Improved Boundary Element Method Research Articles

An Improved Boundary Element Method for Predicting Half-Space Scattered Noise Combined with Permeable Boundaries

The boundary element method is widely used in practical engineering problems, especially in the field of acoustics. For flow-induced noise, the main target of acoustic calculations is to solve the wave equation with the flow field information. However, the sound field distribution of noncompact structures in half-space is especially complex because of the strong scattering effect, while the object surface boundary integration often brings a large workload and generates numerical singularities. In this paper, an improved boundary element method for predicting the aeroacoustic noise of noncompact structures is proposed, which can consider the characteristic distribution of sound field induced by complex structures in half-space. The smooth permeable boundary surrounding the object is used as the integration boundary, while the scattering effect of the ground boundary is investigated by combining the mirror Green’s function method, and the numerical prediction of aeroacoustic noise is carried out for the dipole source and NACA0012 airfoil in half-space. Numerical results show that the far-field noise obtained by using the permeable surface is consistent with that obtained by integrating the direct object boundary under the influence of ground boundary scattering. The mirror image Green’s function method is able to finely capture the ground scattering effect, which has a significant effect on the sound field as the frequency increases.

Tolerance analysis of planar parts with skin modeling considering spatial distribution characteristics of surface morphology and local surface deformations

Purpose This paper aims to develop a method to improve the accuracy of tolerance analysis considering the spatial distribution characteristics of part surface morphology (SDCPSM) and local surface deformations (LSD) of planar mating surfaces during the assembly process. Design/methodology/approach First, this paper proposes a skin modeling method considering SDCPSM based on Non-Gaussian random field. Second, based on the skin model shapes, an improved boundary element method is adopted to solve LSD of nonideal planar mating surfaces, and the progressive contact method is adopted to obtain relative positioning deviation of mating surfaces. Finally, the case study is given to verify the proposed approach. Findings Through the case study, the results show that different SDCPSM have different influences on tolerance analysis, and LSD have nonnegligible and different influence on tolerance analysis considering different SDCPSM. In addition, the LSD have a greater influence on translational deviation along the z-axis than rotational deviation around the x- and y-axes. Originality/value The surface morphology with different spatial distribution characteristics leads to different contact behavior of planar mating surfaces, especially when considering the LSD of mating surfaces during the assembly process, which will have further influence on tolerance analysis. To address the above problem, this paper proposes a tolerance analysis method with skin modeling considering SDCPSM and LSD of mating surfaces, which can help to improve the accuracy of tolerance analysis.

Elastic-Plastic Contact Behaviors Modeling for Tolerance Analysis

This paper proposes a mechanics-based method for calculating the elastic-plastic contact behaviors in tolerance analysis. Specifically, form deviations of geometric features are modeled based on the concept of Skin Model Shapes (SMS). Elastic-plastic contact behaviors are calculated by an improved Boundary Element Method (BEM). The calculation accuracy and efficiency are compared with the Finite Element Method (FEM). The simulation results indicate that the proposed method has good calculation accuracy and significantly improves the calculation efficiency at the same time, which provides a feasible method to consider the effects of elastic-plastic contact behaviors in tolerance analysis.

The coupled method of multi-domain BEM and element differential method for solving multi-scale problems

In this paper, the element differential method (EDM), a new numerical method proposed recently, is coupled with the multi-domain boundary element method (MDBEM), an improved Boundary Element Method (BEM), for solving general multi-scale heat conduction and elasticity problems. The basic algebraic equations in MDBEM are formulated in terms of displacements/temperatures and surface tractions/heat fluxes, which are the same as those in EDM. Therefore, when coupling these two methods, we don't need to transform the variables such as the equivalent nodal forces into the surface tractions as done in the Finite Element Method (FEM). The key task in the proposed coupled method is to use the displacement/temperature consistency conditions and the surface traction/heat flux equilibrium equations at interface nodes to eliminate all BEM nodes except for those on the interfaces, rather than to iterate. After elimination, the coefficient matrix we get is sparse although a small part is dense. The coupled method inherits the advantages of EDM in flexibility and computational efficiency, and the advantage of BEM in the robustness of treating multi-scale problems. Three numerical examples of general heat conduction and mechanical problems are given to demonstrate the correctness and efficiency of this coupled method.

