Improvement of the accuracy in boundary element method based on high-order discretization

The boundary element method (BEM) is a popular method to solve various problems in engineering and physics and has been used widely in the last two decades. In high-order discretization the boundary elements are interpolated with some polynomial functions. These polynomials are employed to provide higher degrees of continuity for the geometry of boundary elements, and also they are used as interpolation functions for the variables located on the boundary elements. The main aim of this paper is to improve the accuracy of the high-order discretization in the two-dimensional BEM. In the high-order discretization, both the geometry and the variables of the boundary elements are interpolated with the polynomial function P_m, where m denotes the degree of the polynomial. In the current paper we will prove that if the geometry of the boundary elements is interpolated with the polynomial function P_m+1 instead of P_m, the accuracy of the results increases significantly. The analytical results presented in this work show that employing the new approach, the order of convergence increases from O(L₀)^m to O(L₀)^m+1 without using more CPU time where L₀ is the length of the longest boundary element. The theoretical results are also confirmed by some numerical experiments.     

Analysis of three-dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method

In this paper, an advanced boundary element method (BEM) is developed for solving three-dimensional (3D) anisotropic heat conduction problems in thin-walled structures. The troublesome nearly singular integrals, which are crucial in the applications of the BEM to thin structures, are calculated efficiently by using a nonlinear coordinate transformation method. For the test problems studied, promising BEM results with only a small number of boundary elements have been obtained when the thickness of the structure is in the orders of micro-scales (10^?6), which is sufficient for modeling most thin-walled structures as used in, for example, smart materials and thin layered coating systems. The advantages, disadvantages as well as potential applications of the proposed method, as compared with the finite element method (FEM), are also discussed.     

Static analysis of soil/pile interaction in layered soil by BEM/BEM coupling

In this article we propose to use the boundary element method (BEM) to analyze soil–foundation interactions. The soil structure is modeled as several dissimilar strata placed one on top of the other, composing a sandwich-like profile. Any of these layers may contain components of the foundations. Each region occupied by a soil layer or by a foundation component is handled as a 3D isotropic, elastic and homogeneous domain, and is analyzed by BEM. As a consequence of the positioning of the various subregions in this model, the technique of successive rigidity can be applied directly, resulting in a considerable reduction in the volume of data being stored and manipulated throughout the analysis.     

Stability improvement to BEM/FEM coupling scheme for 2D scalar wave problems

The stability problem appeared in boundary element method/finite element method (BEM/FEM) coupling is discussed in this paper. As the response at time t_n+1 relates to the excitations and responses at all previous times, i.e. response history, BEM is easier to be unstable compared with FEM. The Newmark method for FEM is unconditionally stable, oscillations appeared at any time would decrease step by step as time goes by. But the oscillation history caused by FEM may be big enough to cause stability problems to the BEM scheme which although may be stable when used independently. A new procedure is used in this paper to reduce the oscillation history caused by FEM so that it will not cause stability problem to BEM scheme and further to the coupling BEM/FEM scheme. Numerical examples show that the proposed procedure can improve significantly to the stability of the coupling BEM/FEM scheme and cause little numerical damping.     

层次式直接边界元计算VLSI三维互连电容

文中将Ａｐｐｅｌ处理多体问题的层次式算法思想实现于直接边界元法,用以计算ＶＬＳＩ三维互连寄生电容。直接边界积分方程同时含有边界上的电势与法向电场强度,能比间接边界元法更方便地处理多介质及有限介质结构,直接边界元法的层次式计算涉及对三种边界（强加边界、自然边界与介质交界面）及两种积分核（１／ｒ与１／ｒ＾３）的处理,显著区别于基于间接边界元法、仅处理强加边界与一种分核的层次式算法。文中以边界元的层次划     

CUDA架构下的三维弹性静力学边界元并行计算

针对传统边界元法计算量大、计算效率低的问题,以三维弹性静力学的边界元法为对象,将基于CUDA的GPU并行计算应用到其边界元计算中,提出了基于CUDA架构的GPU并行算法.该算法首先对不同类型的边界元系数积分进行并行性分析,描述了相关的GPU并行算法,然后阐述了边界元方程组的求解方法及其并行策略.实验结果表明,文中算法较传统算法具有显著的加速效果.     

A BEM formulation for efficient and accurate analysis of dielectric waveguiding structures: Extension to multiboundary topologies

A recently proposed formulation based on the boundary element method (BEM) has been demonstrated to be very accurate and efficient for the modal analysis of arbitrarily shaped dielectric waveguides. This innovative approach is extended here to analyze any topology having multiple contours and/or dielectrics, thus permitting a complete characterization for guiding structures that are frequently utilized in several applications at microwaves, millimeter waves, and optics. Various tests validate the excellent computational properties of this method even for compound structures. © 1998 John Wiley & Sons, Inc. Int J RF and Microwave CAE 8: 355–366, 1998     

An adaptive method for the determination of the order of element for acquiring the desired accuracy in 3D elastostatic FEM analysis

An adaptive method for the determination of the order of element (or element order) was developed for the finite element analysis of 3D elastostatic problems. Here the order of element means the order of polynomial function, which interpolates the displacement distribution in the element. This method was based on acquiring the desired accuracy for each finite element. From the numerical experiments, the relationship ξ=k(1/p)^β was deduced, where ξ is the error of the result of the finite element analysis relative to the exact value, p is the order of element, and k and β are constants. Applying this relationship to the two results of computations with different orders of element, the order of element for the third computation was deduced. A computer program using this adaptive determination method for the order of element was developed and applied to several 3D elastostatic problems of various shapes. The usefulness of the method was illustrated by these application results.     

