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Noise and vibration issues can be dealt with using several approaches. Using the source–transfer path–receiver approach, a vibration issue could be solved by attenuating the source, modifying the transfer path or by influencing the receiver. Applying this approach on a wind turbine gearbox would respectively correspond with lowering the gear excitation levels, modifying the gearbox housing or by trying to isolate the gearbox from the rest of the wind turbine. This paper uses a combination of multi-body modelling and typical transfer path analysis (TPA) to investigate the impact of bearings on the total transfer path and the resulting vibration levels. Structural vibrations are calculated using a flexible multi-body model of a three-stage wind turbine gearbox. Because the high-speed mesh is often the main source of vibrations, focus is put on the four bearings of this gear stage. The TPA method using structural vibration simulation results shows which bearing position is responsible for transmitting the highest excitation levels from the gears to the gearbox housing structure. Influences of bearing stiffness values and bearing damping values on the resulting vibration levels are investigated by means of a parameter sensitivity study and are confirmed with the results from the TPA. Because both the TPA and the parameter sensitivity analysis revealed a big influence on radial stiffness for a certain bearing, this was investigated in more detail and showed the big importance of correct axial bearing position. The main conclusions of this paper are that the total vibration behaviour of a wind turbine gearbox can be altered significantly by changing both bearing properties such as stiffness, damping and position, and bearing support stiffness. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper the flow of liquid film on a vertical fiber is simulated using a multi-fluid model. It is demonstrated that nearly sinusoidal, as well as solitary waves can be simulated using an appropriate interface capturing model. Initial instabilities, which grow and cause wavy patterns, are introduced by disturbing the fluid inlet velocity. A constant disturbance frequency as well as white noise disturbance is used in numerical simulations. Waves travel on a substrate of constant height. The velocity of the wavy film expressed relative to a reference frame, which moves with film waves, shows recirculating motions. Bead velocities, frequencies, and amplitudes agree well with those reported in the literature. It is shown that disturbance frequencies above the so-called cutoff frequency and white noise disturbance lead to a “natural” like wave development, phenomena also observed in experiments.

The construction of the impedance matrix in the method of moments requires the calculation of interaction integrals between the expansion functions, through the Green's function and its derivatives. The singular behavior of the Green's function poses considerable problems for an accurate numerical evaluation of these integrals, requiring techniques such as singularity extraction or cancellation. In this contribution we will show why these methods fail when the medium is highly conductive. A novel technique is proposed to handle these highly challenging integrals. The complexity of the new method is independent of the conductivity.

We present the design, processing and testing of a W-band finite by infinite and a finite by finite Grounded Frequency Selective Surfaces (FSSs) on infinite background. The 3D full wave solver Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA) is used to simulate the FSSs. As NSPWMLFMA solver improves the complexity matrix-vector product in an iterative solver from O(N(2)) to O(N log N) which enables the solver to simulate finite arrays with faster execution time and manageable memory requirements. The simulation results were verified by comparing them with the experimental results. The comparisons demonstrate the accuracy of the NSPWMLFMA solver. We fabricated the corresponding FSS arrays on quartz substrate with photolithographic etching techniques and characterized the vector S-parameters with a free space Millimeter Wave Vector Network Analyzer (MVNA).

A novel method, called the nondirective stable plane wave multilevel fast multipole algorithm (NSPWMLFMA), is presented to evaluate the low-frequency (LF) interactions that cannot be handled by the multilevel fast multipole algorithm (MLFMA). It is well known that the MLFMA cannot be used for LF interactions, since it suffers from numerical instability. Contrary to current techniques, the proposed technique is not based on the spectral representation of the Green function. Instead the addition theorem of the MLFMA is manipulated into a form that allows numerically stable translations along the z axis. The translation operator for these translations is derived in closed form. A QR-based method is devised to allow stable translations in all the other directions. Interpolations and anterpolations are also provided, allowing a full multilevel algorithm. Since the NSPWMLFMA is based on the same mathematical foundations as the MLFMA, it requires limited adaptations to existing MLFMA codes. The fact that a QR is needed limits this algorithm to LF interactions. However, a coupling with the MLFMA is straightforward, allowing the easy construction of a broadband algorithm. The DC limit of the algorithm is also presented and it is shown that the algorithm remains valid for static problems. Finally, it is shown that the error introduced in the different steps of the algorithm is controllable, and a single-level vectorial version of the algorithm is applied to a generic scattering application to demonstrate its validity.

