A validation of some recent BEM and FEM techniques for ...past.isma-isaac.be/downloads/isma2014/papers/isma2014_0543.pdf · available in LMS Virtual.Lab and other acoustic met hodologies

A validation of some recent BEM and FEM techniques for predicting exterior acoustic transfer functions for a mockup of an engine installed in the engine bay

G. Miccoli1, K. Vansant

2, C. Bertolini

3

1 IMAMOTER Institute, Italian National Research Council (C.N.R.)

Cassana (FE), Italy

e-mail: [email protected]

2 Siemens PLM Software

Leuven, Belgium

3 Autoneum Management AG

Winterthur, Switzerland

Abstract As legislation for exterior automotive noise has recently become more challenging, the industry is looking into further optimizing engine and engine bay design. Together with the new legal evolutions, also the

engine downsizing trend and therewith the increased use of for instance direct injection and air loading

systems requires re-evaluation of the current design guidelines and dedicated studies to reach the quietest design. Simulation provides a relatively inexpensive approach to accomplish this: many design

alternatives can be tested before any prototype is actually tested. In order for the simulation path to be

successful, it is paramount that the approaches are sufficiently fast and accurate. This paper discusses

some of the more recent evolutions in Finite and Boundary Element Methods and their solver technologies. The case study concerns prediction of acoustic transfer functions for an engine bay mockup

model. Results are overlaid with measurements and the time and memory performance of each method is

compared.

1 Introduction

Until several years ago, automotive engineers ensured that exterior engine noise remained within limits by

relying on their experience for designing engines and engine bays with appropriate acoustic treatments. A

real need to make several designs and find an acoustically optimal design was not that imminent as today. The evolutions in legislation, for instance for Pass By Noise (PBN) (now 70 dB(A)), and downsized

engine and accessories noise sources, now call for more efforts and dedicated studies. It is clear that

engineering insight in the acoustic optimization task is crucial already in the early design stages. This explains the regained interest in using simulation models first before any costly prototype is made. A

further reason supporting a simulation approach are the recent advances made in modeling and solver

technologies. These serve not only the prediction of engine radiated noise in free condition but also in

installed condition, i.e. the engine in the engine bay. The latter case requires advanced methods to obtain results in a reasonable amount of time, thus allowing for examining multiple sound proofing design

layouts. The challenge is that the models for such applications are quite large, as they need to represent the

engine bay part of the vehicle or even the full vehicle. Moreover they should allow to cover a broad frequency range up to 4 or 5 kHz (for PBN) and results are typically required in narrowband.

This paper gives an outline of the extensive benchmarking activity carried out by the authors since a few

years on the assessment of the computational accuracy and performance of acoustic simulation approaches available in LMS Virtual.Lab and other acoustic methodologies. Subject of the analyses is the prediction

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of the powertrain exterior Acoustic Transfer Functions (ATFs) for a mockup model of an engine in the

engine bay. The accuracy of the ATFs obtained by the different methodologies is compared with

experimental results and the simulations’ computing performance, in terms of time and required hardware memory, is compared between each other.

2 Experimental activity

A car engine bay mockup was built using stiff plywood (figure 1 and figure 2), trying to keep the

dimensions and the shape of the mockup close to those of a real engine bay. The presence of the engine was taken into account by putting another stiff plywood structure inside the engine-bay mockup (figure 2).

A few apertures were made on the external walls of the engine bay mockup, in order to simulate those

normally present on the boundary of a real vehicle engine bay: one front aperture (radiator), one rear aperture (driving shaft), two apertures on the bottom surface (apertures normally present in the under-

engine shield for ventilation purposes) and two side apertures (wheel-house apertures for wheel axles). Six

flat microphones were applied approximately at the center of the six engine mockup walls (figure 3) and a

volume velocity calibrated monopole acoustic source was placed outside of the engine bay mockup at two fixed positions, frontal (1500 mm far from the mockup frontal face and 1700 mm high above the floor)

and lateral (1700 mm far from the mockup lateral face and 1700 mm high above the floor, figure 1).

Lastly, an acoustic treatment consisting in a 20 mm thick single layer felt, was applied inside the car engine bay mockup on 3 different walls: under the hood, under the engine and on the back wall, i.e. the

wall simulating the firewall panel (figure 2).