An improved boundary element method for modelling a self-reacting point absorber wave energy converter

A numerical model based on a boundary element method (BEM) is developed to predict the performance of two-body self-reacting floating-point absorber (SRFPA) wave energy systems that operate predominantly in heave. The key numerical issues in applying the BEM are systematically discussed. In particular, some improvements and simplifications in the numerical scheme are developed to evaluate the free surface Green’s function, which is a main element of difficulty in the BEM. For a locked SRFPA system, the present method is compared with the existing experiment and the Reynolds-averaged Navier–Stokes (RANS)-based method, where it is shown that the inviscid assumption leads to substantial over-prediction of the heave response. For the unlocked SRFPA model we study in this paper, the additional viscous damping primarily induced by flow separation and vortex shedding, is modelled as a quadratic drag force, which is proportional to the square of body velocity. The inclusion of viscous drag in present method significantly improves the prediction of the heave responses and the power absorption performance of the SRFPA system, obtaining results excellent agreement with experimental data and the RANS simulation results over a broad range of incident wave periods, except near resonance in larger wave height scenarios. It is found that the wave overtopping and the re-entering impact of out-of-water floating body are observed more frequently in larger waves, where these non-linear effects are the dominant damping sources and could significantly reduce the power output and the motion responses of the SRFPA system.

A calculation method for finite depth free-surface green function

ABSTRACT: An improved boundary element method is presented for numerical analysis of hydrodynamic behavior of marine structures. A new algorithm for numerical solution of the finite depth free-surface Green function in three dimensions is developed based on multiple series representations. The whole range of the key parameter R / h is divided into four regions, within which different representation is used to achieve fast convergence. The well-known epsilon algorithm is also adopted to accelerate the convergence. The critical convergence criteria for each representation are investigated and provided. The proposed method is validated by several well-documented benchmark problems.

Improved Boundary Element Method for Fast 3-D Interconnect Resistance Extraction

SUMMARY Efficient extraction of interconnect parasitic parameters has become very important for present deep submicron designs. In this paper, the improved boundary element method (BEM) is presented for 3D interconnect resistance extraction. The BEM is accelerated by the recently proposed quasi-multiple medium (QMM) technology, which quasicuts the calculated region to enlarge the sparsity of the overall coefficient matrix to solve. An un-average quasi-cutting scheme for QMM, advanced nonuniform element partition and technique of employing the linear element for some special surfaces are proposed. These improvements considerably condense the computational resource of the QMM-based BEM without loss of accuracy. Experiments on actual layout cases show that the presented method is several hundred to several thousand times faster than the well-known commercial software Raphael, while preserving the high accuracy.

An improved boundary element method for realistic volume-conductor modeling.

An improved boundary element method (BEM) with a virtual triangle refinement using the vertex normals, an optimized auto solid angle approximation, and a weighted isolated problem approach is presented. The performance of this new approach is compared to analytically solvable spherical shell models and highly refined reference BEM models for tangentially and radially oriented dipoles at different eccentricities. The lead fields of several electroencephalography (EEG) and magnetoencephalography (MEG) setups are analyzed by singular-value decompositions for realistically shaped volume-conductor models. Dipole mislocalizations due to simplified volume-conductor models are investigated for EEG and MEG examinations for points on a three dimensional (3-D) grid with 10-mm spacing inside the conductor and all principal dipole orientations. The applicability of the BEM in view of the computational effort is tested with a standard workstation. Finally, an application of the new method to epileptic spike data is studied and the results are compared to the spherical-shells approximation.

An improved boundary element method for analysis of profile polymer extrusion

An improved boundary element method for non-linear viscoelastic flow analysis is reported. In this method, the domain integral representing the non-linear effects is calculated using a more efficient approximating technique. This is achieved by first transforming the domain integral into a form that can be approximated by particular solutions to the original problem. These particular solutions are in fact expressed as a linear combination of radial basis functions, whose coefficients are found by data fitting technique. As a result, the numerical computation of the volume integral is eliminated and a significant reduction of CPU time is achieved. The routines are tested with simple flows and then applied to solve complex three-dimensional direct and inverse extrusion problems of polymeric fluids, such as thermoplastic melts. Inverse extrusion process, where an extrusion die profile needs to be computed for a given profile extrudate, is a very important practical engineering application which is successfully analysed by the present method. Relative to a previous BEM implementation where the volume integral is computed directly using numerical quadratures, a CPU time reduction ranging from 40 to 70% is achieved.

An improved boundary element method with FEM facilities

To efficiently improve the BEM performance, one starts from some new integral relations in a potential field. The approach consists in the treatment of the boundary by portions. The functional equation of the potential and its normal derivative on the boundary is established and the discretized equation system is set up. A very simple algorithm is achieved, enabling a drastic cut down of the computer requirements. Nonlinear problems may also be solved.

Two-Dimensional Thermal Stress Analysis under Unsteady State by Improved Boundary Element Method.

If initial temperature is assumed to be constant, the boundary element method (BEM) does not need a domain integral in unsteady thermoelastic problems without heat generation. However, under heat generation or nonuniform initial temperature distribution, the domain integral is necessary. This paper shows that the problem of unsteady thermoelasticity under nonuniform heat generation and with nonuniform initial temperature distribution over the region can easily be solved without a domain integral by means of the boundary element method. This method can also be applied to unsteady thermal stress problems under general complicated heat generation. However, for general heat generation the domain must be divided into small domains, where distributions of heat generation satisfy the Laplace equation.

