Hybrid Boundary Element Method Research Articles

Investigation of pumping mechanism for non-Newtonian blood flow with AC electrothermal forces in a microchannel by hybrid boundary element method and immersed boundary-lattice Boltzmann method.

Efficient pumping of blood flow in a microfluidic device is essential for rapid detection of bacterial bloodstream infections (BSI) using alternating current (AC) electrokinetics. Compared with AC electro-osmosis (ACEO) phenomenon, the advantage of AC electrothermal (ACET) mechanism is its capability of pumping biofluids with high electrical conductivities at a relatively high AC voltage frequency. In the current work, the microfluidic pumping of non-Newtonian blood flow using ACET forces is investigated in detail by modeling its multi-physics process with hybrid boundary element method (BEM) and immersed boundary-lattice Boltzmann method (IB-LBM). The Carreau-Yasuda model is used to simulate the realistic rheological behavior of blood flow. The ACET pumping efficiency of blood flow is studied in terms of different AC voltage magnitudes and frequencies, thermal boundary conditions of electrodes, electrode configurations, channel height, and the channel length per electrode pair. Besides, the effect of rheological behavior on the blood flow velocity is theoretically analyzed by comparing with the Newtonian fluid flow using scaling law analysis under the same physical conditions. The results indicate that the rheological behavior of blood flow and its frequency-dependent dielectric property make the pumping phenomenon of blood flow different from that of the common Newtonian aqueous solutions. It is also demonstrated that using a thermally insulated electrode could enhance the pumping efficiency dramatically. Besides, the results conclude that increasing the AC voltage magnitude is a more economical pumping approach than adding the number of electrodes with the same energy consumption when the Joule heating effect is acceptable.

Validation of a hybrid boundary and finite element method for the simulation of large membrane-based piezoelectric transducer arrays in immersion

Membrane-based piezoelectric ultrasonic transducers, especially piezoelectric micromachined ultrasonic transducers (PMUTs), are a promising technology for the realization of large transducer arrays for use in integrated imaging, sensing, and actuation where a broadband response is desirable. In this work, a hybrid boundary and finite element method is proposed for the transmit simulation of large PMUT arrays in immersion. Finite element software (COMSOL) readily handles the simulation of single membrane structures, from which static deformation (stiffness) and harmonic displacement data is extracted. A boundary element formulation based on these inputs handles the membrane-to-membrane acoustic cross-coupling through the calculation of a mutual impedance matrix. For arrays consisting of hundreds of membranes or more, the problem of quadratic storage and cubic time complexity for boundary element is avoided by employing a multi-level fast multipole algorithm (Shieh et al., IEEE Trans. UFFC, 63, 1967-1979). We validate this hybrid method for common membrane geometries, including square and circular membranes with varying degrees of electrode coverage.

A fast multipole implementation of the simplified hybrid boundary element method: application to 2D potential problems

The ultimate subject of this work is the implementation and testing of a novel numerical tool that can simulate on a personal computer and only in a few minutes a problem with many millions of degrees of freedom. The authors have already successfully developed and tested a technique that turned out to be a modified, reverse fast-multipole implementation for the conventional BEM. The variationally based hybrid BEM leads to a computationally less intensive formulation than in the conventional BEM for large-scale 2D and 3D problems of potential and elasticity. This formulation is especially advantageous for problems of complicated geometry and topology or requiring complicated fundamental solutions. The proposed implementation of the fast multipole method (FMM) for the simplified, hybrid BEM deals with the transpose of the double-layer potential matrix as well as with the nodal matrix expression of the potential fundamental solution. The basic aspects of the FMM are firstly introduced for the conventional BEM as well as for its expedite version. This takes most part of the present paper, which ends up with some validating numerical results. The FMM outline for the simplified hybrid BEM is shown in a separate section, as its numerical implementation is still in progress.