We present a full-wave homogenization method to determine the effective material parameters of metamaterials by considering a spherical piece of metamaterial. We use a T-matrix approach that is accelerated by a multilevel fast multipole method that is stable at low frequencies. To determine the T-matrix of one inclusion in the metamaterial a Method of Moments surface integral equation is used that is also accelerated using another multilevel fast multipole method that is stable at low frequencies. We also derive a new closed-form expression to extract the effective material parameters from the T-matrix of the spherical piece of material. Examples verify the accuracy and limitations of the method. We show results for metamaterials comprising more than 40,000 particles.

Although wind turbine noise is mainly dominated by aero-acoustic noise, mechanical noise, coming from gearbox or generator, could—especially when it contains audible tonal components—result in nonconformity to local noise regulations. To reduce the mechanical noise from the gearbox, focus is put on first time right design. To achieve this, simulation models are being used earlier in the design process to predict possible issues. This paper starts with a short overview of the used model and gives additional insight in how forces from planetary gear stages should be introduced in the flexible housing. Main focus of this paper however is the approach that is being used to validate such a complex multibody model of a wind turbine gearbox. The validation approach consists of five levels: (1) individual components, (2) assembly of the empty gearbox housing, (3) the assembled gearbox, (4) the gearbox on the end-of-line (EOL) test rig, and (5) the gearbox in the wind turbine. This paper focuses on the experimental measurement results, the correlation approach for such complex models, and the results of this correlation for the first four levels showing the usability of these models to accurately predict the modal behavior.

One main contributor for gearbox rated lifetime estimation is the assessment of bearing loading during predicted operating conditions. This paper investigates an approach to determine input bearing loading by means of a TPA (Transfer Path Analysis) approach. TPA is suggested to retrieve internal bearing forces from acceleration measurements acquired at the outside of the gearbox housing. However, classical TPA methods would require the gearbox to be dismantled during the transfer path determination process. This poses significant practical challenges. To overcome this issue, this paper investigates the possibility of using a flexible multibody simulation model to calculate the different frequency response functions between bearings forces and acceleration sensors. All simulations use a flexible multibody modeling approach, which has been extensively validated. Main results of this validation process have been published by the authors in the past. The paper discusses the results of such analysis on a multi-megawatt wind turbine gearbox. Here, simulated acceleration measurements on the gearbox housing are processed into bearing forces. The feasibility of using these forces for a rating life calculation is investigated.

[1] Boundary element methods (BEMs) are an increasingly popular approach to model electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullulated from the research into BEMs, enhancing its efficiency and applicability. In designing a viable implementation of the BEM, both theoretical and practical aspects need to be taken into account. Theoretical aspects include the choice of an integral equation for the sought after current densities on the geometry's boundaries and the choice of a discretization strategy (i.e. a finite element space) for this equation. Practical aspects include efficient algorithms to execute the multiplication of the system matrix by a test vector (such as a fast multipole method) and the parallelization of this multiplication algorithm that allows the distribution of the computation and communication requirements between multiple computational nodes. In honor of our former colleague and mentor, F. Olyslager, an overview of the BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from F. Olyslager's scientific endeavors are included in the survey.

This paper presents the progress in the development of a scalable parallel MultiLevel Fast Multipole Algorithm (MLFMA) for three-dimensional (3D) electromagnetic problems. Scalability stands for the ability to handle a larger problem on a proportionally larger parallel computer architecture. As a partitioning scheme, hierarchical partitioning (HP) is used, which divides the work load in a very balanced way. This prevents the time, memory and communication complexity per cpu-core from increasing rapidly as a function of the number of cpu-cores and unknowns.

[1] In this paper, the full wave simulation of a 2-D Luneburg lens is reported, using the Multilevel Fast Multipole Algorithm (MLFMA). To stabilize the MLFMA at low frequencies, it is augmented with a normalized plane-wave method, yielding a fully broadband solver. To test the proposed method, the Luneburg lens is partitioned into concentric shells with a constant permittivity, resulting in a complex simulation target that consists of multiple embedded dielectric objects. The numerical results are in good agreement with the analytical solutions for both the continuous and discretized lens.

