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A technique combining finite elements and boundary elements is promising for unbounded field problems. A hypothetical boundary is assumed in the unbounded domain, and the usual finite element method is applied to the inner region, while the boundary element method is applied to the outer infinite region. On the coupling boundary, therefore, both potential and flux must be compatible. In the finite element method, the flux is defined as the derivative of the potential for which a trial function is defined. In the boundary element method, on the other hand, the same polynomial function is chosen for the potential and the flux. Thus, the compatibility cannot be satisfied unless a special device is considered. In the present paper, several compatibility conditions are discussed concerning the total flux or energy flow continuity across the coupling boundary. Some numerical examples of Poisson and Helmholtz problems are demonstrated.

The boundary element method is a useful method for the analysis of field problems involving unbounded regions. Therefore, the method can be used advantageously in combination with the finite element method. This is sometimes called a combination method and it is suitable as a picture‐frame technique. Although this technique attains good accuracy, the matrix of the discretized equation is not banded, since it is a dense matrix. In this paper, we propose an infinite boundary element which divides the unbounded region radially. By the use of this element, the bandwidth of the discretized system matrix does not increase beyond that of the finite element region and its original matrix structure is maintained. The infinite boundary element can also be applied to homogeneous unbounded field problems, for which the Green's function of the mirror image is difficult to use. To illustrate the validity of the proposed technique, some numerical calculations are demonstrated and the results are compared with those of the usual combination method and the method using the hybrid‐type infinite element.

A hybrid formulation is proposed that incorporates finite element substructuring and Galerkin boundary elements in the numerical solution of Poisson's or Laplace's equation with open boundaries. Substructuring the problem can dramatically decreases the size of matrix to be solved. It is shown that the boundary integration that results from application of Green's first theorem to the weighted residual statement can be used to advantage by imposing potential and flux continuity through the contour which separates the interior and exterior regions. In fact, the boundary integration is of exactly the same form as that found in Galerkin boundary elements.

The combination method, combined finite element‐boundary element approach, is suitable for unbounded field problems. Although this technique attains a high degree of accuracy, the matrix of the discretized system equation is not banded but sometimes densely or sparsely populated. We reported the development of an infinite boundary element for 2‐D Laplace problems, with which the bandwidth of the discretized system matrix does not increase beyond that of the finite element region. In this paper, we extend this approach and propose another infinite boundary element for 2‐D Helmholtz problems. To illustrate the validity of the proposed technique, some numerical examples are given and their results are compared with those of other methods.

Introducing the concept of a design domain to truss topology optimization, this paper presents an algorithm generating geometrically admissible ground structures on possibly concave (or even disconnected) 3D design domains. That is a set of connections between nodal points actually respecting the geometry of the design domain. Since ground structures may be applied in other contexts the presentation does not assume any specifics of truss topology optimization. However, in the example section an application of ground structures in a truss topology optimization problem may be found.

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 methodology, based on the fast Fourier transform (FFT), that improves prior established techniques to solve axisymmetric potential problems with non‐axisymmetric boundary conditions using the boundary element method (BEM). The proposed methodology is highly effective, especially in cases where a large number of harmonics is required. Furthermore, it is optimised at several levels, reaching the maximum possible efficiency. Special concern is given on its implementation on quadratic elements that are of current practice. The method is applicable to any type of boundary elements as well as to a wider class of static and dynamic axisymmetric boundary value problems.

The boundary element and finite element methods have been combined so as to allow for arbitrary intermixing of element types in modelling problems of axisymmetric thermoelasticity, including body forces due to rotational inertia. The formulation for combining the methods is given, and a general purpose, finite element program has been generalized to accommodate both types of elements and to determine stresses within and on the boundary of boundary‐type elements after the primary solution for the displacements. Example problems demonstrate the validity and accuracy of the technique.

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 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.