Computation of Lorentz Force and 3-D Eddy Current Distribution in Translatory Moving Conductors in the Field of a Permanent Magnet

Determination of the 3-D eddy current distribution inside a translatory moving conductor under a permanent magnet can accurately be done by using finite-element method (FEM). However, FEM calculations are very expensive, as they require discretization of the whole conductor volume. In this paper, we propose a new technique, to be called boundary element source method (BESM), where only boundary layers are discretized. The BESM is a modification of the hybrid boundary element method (HBEM). In the BESM, the concentrated point sources placed at the centers of boundary elements for the HBEM are replaced by distributed charge density over the area of the boundary element. This is especially useful in the regions, where neighboring boundary meshes significantly affect one another and when calculation point of eddy current is very close or belong to the surface of a boundary element. The method can handle arbitrary geometries of the specimen as well as the defect and arbitrary orientation of the magnetization vector. The accuracy of the proposed method is verified by comparing the results with the solutions obtained from a finite-element model. The proposed BESM approach is shown to be simple, robust, and computationally accurate.

On the fast-multipole implementation of the simplified hybrid boundary element method

The present paper is part of a research line to implement, test and apply a novel numerical tool that can simulate on a personal computer and in just a few minutes a problem of potential or elasticity with up to tens of millions of degrees of freedom. We have already developed our own version of the fast-multipole method (FMM), which relies on a consistent construction of the collocation boundary element method (BEM), so that ultimately only polynomial terms are required to be integrated – and in fact can be given as a table of pre-integrated values – for generally curved segments related to a given field expansion pole and no matter how complicated the problem topology and the underlying fundamental solution. The simplified hybrid BEM has a variational basis and in principle leads to a computationally less intensive analysis of large-scale 2D and 3D problems of potential and elasticity – particularly if implemented in an expedite version. One of the matrix-vector products of this formulation deals with an equilibrium transformation matrix that comes out to be the transpose of the double-layer potential matrix of the conventional BEM. This in principle requires a reverse strategy as compared to our first developed (and reverse) FMM. The effective application of these strategies to any high-order boundary element and any curved geometry needs to be adequately assessed for both numerical accuracy and computational effort. This is the subject of the present investigations, which are far from a closure. A few numerical examples are shown and some initial conclusions can already be drawn. Keywords: Boundary elements, Hybrid boundary elements, Fast multipole method, Variational methods

Frequency-adapted Galerkin boundary element methods for convex scattering problems

We introduce a class of hybrid boundary element methods for the solution of sound soft scattering problems in the exterior of two-dimensional smooth convex obstacles. To facilitate the applicability of our algorithms throughout the entire frequency spectrum, we have enriched our Galerkin approximation spaces, through incorporation of oscillations in the incident field of radiation, into the algebraic and trigonometric polynomial approximation spaces. The resulting methodologies have three distinctive properties. Indeed, from a theoretical point of view (1) they can be tuned to demand only an$$\mathcal {O}(k^{\varepsilon })$$O(kź)increase (for any $$\varepsilon >0)$$ź>0)in the number of degrees of freedom to maintain a fixed accuracy with increasing wavenumberk, owing to the optimal adaptation of approximation spaces to asymptotic stretching (shrinking) of illuminated and deep shadow regions (shadow boundaries), and (2) they are convergent for each fixed wavenumberk, thanks to the additional approximation spaces in the deep shadow region. Perhaps more importantly, from a practical point of view (3) they give rise to linear systems with significantly enhanced condition numbers and this, in turn, allows for more accurate solutions if desired.

Shielded coupled multilayered microstrip lines analysis using HBEM

Shielded symmetrical coupled multilayered microstrip lines analysis have been done using the hybrid boundary element method (HBEM), which is developed a few years ago at the Faculty of Electronic Engineering in Nis. The quasi-TEM approximation is applied. Influences of different parameters as well as dimensions of such microstrip lines on characteristic parameters distribution are investigated. The results are presented in graphs and tables. In order to verify the obtained results, some comparative results are shown. The authors found them to be in very good agreement with the HBEM results.