Novel formulas are presented that allow the rapid estimation of the number of terms L that needs to be taken into account in the translation operator of the vectorial Nondirective Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA). This is especially important for low frequencies, since the L needed for error- controllability can be substantially higher than the L required in the scalar case. Although these formulas were originally derived for use in the NSPWMLFMA, they are equally useful in at least three other fast matrix multiplication methods.

During the past decades, much research has been done towards the efficient calculation of impedance integrals in the Method of Moments. However, these results were almost always uniquely concerned with penetrable media. In this contribution, it will be shown how the integrals can be treated in highly conductive media as well. The rapid exponential decline of the Green's function, due to the losses, is the root of all additional complexities. The method as presented here takes care of these problems in a scalable way, i.e. the computation time becomes independent of the conductivity of the material. It is not meant as a replacement for techniques in penetrable media, due to some additional costs, but is - to our knowledge - the only approach that currently exists to efficiently handle conductive media. This paper presents the ideas and techniques in a fairly condensed manner. More information can be found in [1].

Boundary element methods (BEMs) are an increasingly popular approach to the modeling of electromagnetic scattering both by perfect conductors and dielectric objects. Several mathematical, numerical, and computational techniques pullu-lated from the research into BEMs, enhancing its efficiency. The Fast Multipole Method (FMM) and its descendants accelerate the matrix-vector product that constitutes the BEM's computational bottleneck. In particular, dedicated FMMs have been conceived for the computation of the electromagnetic scattering at complex metallic and/or dielectric objects in free space and in layered background media. Caldero n preconditioning of the BEM's system matrix lowers the number of matrix-vector products required to reach an accurate solution, and thus the time to reach it. Parallelization distributes the remaining workload over a battery of affordable computational nodes, diminishing the wall-clock computation time. In honor of our former colleague and mentor, Prof. F. Olyslager, an overview of some dedicated BEMs for large and complex EM problems developed within the Electromagnetics Group at Ghent University is presented. Recent results that ramified from Prof. Olyslager's scientific endeavors are included in the survey.

Until recently, the doubling of the number of transistors in integrated circuits every 18 months (Moore's Law), allowed for an exponential increase in computing power that could be obtained from a single processor. The introduction of multi-core processors in 2004, which contain multiple independent processing elements or so-called cores, is the new trend to increase the computing power of a single chip. Faster processors are now obtained by adding more cores, rather than increasing the speed of the cores. In order to take advantage of a multi-core chip, existing sequential algorithms have to be redesigned for parallel execution by independent computing elements.

Scattering of time-harmonic waves by dielectric objects can be described by several integral equations. All of these result from the Stratton-Chu intergral representation formulas for the fields in the interior and exterior region. The most popular integral equations are the Poggio-Miller-Chew-Harrington-Wu-Tsai equation (PMCHWT) and the Muller equation. The former results from subtracting the interior and exterior representation formulas. The PMCHWT equation is typically discretized using Rao-Wilton-Glisson (RWG) basis functions.

The Method of Moments (MoM) is one of the most popular techniques for solving electromagnetic scattering problems. Its main advantage is that, when used to discretise a Boundary Integral Equation (BIE), only the surface of the objects needs to be discretised. Many other techniques require discretisation of the volume as well, leading to an increase of unknowns and requiring an artificial boundary to emulate infinity. The downside of the MoM is that the resulting linear system is dense, due to the Green's function, and often ill-conditioned. The density of the impedance matrix would lead to a prohibitive O (N2) complexity for both the CPU time and the memory. A number of techniques have been developed in the past, reducing this complexity. Among the most succesful are the Fast Multipole Methods (FMM), which reduce the complexity for a matrix-vector product to O(NlogN). This matrix-vector product is the bottleneck of an iterative solution of the linear system. However, an iterative solution can only be efficient if the problem is sufficiently well-conditioned. The choice of BIE influences the conditioning number of the impedance matrix. The Electric Field Integral Equation (EFIE) leads to a highly accurate solution but is notoriously ill-conditioned. In comparison, the Magnetic Field Integral Equation (MFIE) is less accurate (for the same level of discretisation) but is well-posed. Also, on open surfaces the MFIE is not applicable. In order to alleviate the problems with the EFIE, a powerful preconditioner is required to stabilise the breakdown, which occurs in particular at low frequencies (LF). Recently, an approach has been proposed, allowing multiplication of the EFIE impedance matrix with itself, leading to a well-conditioned problem. In the next section, this approach will be briefly revisited. In order to maintain the O(NlogN) complexity for the global solution, we employ FMM to accelerate the Calder´on Preconditioner as well. A number of difficulties occur, but these can all be overcome. This combination of FMM and Calder´on Preconditioning will be dealt with in the remaining sections. At the time of the conference, examples will be shown to illustrate the novel techniques.

