

Inverse heat conduction problems (IHCPs) appear in many important scientific and technological fields. Hence analysis, design, implementation and testing of inverse algorithms are also of great scientific and technological interest. The numerical simulation of 2-D and –D inverse (or even direct) problems involves a considerable amount of computation. Therefore, the investigation and exploitation of parallel properties of such algorithms are equally becoming very important. Domain decomposition (DD) methods are widely used to solve large scale engineering problems and to exploit their inherent ability for the solution of such problems.

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.

Development of a domain decomposition method for computational aeroacoustics

Abstract not available

Scalable unstructured mesh decomposition

As the efficiency of parallel software increases it is becoming common to measure near linear speedup for many applications. For a problem size N on P processors then with software running at O(N=P ) the performance restrictions due to file i/o systems and mesh decomposition running at O(N) become increasingly apparent especially for large P . For distributed memory parallel systems an additional limit to scalability results from the finite memory size available for i/o scatter/gather operations. Simple strategies developed to address the scalability of scatter/gather operations for unstructured mesh based applications have been extended to provide scalable mesh decomposition through the development of a parallel graph partitioning code, JOSTLE [8]. The focus of this work is directed towards the development of generic strategies that can be incorporated into the Computer Aided Parallelisation Tools (CAPTools) project.