Reducing the impact of ELF electromagnetic fields of HV power cables on the environment by modeling the cable accessories

Purpose – Underground cables can produce higher electromagnetic fields directly above them than an overhead line. The majority of cable failures on distribution system are caused by defects in the cable accessories. Nowadays, significant research has been carried out worldwide into examining whether electricity, and in particular, the presence of electric and magnetic fields have an adverse impact on health, especially the occurrence of cancer and childhood leukemia. The purpose of this paper is to optimize the electric field distribution in underground cable accessories. This reduces the impact of the harmful effects of the fields on living beings and humans. Design/methodology/approach – Cable terminations and joints are designed to eliminate the stress concentration at the termination screen to avoid the breakdown of the cable and high values of electric field at these points. Any improvement in the cable termination and joints construction is of great interest. There are several methods for the solution of electric field distribution. These can be summarized as analytical, experimental, free-hand field mapping, analogue methods and numerical methods. In this paper cable accessories are modeled by using multilayer dielectric system and very thin deflector’s cones. Findings – This model includes specific insulators design and smart choice of electrodes position. Stress-grading nonlinear materials in form of tapes and tubes were used with much success. In order to optimize the cable joint parameters, two criteria were monitored – total electric field magnitude and magnitude of the tangential component. More than 30 percent is reduced impact of cables on the environment. Originality/value – In order to investigate the accuracy of the applied numerical model, various configurations of the cable accessories are studied. The first time is applied new Hybrid Boundary Elements Method on the protection of the environment.

Quantification and imaging of corrosion wall thinning using shear horizontal guided waves generated by magnetostrictive sensors

Ultrasonic guided wave tomography provides an imaging potential over a hidden and inaccessible damage zone. The use of shear horizontal guided waves has been proposed as an attractive technique for surface defect characterization. In this study, the quantification and imaging of corrosion wall thinning in a plate are investigated by using shear horizontal guided waves. Simulations of shear horizontal wave propagation in the specimens using hybrid boundary element method are studied in this paper. Magnetostrictive patch transducers are designed to generate and measure the shear horizontal wave mode experimentally. The quantification via imaging of wall thinning is achieved by a modified reconstruction algorithm for the probabilistic inspection of damage tomography algorithm. The comparisons of the imaging obtained by modeling data and experimental ones of defects with different shapes in the specimens are presented in this paper. The results obtained by experimental tests are comparable with that produced by boundary elements method. The present approach provides an alternative tool, that can be applied to detecting, locating and imaging the wall thinning defects in plate-like structures.

Hybrid Natural Element Method-Boundary Element Method for Unbounded Problems

This paper presents a hybrid approach coupling natural element method (NEM) and boundary element method (BEM) for the treatment of unbounded problems. The goal is to combine the accuracy of the NEM and ability of the BEM in modeling linear and deformable domains without a mesh. The performance of the proposed scheme is compared with a finite-element method-BEM coupling in terms of accuracy. Results show that for a given number of degrees of freedom, the proposed approach (NEM-BEM) is able to provide more accurate solutions.

Assessment on transient sound radiation of a vibrating steel bridge due to traffic loading

Structure-borne noise induced by vehicle–bridge coupling vibration is harmful to human health and living environment. Investigating the sound pressure level and the radiation mechanism of structure-borne noise is of great significance for the assessment of environmental noise pollution and noise control. In this paper, the transient noise induced by vehicle–bridge coupling vibration is investigated by employing the hybrid finite element method (FEM) and boundary element method (BEM). The effect of local vibration of the bridge deck is taken into account and the sound responses of the structure-borne noise in time domain is obtained. The precision of the proposed method is validated by comparing numerical results to the on-site measurements of a steel girder-plate bridge in service. It implies that the sound pressure level and its distribution in both time and frequency domains may be predicted by the hybrid approach of FEM–BEM with satisfactory accuracy. Numerical results indicate that the vibrating steel bridge radiates high-level noise because of its extreme flexibility and large surface area for sound radiation. The impact effects of the vehicle on the sound pressure when leaving the bridge are observed. The shape of the contour lines in the area around the bridge deck could be explained by the mode shapes of the bridge. The moving speed of the vehicle only affects the sound pressure components with frequencies lower than 10Hz.