Boundary integral equations are the principal tools for efficiently simulating electromagnetic fields in structures with piecewise constant material parameters. A specific trait of boundary integral equations is that the Green function of the Helmholtz equation appears as the integration kernel. Hence, discretizing a boundary integral equation leads to a dense linear system. Since a direct O(N2) (N3) solution of such a system is very computationally expensive, iterative techniques are often used in conjunction with an acceleration scheme that reduces the computational complexity of a matrix-vector multiplication from O (N2) to O (N) or O (N log N). Many such acceleration schemes exist, for example the renowned Multilevel Fast Multipole Algorithm (MLFMA).

Calderon preconditioners have recently been demonstrated to be very successful in stabilizing the electric field integral equation (EFIE) for perfect electric conductors at lower frequencies. Previous authors have shown that, by using a dense matrix preconditioner based on the Calderon identities, the low frequency instability is removed while still maintaining the inherent accuracy of the EFIE. It was also demonstrated that the spectral properties of the Calderon preconditioner are conserved during discretization if the EFIE operator is discretized with Rao-Wilton-Glisson expansion functions and the preconditioner with Buffa-Christiansen expansion functions. In this article we will show how the Calderon multiplicative preconditioner (CMP) can be combined with fast multipole methods to accelerate the numerical solution, leading to an overall complexity of O(N long N) for the entire iterative solution. At low frequencies, where the CMP is most useful, the traditional multilevel fast multipole algorithm (MLFMA) is unstable and we apply the nondirectional stable plane wave MLFMA (NSPWMLFMA) that resolves the low frequency breakdown of the MLFMA. The combined algorithm will be called the CMP-NSPWMLFMA. Applying the CMP-NSPWMLFMA at open surfaces or very low frequencies leads to certain problems, which will be discussed in this article.

A thin film interconnect technology was characterised up to 18 GHz. The focus was put on the analyses of conductive losses. An equivalent model for the conductor internal impedance was extended to include low frequency loss behaviour and the effect of a metal barrier. A good correspondence with the measurements was achieved.

In this contribution, the challenges in designing accurate and efficient boundary integral equation based solvers for electromagnetic scattering are discussed. More in particular, the efficiency of the solvers are enhanced using the following techniques: the number of degrees of freedom required to reach a certain accuracy is decreased by choosing accurate discretization schemes, the number of iterations required by iterative solvers is decreased by using Calderon preconditioned equations, the matrix-vector multiplication is accelerated using broad band multi-level fast multipole algorithms, and the computational workload is distributed using parallel paradigms. These techniques will be elucidated and demonstrated on test cases. Finally, larger and real live results will be presented in which the above mentioned techniques are combined.

The interaction matrices originating from the Method of Moments (MoM) discretization of the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) integral equation pertinent to the analysis from (piecewise) homogeneous penetrable objects become ill-conditioned when either part or the entire scattering surface requires a dense discretization. This behavior is similar to that of the Electric Field Integral Equation (EFIE) for the scattering from perfectly conducting surfaces and finds its origin in the presence of compact and hypersingular components in the integral equation kernel.

Calderon preconditioning is very succesful in stabilising the EFIE and the use of BC functions makes the formalism valid on open surfaces. Through applying a broadband fast multipole method, the complexity can be reduced from O (N2) to O(N log N), allowing the simulation of very large structures. In the high frequency case a localised version of the preconditioner must be used to avoid excessive scattering of the eigenvalues of the combined operator.