Figure 1: Car engine bay mockup and lateral source Figure 2: Microphones placement

Figure 3: Arrangement of microphones positions around the engine block mockup

2316 PROCEEDINGS OF ISMA2014 INCLUDING USD2014

The Acoustic Transfer Functions (ATFs) were measured for the two different positions of the acoustic

source and for different configurations of the acoustic treatment applied on each single internal wall

(present or not) and of the apertures (open or closed). In total, 54 different configurations were measured. Table 1 reports four of these configurations, which were selected to be replicated with numerical

simulations. In [1] and [2], extensive information and details can be found about the experimental

measurement campaign and the results obtained for the different engine bay mockup

configurations considered.

Configuration Apertures Treatments Source

01 all open None both frontal and lateral

03 wheelhouse open only None both frontal and lateral

07 all open All both frontal and lateral

11 wheelhouse open only All both frontal and lateral

Table 1: Some car engine bay mockup configurations simulated

3 CAE analyses

As far as analysis and simulation methods are concerned, here a list follows of all the simulation

technologies tested and compared in order to compute the vehicle engine bay mockup exterior ATFs in the

analysis frequency range up to 3.5 kHz:

• Indirect BEM

• Fast Multipole BEM (FMBEM)

• Patch Transfer Function (PTF) Method

• Wave Based Technique (WBT) Method

• Infinite FEM (IFEM)

• FEM Perfectly Matched Layer (PLM) & Automatically Matched Layer (AML)

• H-Matrix BEM

• FEM AML Adaptive Order (FEM AO)

The underlined methodologies refer to those mainly tested at IMAMOTER Institute which gave very

interesting results.

The first part of this section briefly describes analyses and some results obtained by the authors on the

assessment of the computational accuracy and performance of BEM and FEM methodologies available in

LMS Virtual.Lab. All the results reported in this section were already published and are recalled here just for sake of completeness. References [1] to [3] are only an example taking into consideration also other

simulation methods not directly tested by us (e.g. IFEM).

In the second part some particular attention has been dedicated to the latest innovative approaches developed in LMS Virtual.Lab R12 code, i.e. H-Matrix BEM and FEM AML Adaptive Order (FEM AO)

[4].

3.1 BEM and Fast Multipole BEM analyses

The analysis frequency range (200 Hz to 3500 Hz) was subdivided into 3 frequency sub-ranges: 200 Hz to 1250 Hz, 1250 Hz to 2500 Hz and 2500 Hz to 3500 Hz. For each frequency range, an independent BE

model was developed, using the λ/7 meshing rule. The resulting number of nodes was 4432 for the low-

MEDIUM AND HIGH FREQUENCY TECHNIQUES 2317

frequency model, 17162 for the medium-frequency model and 33529 for the high-frequency model [2].

Figure 4 shows, as an example, the BE model used for the low-frequency range (red areas represent the

acoustic treatments) and figure 5 details some model’s features, including a symmetry plane to mimic the reflecting floor, and the positions of the source and microphone receiver points.

Figure 4: Car engine bay mockup BE model Figure 5: Microphones, rigid plane, frontal source

Given that the model included a closed cavity (the engine-block mockup), the usual counter-measures to

avoid issues related to irregular frequencies were applied. The impedance of the acoustic treatments was

measured in a standard Kundt tube and used in the model as boundary condition in the regions covered by

the treatments themselves [2]. Figure 6 shows a detail of the materials used for the trim parts applied and the treatment absorption coefficient plot. A little absorption was introduced also for the surfaces made

with plywood. Being not possible to measure plywood absorption in a Kundt tube, some literature data

have been used: the absorption coefficient was set as linearly increasing from 0.5% at 200 Hz to 2% at 1250 Hz and then kept constant for higher frequencies.

Figure 6: Trim parts details (left) and Normal Incidence Absorption Coefficient

of the acoustical treatments (right)

Six field points were defined corresponding to the microphones positions (figure 3) in order to compute

the ATFs. Only 4 configurations were simulated (table 1), in order to limit the computation effort.