Finite-difference method for computation of 3-D gas dynamics equations with artificial viscosity

A new numerical method for the solution of gas dynamics problems for three-dimensional (3D) systems in Eulerian variables is presented in the paper. The proposed method uses the approximation O(τ² + h _x ² + h _y ² + h _z ²) in the areas of the solution’s smoothness and beyond the compression waves; τ is the time step; and h _x , h _y , and h _z are space variable steps. In the proposed difference scheme, in addition to Lax-Wendroff corrections, artificial viscosity μ that monotonizes the scheme is introduced. The viscosity is obtained from the conditions of the maximum principle. The results of the computation of the 3D test problem for the Euler equation are presented.     

A distributed algorithm for multi-region problem in BEM

The situation of multi-region problem may oftem appear when boundary element method(BEM)is applied in practical problems especially in VLSI-CAD.It is difficult to deal with this problem if traditional methods are used.Particularly. when the problem to be solved contains a lot of materials,the advantages of using BEM such as simplicity,convenience and rapidity will be weakened due to the complexity of solving complex boundary element equation.In this paper a distributed algorithm for multi-region problem in BEM is presented.This algorithm has been implemented in a distributed system consisting of 3 workstations to extract VLSI layout parameters.The results show that the calculation time of this distributed algorithm is less than that of the traditional methods.The results also demonstrate that this algorithm can speed up the computation and has the features of parallelism and high efficiency.     

Dynamic response of 3-D embedded foundations by the boundary element method

The dynamic response of three-dimensional rigid embedded foundations of arbitrary shape, resting on a linear elastic, homogeneous, and isotropic half-space is numerically obtained. The foundations are subjected either to externally applied forces or to obliquely incident seismic body or surface waves of arbitrary time variation. The time domain boundary element method (BEM) is utilized to simulate the soil medium with the aid of Stokes' fundamental solutions. The dynamic response of the foundation-soil system is obtained in a step-by-step time-marching solution. Use of this time domain BEM requires a minimum amount of surface discretization only and provides the basis for an extension to nonlinear soil-structure interaction (SSI) problems.     

Comparison of FEM and BEM for interactive object simulation

There are two major approaches for real-time object simulation namely, the geometry (non-physically) based and the physically based approaches. Geometry based approaches such as free-form deformation (FFD) employ purely geometric techniques to model deformation. Physically based approaches usually adopt mass-spring system, finite element method (FEM) or boundary element method (BEM) for simulation. The mass-spring system is simple and only gives a coarse estimation of object deformation. Recently, FEM and BEM have been extensively used in object simulation because of the demand for more realistic simulation. However, a major drawback of FEM and BEM is their difficulty to achieve real-time deformation. In this article, we compare two different physically based approaches, FEM and BEM, according to their accuracy and computational complexity. Several experiments were conducted to compare the time required for the pre-computation process and the deformation process. In addition, the BEM with linear boundary elements is implemented and tested. At the current state of investigation, for the meshes with triangular elements, BEM with linear boundary elements is significantly faster than BEM with constant boundary elements under most of the circumstances. With the band matrix of FEM, the pre-computation process is faster than the BEM for a model with small mesh size. However if the mesh size of the model is large, the pre-computation process of BEM with linear boundary elements is the fastest.     

Low‐cost and wideband circularly polarized slot antenna array

A slot antenna with wideband circular polarization (CP) array, which operates on millimeter waves band, is proposed. A four‐direction sequential rotation technique is used in the feed network to feed the 2 × 2 slot element based on waveguide. The shot element resonates at both the fundamental mode and the high‐order mode. The slot element is studied in high order mode, and the radiation lobe can be redirected by changing the size of the slot element, thus improving the multi‐lobe problem. A strong single lobe is formed in the +z‐direction by using the ground edge diffraction characteristics of the slot element in the waveguide. The designed broadband characteristics are obtained through the appropriate combination of the feed network and CP antenna. The prototype of the antenna with an overall size of 137 mm × 137 mm × 0.6 mm³ is processed and verified by experiments. The prototype of the slot array is processed and examined. The test results display that the device has good performance of |S₁₁| < ?10 dB bandwidth of 3.72 to 6.56 GHz (2.84 GHZ, 55.25%), a 3 dB axial ratio bandwidth of approximately 4.39 to 5.43 GHz (21.18%).     

