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The purpose of this paper is to calculate near field and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method (PVIEM) quantitatively.

The PVIEM is applied for the analysis of elastic wave scattering problems in an unbounded solid containing multiple multilayered anisotropic circular inclusions. It should be noted that this numerical method does not require the use of the Green’s function for the inclusion – only the Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general elastodynamic problems involving inhomogeneous and/or anisotropic inclusions whose shape and number are arbitrary.

A detailed analysis of the SH wave scattering problem is presented for multiple multilayered orthotropic circular inclusions. Numerical results are presented for the displacement fields at the interfaces and the far field scattering patterns for square and hexagonal packing arrays of multilayered circular inclusions in a broad frequency range of practical interest.

To the best of the authors’ knowledge, the solution for scattering of SH waves by multiple multilayered anisotropic circular inclusions in an unbounded isotropic matrix is not currently available in the literature. However, in this paper, calculation of displacements on interfaces and far field scattering patterns of multiple multilayered anisotropic circular inclusions using PVIEM as a pioneer of numerical modeling enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), the multilayer’s geometry, isotropy/anisotropy and softness/hardness.

The purpose of this paper is to supply a numerical analysis tool to solve eddy currents induced in nonlinear materials such as steel by boundary element method (BEM), and then apply it to design and analysis of power devices.

Utilizing integral formulas derived on the basis of rapid attenuation of the electromagnetic fields, the paper formulates eddy currents in steel. In the formulation, nonlinear terms are regarded as virtual sources, which are improved iteratively with the electromagnetic fields on the surface. The periodic electromagnetic fields are expanded in Fourier series and each harmonic is analyzed by BEM. The surface and internal electromagnetic fields are obtained numerically one after the other until convergence by the Newton‐Raphson method.

It is confirmed that this approach gives accurate solutions with meshes much larger than the skin depth and therefore is adequate to apply to a large‐scale application.

The eddy current is formulated by utilizing the impedance boundary condition in order to meet a large‐scale application, and so solutions near the edge are poor. In the case of better solutions being required, some modifications are necessary.

To lessen computer memory consumption, the parallel component of the currents to the steel surface is analyzed as a 2D problem and the normal component is obtained from the parallel component. One 2D equation for one analyzing region is discretized by dividing the region into layers adaptively and then solved. Next, another is solved sequentially. This method gives a compatible numerical analysis tool with finite element method.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to present a novel strategy used for acceleration of free-vibration analysis, in which the hierarchical matrices structure and Compute Unified Device Architecture (CUDA) platform is applied to improve the performance of the traditional dual reciprocity boundary element method (DRBEM).

The DRBEM is applied in forming integral equation to reduce complexity. In the procedure of optimization computation, ℋ-Matrices are introduced by applying adaptive cross-approximation method. At the same time, this paper proposes a high-efficiency parallel algorithm using CUDA and the counterpart of the serial effective algorithm in ℋ-Matrices for inverse arithmetic operation.

The analysis for free-vibration could achieve impressive time and space efficiency by introducing hierarchical matrices technique. Although the serial algorithm based on ℋ-Matrices could obtain fair performance for complex inversion operation, the CUDA parallel algorithm would further double the efficiency. Without much loss in accuracy according to the examination of the numerical example, the relative error appeared in approximation process can be fixed by increasing degrees of freedoms or introducing certain amount of internal points.

The paper proposes a novel effective strategy to improve computational efficiency and decrease memory consumption of free-vibration problems. ℋ-Matrices structure and parallel operation based on CUDA are introduced in traditional DRBEM.

This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non‐Newtonian fluid flow problems which include thermal effects and viscous dissipation. The volume integral arising from non‐linear terms is converted into equivalent boundary integrals by the multi‐domain dual reciprocity method (MD‐DRM) in each subdomain. Augmented thin plate splines interpolation functions are used for the approximation of field variables. The iterative numerical formulation is achieved by viewing the material as divided into small elements and on each of them the integral representation formulae for the velocity and temperature are applied and discretised using linear boundary elements. The final system of non‐linear algebraic equations is solved by a modified Newton's method. The numerical examples include non‐Newtonian problems with viscous dissipation, temperature‐dependent viscosity and natural convection due to bouyancy forces.

The purpose of this paper is to develop Triple Finite Volume Method (tFVM), the author discretizes incompressible Navier-Stokes equation by tFVM, which leads to a special linear system of saddle point problem, and most computational efforts for solving the linear system are invested on the linear solver GMRES.

In this paper, by recently developed preconditioner Hermitian/Skew-Hermitian Separation (HSS) and the parallel implementation of GMRES, the author develops a quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation.

Computational results show that, the quick solver HSS-pGMRES-tFVM significantly increases the solution speed for saddle point problem from incompressible Navier-Stokes equation than the conventional solvers.

Altogether, the contribution of this paper is that the author developed the quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation.

A review is made of methods for calculating parameters characterizing crack tip behaviour in non‐linear materials. Convenient methods of calculating J‐integral type quantities are reviewed, classified broadly into two groups, as domain integrals and virtual crack extension techniques. In addition to considerations of how such quantities may be calculated by finite elements, assessment methods of conducting the actual incremental analyses are described.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

Regularities imposed by an external wall on the random distribution of particles in a packed bed lead to anisotropic wall effects of the bed. The resulting deviations of near—wall porosity from the average bed—porosity markedly affect the average velocity profile, not only near the wall but also some distance into the bed itself. The effect of wall channelling due to such variations in porosity near external boundaries is predicted by means of two different numerical solution methods for a unified model for granular porous media. The results are shown to compare favourably to experimental and numerical results reported in the literature.

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.