We present the application of the Non-directive Stable Plane Wave Multilevel Fast Multipole Algorithm (NSPWMLFMA) to the simulation of the shielding effectiveness of enclosures with complex fillings. The method is parallelized with an asynchronous algorithm in order to allow highly efficient simulations in an inexpensive GRID computing environment. The whole method is fully error controlled. Further increased efficiency is obtained by using Block-Jacobi preconditioners, splay trees (STs) to extract symmetries in the geometry and careful evaluation of self-patch and neighbor-patch integrals. Numerical examples of enclosures with and without equipment illustrate the method. We will also focus on the use of lossy materials to increase the shielding efficiency of metal enclosures around resonance frequencies.

The iterative solution of integral equations containing the Green function of the Helmholtz equation as the integration kernel requires repeated matrix-vector products. These products can be accelerated by means of a so-called fast multipole method (FMM). Of the many fast multipole methods in use today, the multilevel fast multipole algorithm (MLFMA) is arguably among the most successful ones. It allows the simulation of electrically large structures that are intractable with direct or unaccelerated iterative solvers. Testimony to the MLFMAs myriad uses is its implementation in various commercial EM software packages such as FEKO and CST Microwave studio. However, the MLFMA has one big drawback: a numerical instability prevents the method from being used on low frequency (LF) interactions, i.e. interactions between sources and observers that are less than approximately one wavelength apart. As a consequence configurations containing significant sub-wavelength geometrical detail cannot be efficiently treated using the MLFMA alone and a hybrid method is necessary. However, the LF methods in use today are generally less efficient due to non-diagonal translation operators (multipole methods) or the need for six radiation patterns (spectral methods). In this contribution a novel algorithm, called the nondirective stable plane wave multilevel fast multipole algorithm (NSPWMLFMA) [1], will be presented that is stable at LF, exhibits diagonal translation operators and requires only one radiation pattern. The method is based on an analytical expression for a translation operator in the z-direction. This translation operator is made numerically stable using a shift of the integration path into the complex plane. It even has a DC-limit. A QR-based method is then used to extend the applicability to all the other translation directions. The algorithm has also been parallelized using open FMM [2]. Finally some numerical results will be shown.

In this paper we wish to focus on some recent advances in the multilevel fast multipole algorithm (MLFMA). Three different topics will be discussed briefly: a seamless extension of the MLFMA to low frequencies, an asynchronous parallelization of the MLFMA suitable for grid computing environments and a new Calder on based preconditioner for the electric field integral equation (EFIE). This will be illustrated by three scattering examples in frequency and time domain.

In this contribution we extend our work on the application of boundary integral equations to accurately predict the shielding properties of complex enclosure geometries. The focus of this contribution is on the power of the splay tree algorithm to efficiently extract symmetry properties from a geometry. We will show that by using these splay trees in two as well as three dimensions significant savings in CPU time can be achieved allowing for the evaluation of ever more complex structures within a given computation time. We show different results for enclosures in two dimensions and also illustrate the time savings of splay trees in three dimensions. At the time of the conference we will also show three-dimensional shielding problems.

Conductive losses of multichip module interconnections are analyzed. A distributed network model for the conductor surface impedance is extended to include transition to DC resistivity and the effect of barrier and adhesion layers. Using the model, a broadband loss expression suitable for use in fast Fourier transform (FFT)-based transient analysis network simulators for digital signal transmission on lossy interconnections is derived. The expression is used to model measured scattering parameter characteristics up to 18 GHz, for different line types. Excellent correspondence between measurements and simulations is achieved, even when magnetic effects of a thick nickel barrier layer are involved. Finally, the models are incorporated in a transient analysis network simulation program. >

If the interconnection between two integrated circuits is designed for high speed data transmission, not only the physical line parameters matter, but also the on-chip driver and receiver characteristics. The behaviour of the interconnection line is primarely determined by the interconnect technology which is used. Low loss and generally relatively long printed circuit board interconnections behave differently than lossy MCM-type interconnections and require a different approach. For digital signal transmission on uniform interconnections, lines can be described using their equivalent distributed network parameters and the interconnection length. Driver characteristics depend on the IC technology which is used. Further on, the driver behaviour is determined by its circuit design (e.g.): the number of driver stages) and by the dimensions of the driver transistors.