Application of an improved boundary element method on the problem of elastic torsion

An improved boundary element method has been used in analyzing and calculating the problems of the torsion of a prismatic bar with elliptical cross-section. In this paper the calculated results correspond with the values of boundary element method. However, the quantity of data required by the improved boundary element method is much less than that required by boundary element method, and the calculating time will be greatly reduced. Therefore, the procedure of this paper is an economical and efficient numerical computational way for solving Poisson equation problem.

THE STRESS CONCENTRATION AND ITS MODERATION AROUND THE APEX OF DISSIMILAR MATERIALS

Abstract In this paper, the stress distribution around the apex of dissimilar materials is calculated for both two and three dimensional bonded structures by using an improved Boundary Element Method (BEM), and the order of stress singularity is obtained from the numerical solution. It is shown that the numerical solution is very accurate even near the boundary or apex, and for the samples of ceramics (Al2O3) bonded with Cu, it is proved that the order of the stress singularity obtained in this way is in good agreement with Bogy's theory and the numerical solution can be used as an evaluating standard of nondestructive testing. For the three dimensional bonded structure, it is found that the stress singularity is very strong around the apex. This reveals that the possibility of crack generation in this area is very high. Through some detailed investigations about the stress field, a simple method to moderate the stress singularity is suggested.

Edge effect enforced boundary element analysis of multilayered transmission lines

An improved boundary element method (BEM) for the calculation of the capacitance matrix in a multiconductor transmission line structure is presented, where the edge singularities of the charge and current near the corners of the cross-sections of the signal lines are embedded in the basis functions. The new method demonstrates improved accuracy and enhanced computational efficiency in comparison to previous methods. The results for the new algorithm are compared with those for other approaches presented in the literature.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Investigation of Method of Stress Relaxation around the Apex of Ceramics-Metal Bonded Structure. Consideration of Shape Effect of Apex in Three Dimensional Dissimilar Materials.

In the present paper, the stress distribution around the apex of dissimilar materials for two-and three-dimensions is calculated using an improved boundary element method (BEM), and the order of the singularity for the stress distribution is obtained from the numerical results. It is shown that the numerical solution is very accurate even at the internal points near the boundary or apex. For the sample structure bonded with ceramics (Al2O3) and Cu, it is proven that the order of the stress singularity obtained in this way is in good agreement with that of Bogy's theory. For three-dimensional bonded structure, it is found that the stress singularity is very strong around the apex. This indicates that the possibility of crack generation in this part is very high. Through detailed investigation of the stress field, a simple method to moderate the stress concentration is suggested.

An improved boundary element method for the charge density of a thin electrified plate in ℝ3

AbstractA weakly singular integral equation of the first kind on a plane surface piece Γ is solved approximately via the Galerkin method. The determination of the solution of this integral equation (with the single‐layer potential) is a classical problem in physics, since its solution represents the charge density of a thin, electrified plate Γ loaded with some given potential. Using piecewise constant or piecewise bilinear boundary elements we derive asymptotic estimates for the Galerkin error in the energy norm and analyse the effect of graded meshes. Estimates in lower order Sobolev norms are obtained via the Aubin–Nitsche trick. We describe in detail the numerical implementation of the Galerkin method with both piecewise‐constant and piecewise‐linear boundary elements. Numerical experiments show experimental rates of convergence that confirm our theoretical, asymptotic results.

A ULSI 2-D capacitance simulator for complex structures based on actual processes

A two-dimensional (2-D) capacitance simulator for ultra-large-scale integrated (ULSI) circuits using an improved boundary-element method (BEM) is described. The capacitance simulator was linked with a topography/process simulator to estimate the distributed capacitances of complex structures based on actual processes. The utilization of a linear discontinuous element as the shape function is proposed in order to deal with multiregional problems by BEM. Other techniques employed in the simulation program, which enable precise calculation within practical CPU time, are also described. The calculated capacitances show good agreement with the experimental results. >

The modelling of infinitesimal amplitude water waves using an improved boundary element method

A description of the improved boundary element method is presented. Its application to predict the motion of free surface flows is described, and a model of an infinitesimal water waves is demonstrated in particular.

A new boundary element technique for solving plane problems of linear elasticity: improved theory and an application to fracture mechanics

An improved boundary element method for solving plane problems of linear elasticity theory is described. The method is based on the Muskhelishvili complex variable representation for the displacement and stress fields. The paper shows how to take account of symmetry about the x and/or y axes. The potential accuracy of the method is illustrated by its application to the calculation of stress intensity factors associated with cracks in both a square and a circular plate. The crack problem is solved using a Gauss-Chebyshev representation of a singular integral equation by a set of linear algebraic equations. The integral equation involves an analytic function which takes account of the presence of the external boundary. This function is determined directly using the boundary element method. Numerical results are believed to be more accurate than the existing published values which are quoted to four significant figures.