An extension of Purcell's vector method with applications to panel element equations

The classical Purcell's vector method, for the construction of solutions to dense systems of linear equations is extended to a flexible orthogonalisation procedure. Some properties are revealed of the orthogonalisation procedure in relation to the classical Gauss-Jordan elimination with or without pivoting. Additional properties that are not shared by the classical Gauss-Jordan elimination are exploited. Further properties related to distributed computing are discussed with applications to panel element equations in subsonic compressible aerodynamics. Using an orthogonalisation procedure within panel methods enables a functional decomposition of the sequential panel methods and leads to a two-level parallelism.

Simulation of 2-D metal cutting by means of a distributed algorithm

Temperature distributions involved in some metal-cutting or surface-milling processes may be obtained by solving a non-linear inverse problem. A two-level concept on parallelism is introduced to compute such temperature distribution. The primary level is based on a problem-partitioning concept driven by the nature and properties of the non-linear inverse problem. Such partitioning results to a coarse-grained parallel algorithm. A simplified 2-D metal-cutting process is used as an example to illustrate the concept. A secondary level exploitation of further parallel properties based on the concept of domain-data parallelism is explained and implemented using MPI. Some experiments were performed on a network of loosely coupled machines consist of SUN Sparc Classic workstations and a network of tightly coupled processors, namely the Origin 2000.

Virtual manufacturing and design in the real world - implementation and scalability on HPPC systems

Virtual manufacturing and design assessment increasingly involve the simulation of interacting phenomena, sic. multi-physics, an activity which is very computationally intensive. This chapter describes an attempt to address the parallel issues associated with a multi-physics simulation approach based upon a range of compatible procedures operating on one mesh using a single database - the distinct physics solvers can operate separately or coupled on sub-domains of the whole geometric space. Moreover, the finite volume unstructured mesh solvers use different discretization schemes (and, particularly, different ‘nodal’ locations and control volumes). A two-level approach to the parallelization of this simulation software is described: the code is restructured into parallel form on the basis of the mesh partitioning alone, that is, without regard to the physics. However, at run time, the mesh is partitioned to achieve a load balance, by considering the load per node/element across the whole domain. The latter of course is determined by the problem specific physics at a particular location.

Performance evaluation of a distributed algorithm for an inverse heat conduction problem

Numerical solutions of realistic 2-D and 3-D inverse problems may require a very large amount of computation. A two-level concept on parallelism is often used to solve such problems. The primary level uses the problem partitioning concept which is a decomposition based on the mathematical/physical problem. The secondary level utilizes the widely used data partitioning concept. A theoretical performance model is built based on the two-level parallelism. The observed performance results obtained from a network of general purpose Sun Sparc stations are compared with the theoretical values. Restrictions of the theoretical model are also discussed.

Numerical solutions of certain nonlinear models in European options on a distributed computing environment

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. 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. In turn, analysis tools rely on fast numerical algorithms for the solution of financial mathematical models. There are many different financial activities apart from shares buy/sell activities. The main aim of this chapter is to discuss a distributed algorithm for the numerical solution of a European option. Both linear and non-linear cases are considered. The algorithm is based on the concept of the Laplace transform and its numerical inverse. The scalability of the algorithm is examined. Numerical tests are used to demonstrate the effectiveness of the algorithm for financial analysis. Time dependent functions for volatility and interest rates are also discussed. Applications of the algorithm to non-linear Black-Scholes equation where the volatility and the interest rate are functions of the option value are included. Some qualitative results of the convergence behaviour of the algorithm is examined. This chapter also examines the various computational issues of the Laplace transformation method in terms of distributed computing. The idea of using a two-level temporal mesh in order to achieve distributed computation along the temporal axis is introduced. Finally, the chapter ends with some conclusions.

A study on the cost sharing model for supply lead time reduction with component commonality

This paper studies a two-level supply chain consisting of components supplier and product assembly manufacturer, while the manufacturer shares the investment on shortening supply lead time. The objective of this research is to investigate the benefits of cost sharing strategy and adopting component commonality. The result of numerical analysis demonstrates that using component commonality can help reduce the total cost, especially when the manufacture shares a higher fraction of the cost of investment in shortening supply lead time.

