Parallel algorithms of the Purcell method for direct solution of linear systems

In this paper, we first demonstrate that the classical Purcell's vector method when combined with row pivoting yields a consistently small growth factor in comparison to the well-known Gauss elimination method, the Gauss–Jordan method and the Gauss–Huard method with partial pivoting. We then present six parallel algorithms of the Purcell method that may be used for direct solution of linear systems. The algorithms differ in ways of pivoting and load balancing. We recommend algorithms V and VI for their reliability and algorithms III and IV for good load balance if local pivoting is acceptable. Some numerical results are presented.

A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and threedimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted.

An acoustic correction method for extracting sound signals

Sound waves are propagating pressure fluctuations and are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier-Stokes (RANS) equations do not resolve the acoustic fluctuations. Direct numerical simulation of turbulent flow is still a prohibitively expensive tool to perform noise analysis. This paper proposes the acousticcorrectionmethod, an alternative and affordable tool based on a modified defect correction concept, which leads to an efficient algorithm for computational aeroacoustics and noise analysis.

Shear strength analysis of ball grid array (BGA) solder interfaces

Ball shear test is the most common test method used to assess the reliability of bond strength for ball grid array (BGA) packages. In this work, a combined experimental and numerical study was carried out to realize of BGA solder interface strength. Solder mask defined bond pads on the BGA substrate were used for BGA ball bonding. Different bond pad metallizations and solder alloys were used. Solid state aging at 150degC up to 1000 h has been carried out to change the interfacial microstructure. Cross-sectional studies of the solder-to-bond pad interfaces was conducted by scanning electron microscopy (SEM) equipped with an energy dispersive X-ray (EDX) analyzer to investigate the interfacial reaction phenomena. Ball shear tests have been carried out to obtain the mechanical strength of the solder joints and to correlate shear behaviour with the interfacial reaction products. An attempt has been taken to realize experimental findings by Finite Element Analysis (FEA). It was found that intermetallic compound (IMC) formation at the solder interface plays an important role in the BGA solder bond strength. By changing the morphology and the microchemistry of IMCs, the fracture propagation path could be changed and hence, reliability could be improved

Direct measurement of powder flavor adhesion onto crisp surface using a novel adhesion tester

A new experimental procedure has been implemented and a prototype of a novel adhesion tester has been designed and constructed using rapid prototyping technology. A tumbler mixer has been designed and constructed for coating powder material onto a crisp substrate. In the impact separation experiment, the amount of powder detached from one side of a crisp substrate by the effect of impact forces (48g, 77g, 102g) generated by the tester was measured. Salt particles with different size fractions (63-125, 125-180, and 180-250m) and several flavoring powders have been tested extensively. By plotting the detachment versus impact force, the difference obtained between adhesion strength of different flavoring powders (which is a strong function of particle size and surface oil content of the crisp) has been discussed. The detachment rate of salt particles increased (from 1% to 2%) with particle size (from 63 to 250m) in the presence of oil on the surface of the crisp substrate and decreased rapidly with the increase in the amount of oil applied (from 0 to 1%).

A revised classification for direct tooth-colored restorative materials

Composite resins and glass-ionomer cements were introduced to dentistry in the 1960s and 1970s, respectively. Since then, there has been a series of modifications to both materials as well as the development other groups claiming intermediate characteristics between the two. The result is a confusion of materials leading to selection problems. While both materials are tooth-colored, there is a considerable difference in their properties, and it is important that each is used in the appropriate situation. Composite resin materials are esthetic and now show acceptable physical strength and wear resistance. However, they are hydrophobic, and therefore more difficult to handle in the oral environment, and cannot support ion migration. Also, the problems of gaining long-term adhesion to dentin have yet to be overcome. On the other hand, glass ionomers are water-based and therefore have the potential for ion migration, both inward and outward from the restoration, leading to a number of advantages. However, they lack the physical properties required for use in load-bearing areas. A logical classification designed to differentiate the materials was first published by McLean et al in 1994, but in the last 15 years, both types of material have undergone further research and modification. This paper is designed to bring the classification up to date so that the operator can make a suitable, evidence-based, choice when selecting a material for any given situation.

Direct measurement of powder flavour adhesion on to a food surface using a novel adhesion tester

The firm adhesion of flavouring particles onto crisp surfaces during coating processes is a major concern in the snack production industry. Detachment of flavouring powders from products during handling and production stages can lead to substantial financial losses for the industry, in terms of variable flavour performance and extended cleaning down time of fugitive particle build-up on process equipment. Understanding the adhesion strength of applied bulk particulates used for flavouring formulations will help analysts to evaluate the efficiency of coating processes and potentially enable them to assess the adhesion strength of newly formulated flavouring powder prior to commitment to full scale plant trials. A rapid prototype of a novel adhesion tester has been designed and constructed. The apparatus operates according to the principle of impact force acting on particles attached to the surface of the food substrate. The main component is a circular plate to which four sample holders are attached and which is subjected to vertical travel down a guide shaft. Several flavouring powders have been tested extensively. By plotting the detachment versus impact force, the difference obtained between adhesion strength of different flavouring powders (which is a strong function of particle size) has been discussed.

A semi-Lagrangian finite volume method for solving viscoelastic flow problems

Recently, there has been considerable interest in solving viscoelastic problems in 3D particularly with the improvement in modern computing power. In many applications the emphasis has been on economical algorithms which can cope with the extra complexity that the third dimension brings. Storage and computer time are of the essence. The advantage of the finite volume formulation is that a large amount of memory space is not required. Iterative methods rather than direct methods can be used to solve the resulting linear systems efficiently.