Stochastic sensitivity of the electromagnetic distributions inside a human eye modeled with a 3D hybrid BEM/FEM edge element method

This contribution was dedicated to the assessment of the electromagnetic (EM) distributions inside a 3D modeled human eye. Since the use of accurate and efficient electromagnetic tools is crucial to obtain such results, an original hybrid boundary element method (BEM)/finite element method (FEM) is presented through the example of an EM wave impinging on the eye corneal region. Due to the variability inherent to the characterizing of living parameters (regarding our frequency range of interest about a few GHz), an accurate modeling of those mostly electrical data is necessary. A simple formalism based upon a “philosophy” close to Monte Carlo requirements is proposed in this paper in order to integrate efficiently and precisely uncertainties in the proposed results. The analysis of the sensitivity of different electrical parameters aims to increase a better knowledge of the EM fields distribution inside an eye. Obviously, both the deterministic EM modeling and the stochastic theoretical basis will be presented. The whole model will be illustrated on numerical examples including different random variables.

Covered microstrip line with ground planes of finite width

Characteristic parameters of a covered microstrip line with ground planes of finite width are determined using hybrid boundary element method (HBEM). This method, developed at the Faculty of Electronic Engineering of Nis is based on the combination of equivalent electrodes method (EEM) and boundary element method (BEM). Results for the characteristic impedance of the observed microstrip line are compared with the corresponding ones obtained by the finite element method.

Application of hybrid boundary element method: Example of semishperical ground inhomogeneity

One new, so-called hybrid boundary element method (HBEM) is presented in this paper. It is a recently proposed numerical method for stationary and quasi-stationary EM field analysis. The method application is illustrated on the example of solving the problem of modelling hemispherical ground inhomogeneity influence on grounding system. The applied procedure also includes using of quasi-stationary image-theory. The obtained results are compared with those ones based on using the Green?s function for the point source inside semi-spherical inhomogeneities as well as with the results obtained by applying COMSOL program package.

Effect of material on hydro-elastic behaviour of marine propeller by using BEM-FEM hybrid software

ABSTRACT This paper studies the effect of material on the hydro-elastic behaviour. The geometry of flexible propeller changes due to hydrodynamic and inertial forces acting on the propeller. By using prepared software (called HYDRO-BEM and ELASTIC-FEM) the hydro-elastic features of the propeller made of various materials are analyzed. In the software the hybrid boundary element and finite element methods are used. First, the load acting on the propeller is determined by using the BEM and deformed propeller geometry is then obtained by the FEM. In the next step, the load on the deformed propeller is determined by the BEM and a new shape is obtained. The iterative procedure is repeated till the blade deflection and hydrodynamic characteristics (thrust, torque and efficiency) of the propeller become converged. Four different materials are examined. It is concluded that the hydro-elastic behaviour of the composite propeller is strongly affected by its flexibility due to light material.

A hybrid boundary element-finite element approach to modeling plane wave 3D electromagnetic induction responses in the Earth