Green element computation of the Sturm-Liouville equations

A mathematical derivation of a new numerical procedure called the Green element method (GEM) is presented and applied to the solution of Sturm-Liouville problems. The GEM is a numerical technique which expands the scope of application of the boundary element method (BEM) by implementing the singular boundary integral theory in an element-by-element fashion; and like the finite element method (FEM) gives rise to a banded coefficient matrix which is easy to handle numerically. For this application, the location of both the field and the source nodes within the same element makes it possible for integrations to be carried out accurately, thereby enhancing the accuracy of discrete equations. The method is therefore easy to apply and, because of its domain based implementation, it maintains the flexibility of the FEM. We apply the GEM to the solution of boundary value differential equations which represent the form of Sturm-Liouville problems, and its capability is demonstrated by comparing the results with those of the finite element methods available in the literature. Satisfactory results and a second-order accuracy were found to be exhibited.     

GPU-accelerated indirect boundary element method for voxel model analyses with fast multipole method

An indirect boundary element method (BEM) that uses the fast multipole method (FMM) was accelerated using graphics processing units (GPUs) to reduce the time required to calculate a three-dimensional electrostatic field. The BEM is designed to handle cubic voxel models and is specialized to consider square voxel walls as boundary surface elements. The FMM handles the interactions among the surface charge elements and directly outputs surface integrals of the fields over each individual element. The CPU code was originally developed for field analysis in human voxel models derived from anatomical images. FMM processes are programmed using the NVIDIA Compute Unified Device Architecture (CUDA) with double-precision floating-point arithmetic on the basis of a shared pseudocode template. The electric field induced by DC-current application between two electrodes is calculated for two models with 499,629 (model 1) and 1,458,813 (model 2) surface elements. The calculation times were measured with a four-GPU configuration (two NVIDIA GTX295 cards) with four CPU cores (an Intel Core i7-975 processor). The times required by a linear system solver are 31 s and 186 s for models 1 and 2, respectively. The speed-up ratios of the FMM range from 5.9 to 8.2 for model 1 and from 5.0 to 5.6 for model 2. The calculation speed for element-interaction in this BEM analysis was comparable to that of particle-interaction using FMM on a GPU.     

The NCAR spectral element climate dynamical core: Semi-implicit eulerian formulation

A prototype dynamical core for the Community Atmospheric Model (CAM) component of the Community Climate System Model (CCSM) is presented. The 3D governing primitive equations are specified in curvilinear coordinates on the cubed-sphere combined with a hybrid pressureη vertical coordinate. The horizontal space discretisation is based on a ℙ _N − ℙ _N spectral element variational formulation. A semi-implicit time integration scheme is derived in order to circumvent the severe time step restrictions associated with gravity waves. Eigen-mode decomposition of the vertical structure matrix results in a set of decoupled 2D modified Helmholtz problems which are solved using a preconditioned conjugate gradient iteration. An idealized climate simulation is presented, where the semi-implicit scheme permits a much larger time step.     

Parameter-Free Elastic Deformation Approach for 2D and 3D Registration Using Prescribed Displacements

A parameter-free approach for non-rigid image registration based on elasticity theory is presented. In contrast to traditional physically-based numerical registration methods, no forces have to be computed from image data to drive the elastic deformation. Instead, displacements obtained with the help of mapping boundary structures in the source and target image are incorporated as hard constraints into elastic image deformation. As a consequence, our approach does not contain any parameters of the deformation model such as elastic constants. The approach guarantees the exact correspondence of boundary structures in the images assuming that correct input data are available. The implemented incremental method allows to cope with large deformations. The theoretical background, the finite element discretization of the elastic model, and experimental results for 2D and 3D synthetic as well as real medical images are presented.     

The application of boundary element method to the resistance calculation problem in designing flat panel displays

Several techniques are presented for the efficient resistance calculation of wiring structures in flat panel display (FPD). The techniques are based on two‐dimensional boundary element method (BEM), suitable for the geometry characteristics of the FPD structures. With an automatic strategy for boundary element partition and the analytical BEM‐coupled approach, the proposed resistance solver shows good accuracy and fast computational speed. Numerical experiments demonstrate that the solver can be more than 10,000 times faster than the finite difference solver raphael while preserving good accuracy. And the proposed techniques accelerate the original BEM remarkably. Structures from real FPD designs have validated the efficiency of the proposed techniques.     

A Boundary Element Method for Simulation of Deformable Objects

In this paper,a boundary element method is first applied to real-tim animation of deformable objects and to simplify data preparation.Next,the visibleexternal surface of the object in deforming process is represented by B-spline surface,whose control points are embedded in dynamic equations of BEM.Fi-nally,the above method is applied to anatomical simulation.A pituitary model in human brain,which is reconstructed from a set of anatomical sections, is selected to be the deformable object under action of virtual tool such as scapel or probe.It produces fair graphic realism and high speed performance.The results show that BEM not only has less computational expense than FEM,but also is convenient to combine with the 3D reconstruction and surface modeling as it enables the reduction of the dimensionality of the problem by one.