Hybrid Boundary Element Research Articles

Multi-DOF WEC Performance in Variable Bathymetry Regions Using a Hybrid 3D BEM and Optimization

In the present work a hybrid boundary element method is used, in conjunction with a coupled mode model and perfectly matched layer model, for obtaining the solution of the propagation/diffraction/radiation problems of floating bodies in variable bathymetry regions. The implemented methodology is free of mild-slope assumptions and restrictions. The present work extends previous results concerning heaving floaters over a region of general bottom topography in the case of generally shaped wave energy converters (WECs) operating in multiple degrees of freedom. Numerical results concerning the details of the wave field and the power output are presented, and the effects of WEC shape on the optimization of power extraction are discussed. It is demonstrated that consideration of heave in combination with pitch oscillation modes leads to a possible increase of the WEC performance.

Efficient Simulation of Substrate-Integrated Waveguide Antennas Using a Hybrid Boundary Element Method

This paper presents a hybrid boundary element method for the efficient simulation of substrate-integrated waveguide (SIW) horn antennas. It is applicable with good accuracy to relatively thin structures with conventional circular ground vias. In the multiscale simulations, a 2-D contour integral method is used for the modeling of the fields inside the structure with numerous vias and a method of moments is used for the radiated fields outside. The contour integral method is extended in this paper by a new waveguide port of finite size based on the unit cell analysis of an SIW segment. Several SIW horn antennas are studied to validate the proposed method in terms of the input impedance, the field distribution on the aperture, and the radiation diagram. The proposed method shows good to reasonable accuracy and has a numerical efficiency which is about 2–3 orders higher than FEM-based full-wave simulations. It is therefore well suited for fast optimizations.

Topology optimization of sound absorbing layer for the mid-frequency vibration of vibro-acoustic systems

Due to the significant difference of dynamic properties between the fluid medium and the structure, when a vibro-acoustic system is subjected to a higher frequency excitation, it may typically exhibit mid-frequency behavior which involves different wavelength deformations and is very sensitive to the uncertainties of the system. This paper deals with optimized distribution of a sound absorbing layer for the mid-frequency vibration of vibro-acoustic systems by using hybrid boundary element analysis and statistical energy analysis. Based on the solid isotropic material with penalization approach, an artificial sound absorbing material model is suggested and the relative densities of the sound absorbing material are taken as design variables. The sound pressure level at a specified point in the acoustic cavity is to be minimized by distributing a given amount of sound absorbing material. An efficient direct differentiation scheme for the response sensitivity analysis is proposed. Then, the optimization problem is solved by using the method of moving asymptotes. A numerical example illustrates the validity and effectiveness of the present optimization model. Impact of the excitation frequency on optimized topology is also discussed.

Dynamics of a capsule flowing in a tube under pulsatile flow

We analyze numerically the behavior of a deformable micro-capsule confined in a pipe under a pulsatile flow. The capsule moves and is deformed by the action of a pulsatile flow inside the tube with a non-null mean velocity. This configuration can be found in the nature and in many bioengineering systems where artificial capsules are driven by micro-pumps through micro-channels. The capsule is considered as a thin hyperelastic membrane, which encloses an internal fluid. As it has been demonstrated in the literature, this model represents a wide range of artificial capsules, for example, the alginate-based capsules, typically used in bioengineering applications. A hybrid isogeometric finite element method and boundary element method based on a T-spline discretization and formulated in the time domain is used to solve the mechanical and hydrodynamical equations. The influence of the relative rigidity of the membrane, frequency and amplitude of the pulsatile flow is studied. Results show that the behavior of the capsule differs from steady flows and it depends strongly on the frequency of the flow and mechanical characteristic of the capsule.

ANALYSIS OF BOWMAN SQUARES USING HYBRID BOUNDARY ELEMENT METHOD

The characteristic parameters of the Bowman squares are determined using the hybrid boundary element method. Influences of different parameters on characteristic impedance values are analysed. Also, the case of multilayered dielectric is considered. The results for the characteristic impedance have been compared with the results obtained by other methods. Key words: Bowman squares, characteristic impedance, diamondwise structure, finite element method, hybrid boundary element method.

RADIALLY MAGNETIZED RING PERMANENT MAGNET MODELLING IN THE VICINITY OF SOFT MAGNETIC CYLINDER

Radially magnetized ring permanent magnet placed above the soft magnetic cylinder is modelled in this paper using Hybrid Boundary Element Method (HBEM) and a discretization approach based on fictitious magnetic charges. The obtained results are compared to those obtained with Finite Element Method results (FEM). Key words: Hybrid boundary element method (HBEM), magnetization charges, magnetic force, permanent magnet (PM).

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.

A Hybrid Boundary Element Model for Simulation and Optimization of Large Piezoelectric Micromachined Ultrasonic Transducer Arrays.

A hybrid boundary element model is proposed for the simulation of large piezoelectric micromachined ultrasonic transducer (PMUT) arrays in immersion. Multiphysics finite element method (FEM) simulation of a single-membrane structure is used to determine stiffness and piezoelectrically induced actuation loading of the membranes. To simulate the arrays of membranes in immersion, a boundary element method is employed, wherein membrane structures are modeled by a surface mesh that is coupled mechanically by mass, stiffness, and damping matrices, and acoustically by a mutual impedance matrix. A multilevel fast multipole algorithm speeds up computation time and reduces memory usage, enabling the simulation of thousands of membranes in a reasonable time. The model is validated with FEM for a small 3 3 matrix array for both square and circular membrane geometries. Two practical optimization examples of large PMUT arrays are demonstrated: membrane spacing of a 7 7 matrix array with circular membranes, and material choice and top electrode coverage of a 32-element linear array with 640 circular membranes. In addition, a simple analytical approach to electrode optimization based on normal mode theory is verified.

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

Simulation of short crack propagation under hydrogen influence using a hybrid boundary element technique for anisotropic elastic solids

AbstractA two‐dimensional model for stage I short crack propagation on multiple slip planes under the influence of hydrogen is presented. It considers elastic‐plastic material behaviour by allowing sliding on the active slip planes in the corresponding slip directions. A crack propagation law based on the crack tip sliding displacement is used to simulate crack growth. The activation of slip bands and the sliding on these active slip bands will be influenced by the local hydrogen concentration. The model is solved numerically using the boundary element method. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications.

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.