A novel hybrid boundary element-finite element scheme which is accelerated by an adaptive multi-level fast multipole algorithm is presented to simulate 3D plane wave electromagnetic induction responses in the Earth. The remarkable advantages of this novel scheme are the complete removal of the volume discretization of the air space and the capability of simulating large-scale complicated geo-electromagnetic induction problems. To achieve this goal, first the Galerkin edge-based finite-element method (FEM) using unstructured meshes is adopted to solve the electric field differential equation in the heterogeneous Earth, where arbitrary distributions of conductivity, magnetic permeability and dielectric permittivity are allowed for. Second, the point collocation boundary-element method (BEM) is used to solve a surface integral formula in terms of the reduced electrical vector potential on the arbitrarily shaped air–Earth interface. Third, to avoid explicit storage of the system matrix arising from large-scale problems and to reduce the horrendous time complexity of the product of the system matrix with an initial vector of unknowns, the adaptive multilevel fast multipole method is applied. This leads to a matrix-free form suitable for the application of iterative solvers. Furthermore, a highly sparse problem-dependent preconditioner is developed to significantly reduce the number of iterations used by the iterative solvers.The efficacy of the presented hybrid scheme is verified on two synthetic examples against different numerical techniques such as goal-oriented adaptive finite-element methods. Numerical experiments show that at low frequencies, where the quasi-static approximation is applicable, standard FEM methods prove to be superior to our hybrid BEM–FEM solutions in terms of computational time, because the FEM method requires only a coarse discretization of the air domain and offers an advantageous sparsity of the system matrix. At radio-magnetotelluric frequencies of a few hundred kHz, the hybrid BEM–FEM scheme outperforms the FEM method, because it avoids explicit storage of the system matrices as well as dense volume discretization of the air domain required by FEM methods at high frequencies. In summary, to the best of our knowledge, this study is the first attempt at completely removing the air space for large scale complicated electromagnetic induction modeling in the Earth.

An efficient hybrid BEM–RBIE method for solving conjugate heat transfer problems

In this paper, a hybrid boundary element method (BEM) — radial basis integral equation (RBIE) method is derived to solve conjugate heat transfer (CHT) problems. The BEM is used to solve the heat transfer in the solid region, while the fluid region is solved by using the RBIE. The capability of the RBIE to calculate the potential and the spatial gradients, while advantageous when knowledge of the spatial gradients is of primary importance, can lead to unnecessary increases in the computational cost when solving CHT problems due to the additional equations imposed per node. By using the BEM to solve the heat transfer in the solids, a significant reduction in the size of the system matrix compared to the case of using the RBIE for both the heat transfer in the solid and fluid regions can be achieved. A case study that examines the CHT inside the human eye is solved using the derived hybrid BEM–RBIE method.

A Hybrid Boundary Element Method-Reluctance Network Method for Open Boundary 3-D Nonlinear Problems

A scalar potential formulation coupling a hybrid boundary element method and a reluctance network method is presented to solve 3-D nonlinear magnetostatic problems. The computation times and the accuracy of this approach are compared with those of the finite element method in the context of force and torque evaluations. It is shown that this method could efficiently be used for the presizing of actuators. Discussion concerning the advantages of this approach compared to a pure reluctance network method is also presented.

A Wire Electrode inside Parallelepipedicaly-Shaped Ground Inhomogeneity: Comparison of Two Solutions

The results for the resistance of the wire electrode inside parallelepipedicaly-shaped domain surrounded with homogeneous ground obtained by one recently proposed procedure for modeling described structure are compared with recently published results realized applying one new hybrid boundary element method. The first approach is based on the approximating system wire-parallelepiped with one wire conductor off equivalent length and cross-section radius. The hybrid method is based on equivalent electrodes method and point matching method applied on matching values for potential of wire electrode and normal component of electric field on the boundary surface between conductive media. The quasi-stationary approach is applied. DOI: http://dx.doi.org/10.5755/j01.eee.19.5.1845

Hybrid Boundary Element Method and Quasi-TEM Analysis of Two-Dimensional Transmission Lines—Generalization

The hybrid boundary element method, based on the equivalent electrodes method and the boundary element method, is presented in this article. This method is applied on several examples for calculating the characteristic impedance of transmission lines. It should be emphasized that the combination of the equivalent electrodes method and a new variant of the boundary element method can be efficiently implemented in quasi-transverse electromagnetic analysis of transmission lines without loss of accuracy. All results for the characteristic impedance of the observed transmission lines are compared to corresponding ones obtained by the finite-element method.