Accuracy Of Boundary Element Method Research Articles

Heat transfer comparison investigation of the permanent magnet synchronous motor for electric vehicles based on the BEM and the FEM

In the field of heat transfer in permanent magnet synchronous motors (PMSM) for electric vehicles, the boundary element method (BEM) has been applied for the first time to calculate the steady-state temperature of the PMSM with a spiral water-cooled system. In this investigation, the boundary-integration equation for the steady-state heat transfer problem of a water-cooled PMSM is first derived on the basis of thermodynamic theory, and the system of constant coefficient differential equations is obtained by discretizing its boundaries, while the temperature results obtained from the BEM are compared with the finite element method (FEM) results. Furthermore, the temperature distribution and heat transfer characteristics obtained from the FEM and BEM were verified twice using the PMSM prototype and test platform. The results show that the maximum relative error between the temperature calculation results of FEM and BEM is 1.97%, and the maximum relative error between the results of BEM and the test does not exceed 3%, which finally verifies the validity and accuracy of BEM in solving the heat transfer problems of water-cooled PMSM.

A hybrid virtual–boundary element formulation for heterogeneous materials

In this work, a hybrid formulation based on the conjoined use of the recently developed Virtual Element Method (VEM) and the Boundary Element Method (BEM) is proposed for the effective computational analysis of multi-region domains, representative of heterogeneous materials. VEM has been recently developed as a generalisation of the Finite Element Method (FEM) and it allows the straightforward employment of elements of general polygonal shape, maintaining a high level of accuracy. For its inherent features, it allows the use of meshes of general topology, including non-convex elements. On the other hand, BEM is an effective technique for the numerical solution of sets of boundary integral equations, employed as the original model of the represented physical problem. For several classes of problems, BEM offers some advantages over more popular techniques, namely the reduction of the dimensionality of the problem, with associated computational savings. In this study, the inherent advantages of VEM and BEM are simultaneously employed for the study of heterogeneous material microstructures.The method has been applied to i) the elastic analysis and ii) computational homogenization of fibre-reinforced composite materials and to iii) the analysis of composite unit cells exhibiting matrix isotropic damage. The discussed results show how the hybrid technique inherits the generality of VEM and the modelling simplification and accuracy of BEM, ensuring high accuracy and fast convergence and providing a versatile tool for the analysis of multiphase materials, also including non-linear behaviour such as material degradation. Further directions of research are identified and discussed after commenting on the presented results.

A novel Green element method by mixing the idea of the finite difference method

This paper proposes a novel Green element method (GEM) by mixing the idea of finite difference method (FDM). In the novel method, We come to the original formula when boundary integral equation is applied to an element, and use difference quotient of the central nodal value on two sides of the shared edge of adjoining elements to approximate the boundary integration ∫ΓG∇p · nds. This treatment is similar to FDM, and the integral operator relevant to element size controls the estimated error. The novel GEM makes the numerical solution correspond to the actual physical meaning, and the coefficient matrix of the global matrix is a banded sparse matrix with larger bandwidth than previous GEMs. Meanwhile, the instability of the original GEM is illuminated. We have proven it by theoretical error analysis and five numerical examples that, the accuracy of the novel GEM is three-order higher than the original GEM, and the novel GEM has a good convergence and stability, which is the property that the original GEM does not have.Indeed, the novel GEM proposed in this paper is essentially a new numerical method mixed with the idea of boundary element method (BEM), finite element method (FEM), and FDM. In contrast with BEM, FEM, FDM and previous GEM, the characteristics of our novel GEM include:(i) Compared with FEM and FDM, the novel GEM has the accuracy of BEM and can better accord with material balance.(ii) Compared with BEM, the novel GEM can solve nonlinear problems with heterogeneous media, which are hard to be handled by BEM.(iii) Compared with previous GEMs, the novel GEM has a three-order accuracy, and has a better convergence that the calculation error can be well controlled by the element size.

Calculation of pressure distribution in heavy oil reservoir with boundary element method

Abstract Boundary element method (BEM) is introduced to calculate the heavy oil seepage in this paper. The pressure contours with different temperatures and arbitrary oil reservoir shapes are obtained by solving the variable coefficients Darcy’s equations. The numerical simulation results indicate that temperature has evident effect on pressure contours when the pressure is lower. Varieties of pressure contours with different boundary conditions coincide well with the heavy oil seepage law, which indicates the validity and accuracy of BEM in dealing with the irregular boundary problem. The numerical simulation results can provide theoretical basis for the heavy oil well pattern.

Integration over simplexes for accurate domain and boundary integral evaluation in boundary element methods

The accuracy of boundary element methods is heavily dependent on the accurate determination of singular domain and boundary integrals on element domains. Many methods have been developed for accurate integral determination but none that is universally applicable across the range of boundary element applications. This paper is concerned with a semi-analytical method that applies to simplexes of arbitrary dimension. The method involves the careful employment of multiple integration where the inner integral is performed along a radial direction. Evaluation of the radial-inner integral on a simplex of dimension n provides n+1 integrals on simplex domains of dimension n−1. It is shown in the paper that provided closed form solutions exist for the inner integrals the method can be repeated on these n+1 simplexes providing a recursive method of integration. Performing radial inner integration on a simplex is shown to be ideal for the correct treatment of the radial singularities present. If a closed form solution is not available then a radial function is added and subtracted to facilitate the use of numerical integration. In addition to singularity annihilation the form of this radial function is selected to facilitate the continued recursive application of radial integration. The method is tested on domain and boundary integrals present in thermoelastostatic, elastodynamic and on simple test problems for which known analytical solutions exist. The results obtained using the semi-analytical simplex approach are shown to be considerably more accurate than those obtained using standard quadrature methods.

Boundary Element Grid Optimization for Stokes Flow With Corner Singularities

The accuracy of boundary-element methods for computing Stokes flow past boundaries with sharp corners where singularities occur is discussed. To resolve the singular behavior, a graded mesh of boundary elements whose length increases in a geometrical fashion with respect to distance from the corners according to a prescribed stretch ratio is used. Numerical results for two-dimensional Stokes flow past bodies with polygonal shapes reveal the existence of an optimal value of the stretch ratio for best accuracy in the computation of the force and torque. When the optimal value is used, fast convergence is achieved with respect to the number of boundary elements.