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The spectral boundary element method for solving two‐dimensional transient heat conduction problems is developed. This method is combined with the fast Fourier transform (FFT) to convert the solution between the time and frequency domains. The fundamental solutions in the frequency domain, required for the present method, are discussed. The resulting line integrations in the frequency domain are discretized using constant boundary elements and used in a Fortran boundary element program. Three examples are used to illustrate the accuracy and effectiveness of the method in both the frequency and time domains. First, the frequency domain solution procedure is verified using the steady‐state example of a semi‐infinite half space with a heat flux applied to a patch of the surface. This spectral boundary element method is then applied to the problem of a circular hole in an infinite solid subjected to a time‐varying heat flux, and solutions in both the frequency and time domains are presented. Finally, the method is used to solve the circular hole problem with a convection boundary condition. The accurary of these results leads to the conclusion that the spectral boundary element method in conjunction with the FFT is a viable option for transient problems. In addition, this spectral approach naturally produces frequence domain information which is itself of interest.

Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems.

An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation.

The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method..

Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.

The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time.

The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered.

FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver.

The present results are limited to linear elasticity.

This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

A wide range of micro‐electro‐mechanical‐systems are based on the electrostatic principle, and for their design the computation of the electric capacities is of great importance. The purpose of this paper is to efficiently compute the capacities as a function of all possible positions of the two electrode structures within the transducer by an enhanced boundary element method (BEM).

A Galerkin BEM is developed and the arising algebraic system of equations is efficiently solved by a CG‐method with a multilevel preconditioner and an appropriate fast multipole algorithm for the matrix‐vector operations within the CG‐iterations.

It can be demonstrated that the piecewise linear and discontinuous trial functions give an approximation, which is almost as good as the one of the piecewise constant trial functions on the refined mesh, at lower computational costs and at about the same memory requirements.

The paper can proof mathematically and demonstrate in practice, that a higher order of convergence is achieved by using piecewise linear, globally discontinuous basis functions instead of piecewise constant basis functions. In addition, an appropriate preconditioner (artificial multilevel boundary element preconditioner, which is based on the Bramble Pasciak Xu like preconditioner) has been developed for the fast iterative solution of the algebraic system of equations.

A computational methodology, based on the coupling of the finite element and boundary element methods, is developed for the solution of magnetothermal problems. The finite element formulation and boundary element formulation, along with their coupling, are discussed. The coupling procedure is also presented, which entails the application of the LU decomposition to eliminate the need for the direct inversion of matrices resulting from FE‐BE formulation, thereby saving computation time and storage space. Corners for both FE‐BE interface and BE regions, where discontinuous fluxes exist, are treated using the double flux concept. Numerical results are presented for three different systems and compared with analytical solutions when available. Numerical experiments suggest that for magnetothermal problems involving small skin depths, a careful mesh distribution is critical for accurate prediction of the field variables of interest. It is found that the accuracy of the temperature distribution is strongly dependent upon that of the magnetic vector potential. A small error in the magnetic vector potential can produce significant errors in the subsequent temperature calculations. Thus, particular attention must be paid to the design of a suitable mesh for the accurate prediction of vector potentials. From all the cases examined, 4‐node linear elements with adequate progressive coarsening of meshes from the surface gave the results with best accuracy.

This paper presents a hybrid finite element — boundary element method for the steady state thermal analysis of energy installations. The coupling of the two techniques is presented: finite elements are used in a bounded region containing thermal sources while the complementary domain is treated with boundary elements. With such a combination the number of unknowns is reduced and an accurate prediction of temperature is obtained. As an example, the temperature rise is computed for the case of three power cables laid in a thermal backfill: the finite element method (FEM) is used for the cables and the backfill while the homogeneous soil is taken into account with the boundary element method (BEM).

Under low level injection conditions, two‐dimensional modeling of many types of solar cells can be done on the basis of the simple diffusion equation. The general semiconductor equations must only be considered in a small space charge layer. Here they can be solved in a quasi‐one‐dimensional way and reduced to a, usually nonlinear, boundary condition for the diffusion equation. The resulting boundary‐value problem is then solved using the boundary‐element method, which proves to be a natural choice for this kind of problem.

When explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area, reducing the computational efficiency of the numerical calculation and limiting the use of viscoelastic artificial boundary elements in the explicit dynamic analysis of large-scale engineering sites. The main purpose of this study is to improve the stability condition of viscoelastic artificial boundary elements.

A stability analysis method based on local subsystems was adopted to analyze and improve the stability conditions of three-dimensional (3D) viscoelastic artificial boundary elements. Typical boundary subsystems that can represent the localized characteristics of the overall model were established, and their analytical stability conditions were derived with an analysis based on the spectral radius of the transfer matrix. Then, after analyzing the influence of each physical parameter on the analytical-stability conditions, a method for improving the stability condition of the explicit algorithm by increasing the mass density of the artificial boundary elements was proposed.

Numerical wave propagation simulations in uniform and layered half-space models show that, on the premise of ensuring the accuracy of the viscoelastic artificial boundary, the proposed method can effectively improve the numerical stability and the efficiency of the explicit dynamic calculations for the overall system.

The stability improvement method proposed in this study are significant for improving the applicability of viscoelastic artificial boundary elements in explicit dynamic calculations and the calculation efficiency of wave analysis at large-scale engineering sites.

The axisymmetric steady‐state convective‐diffusive thermal field problem associated with direct‐chill, semi‐continuously cast billets has been solved using the dual reciprocity boundary element method. The solution is based on a formulation which incorporates the one‐phase physical model, Laplace equation fundamental solution weighting, and scaled augmented thin plate splines for transforming the domain integrals into a finite series of boundary integrals. Realistic non‐linear boundary conditions and temperature variation of all material properties are included. The solution is verified by comparison with the results of the classical finite volume method. Results for a 0.500[m] diameter Al 4.5 per cent Cu alloy billet at typical casting conditions are given.

This paper presents a boundary element formulation for transient uncoupled thermoelasticity employing a multiple reciprocity method (MRM) approximation for calculating the thermal stress field. An intermediate step, which involves curve fitting, is necessary for processing the results of the heat conduction analysis into a form suitable for the MRM. Numerical results are included which validate the present technique.