Multiscale numerical modelling of crack propagation in two-dimensional metal plate

A novel multiscale model of brittle crack propagation in an Ag plate with macroscopic dimensions has been developed. The model represents crack propagation as stochastic drift-diffusion motion of the crack tip atom through the material, and couples the dynamics across three different length scales. It integrates the nanomechanics of bond rupture at the crack tip with the displacement and stress field equations of continuum based fracture theories. The finite element method is employed to obtain the continuum based displacement and stress fields over the macroscopic plate, and these are then used to drive the crack tip forward at the atomic level using the molecular dynamics simulation method based on many-body interatomic potentials. The linkage from the nanoscopic scale back to the macroscopic scale is established via the Ito stochastic calculus, the stochastic differential equation of which advances the tip to a new position on the macroscopic scale using the crack velocity and diffusion constant obtained on the nanoscale. Well known crack characteristics, such as the roughening transitions of the crack surfaces, crack velocity oscillations, as well as the macroscopic crack trajectories, are obtained.

A multi-scale atomistic-continuum modelling of crack propagation in a two-dimensional macroscopic plate

A novel multi-scale seamless model of brittle-crack propagation is proposed and applied to the simulation of fracture growth in a two-dimensional Ag plate with macroscopic dimensions. The model represents the crack propagation at the macroscopic scale as the drift-diffusion motion of the crack tip alone. The diffusive motion is associated with the crack-tip coordinates in the position space, and reflects the oscillations observed in the crack velocity following its critical value. The model couples the crack dynamics at the macroscales and nanoscales via an intermediate mesoscale continuum. The finite-element method is employed to make the transition from the macroscale to the nanoscale by computing the continuum-based displacements of the atoms at the boundary of an atomic lattice embedded within the plate and surrounding the tip. Molecular dynamics (MD) simulation then drives the crack tip forward, producing the tip critical velocity and its diffusion constant. These are then used in the Ito stochastic calculus to make the reverse transition from the nanoscale back to the macroscale. The MD-level modelling is based on the use of a many-body potential. The model successfully reproduces the crack-velocity oscillations, roughening transitions of the crack surfaces, as well as the macroscopic crack trajectory. The implications for a 3-D modelling are discussed.

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.

Design for reliability for wafer level system in package

This paper discusses the Design for Reliability modelling of several System-in-Package (SiP) structures developed by NXP and advanced on the basis of Wafer Level Packaging (WLP). Two different types of Wafer Level SiP (WLSiP) are presented and discussed. The main focus is on the modelling approach that has been adopted to investigate and analyse the board level reliability of the presented SiP configurations. Thermo-mechanical non-linear Finite Element Analysis (FEA) is used to analyse the effect of various package design parameters on the reliability of the structures and to identify design trends towards package optimisation. FEA is used also to gain knowledge on moulded wafer shrinkage and related issues during the wafer level fabrication. The paper provides a brief outline and demonstration of a design methodology for reliability driven design optimisation of SiP. The study emphasises the advantages of applying the methodology to address complex design problems where several requirements may exist and uncertainties and interactions between parameters in the design are common.

Vibrational spectroscopic studies of the structure of di-amino acid peptides. Part II: cyclo(L-Asp-L-Asp) in the solid state and in aqueous solution

Solid-state protonated and N,O-deuterated Fourier transform infrared (IR) and Raman scattering spectra together with the protonated and deuterated Raman spectra in aqueous solution of the cyclic di-amino acid peptide cyclo(L-Asp-L-Asp) are reported. Vibrational band assignments have been made on the basis of comparisons with previously cited literature values for diketopiperazine (DKP) derivatives and normal coordinate analyses for both the protonated and deuterated species based upon DFT calculations at the B3-LYP/cc-pVDZ level of the isolated molecule in the gas phase. The calculated minimum energy structure for cyclo(L-Asp-L-Asp), assuming C-2 symmetry, predicts a boat conformation for the DKP ring with both the two L-aspartyl side chains being folded slightly above the ring. The C=O stretching vibrations have been assigned for the side-chain carboxylic acid group (e.g. at 1693 and 1670 cm(-1) in the Raman spectrum) and the cis amide I bands (e.g. at 1660 cm(-1) in the Raman spectrum). The presence of two bands for the carboxylic acid C=O stretching modes in the solid-state Raman spectrum can be accounted for by factor group splitting of the two nonequivalent molecules in a crystallographic unit cell. The cis amide II band is observed at 1489 cm(-1) in the solid-state Raman spectrum, which is in agreement with results for cyclic di-amino acid peptide molecules examined previously in the solid state, where the DKP ring adopts a boat conformation. Additionally, it also appears that as the molecular mass of the substituent on the C-alpha atom is increased, the amide II band wavenumber decreases to below 1500 cm(-1); this may be a consequence of increased strain on the DKP ring. The cis amide II Raman band is characterized by its relatively small deuterium shift (29 cm(-1)), which indicates that this band has a smaller N-H bending contribution than the trans amide II vibrational band observed for linear peptides.