As far as the BEM analysis is concerned, the Fast Multipole method (FMBEM) implemented in LMS Virtual.Lab was used only above 1250 Hz (table 2). The recently developed FMBEM approach differs

from conventional BEM in two ways. The most remarkable difference is that it uses an approximate

formulation to express the interactions between nodes which lie far away from each other on the acoustic

model. The second difference is that the BEM problem is solved in an iterative way. In particular, FMBEM is based on a classical evaluation of the BEM operator in the near field, whereas a clustering of

boundary elements is formed in the far field. The solution is evaluated through a multipole expansion


which allows one to group sources that lie close together and treat them as if they are a single source as

illustrated in figure 7. The superiority of the method is that interaction between well separated sets of

nodes can be treated in one time. Thanks to this property, the FMBEM iterative solver does not require the corresponding matrix elements to be explicitly computed and stored. This leads to considerably less

memory and less CPU time requirements. The computational cost is thus reduced from O(n3) for a

standard BEM analysis to almost O(n*(log10(n))2) with FMBEM, where n is the number of unknown

variables.

Figure 7: Interaction between far nodes in standard BEM and FMBEM

Table 2 shows computation times per calculation frequency, ∆f being the frequency step and all analyses carried out on a 8 node Linux Xeon server. It can be observed how the acoustic treatments application

reduces computational time from about 91 hours to 74 hours. This illustrates the effect of introducing

damping into the model on the convergence speed of the iterative solver used by FMBEM.

3.2 FEM AML analysis

In the FEM AML model, the engine bay volume was meshed with volume elements. The meshed volume

was then extended also to the exterior space, up to a distance of about 5-10 cm from the external plywood

surfaces of the engine-bay mockup (figure 8, left). The external shape of the meshed volume is that of a

rectangular prism with rounded lateral edges (the solver converges faster for this kind of shapes). Acoustical treatments were introduced in a way similar to that described for the BE analyses, i.e. by

imposing the proper impedance on the surfaces covered by the treatments themselves (figure 8, right). On

the external faces of the meshed region, a Perfectly Matched Layer (i.e. a domain with high dissipation, in which the acoustic waves are attenuated) is automatically built at every frequency (from here the name

‘Automatically Matched Layer’) and it is this type of numerical trick that basically manages the

simulation of the open environment.

Figure 8: Engine bay mockup FEM AML model (left); FEM AML model interior skin with highlighted acoustic treatment areas (right)


It makes sure no outwards propagating waves are reflected on the outer boundary of the FEM model. This

to satisfy the Sommerfeld radiation condition and to obtain therefore accurate results within the FEM

domain. From these results, a subset of pressure and pressure gradient results is chosen on a surface to afterwards compute the pressure at any location in space using a Kirchhoff-Helmholtz integral with

appropriate Green’s functions on that surface.

The FEM AML analyses using the LMS Virtual.Lab code were carried out for the 4 configurations in table 1 using the model shown in figure 8 (about 720000 nodes and 4 million tetrahedron elements) in the

200 Hz to 3500 Hz frequency range with step 2 Hz. Computational times of 25 to 35 hours were necessary

for the whole analysis making use of the iterative solver and of the same 8 node Linux Xeon server, 32

GB RAM as for the BEM analyses. Thus, FEM AML simulations are much faster than BEM simulations. Furthermore, with the FEM AML method the whole frequency range could be covered with a single

model and with a fixed frequency step (2 Hz), something that was not feasible with the BE method (3

different models necessary and analysis step from 2 Hz to 10 Hz, table 2).

Table 2 shows the comparison between the computational resources needed to run the BE/FMBEM and

the FEM AML simulations, all carried out on a Linux server with 8 CPUs [1].

Table 2: BEM and FEM AML models computation performance comparison

3.3 Results

The analysis of the experimentally acquired test data allows evaluating the effect on the ATFs of the different apertures and of the acoustic treatments applied. As an example, figure 9 illustrates the

comparison between the experimental ATFs measured in configurations 1 and 7 (table 1) for microphone

6 and front source position. The strong effect of the acoustical treatment is quite apparent.

Figure 9: Experimental ATFs, Configs. 1 & 7, frontal source


Only a few results are here reported about the comparison between experimental ATFs and BEM/FEM

AML simulations, many others can be found in References [1] to [3].

Figure 10 and figure 11 show the measured and computed ATFs for configurations 1 and 3, frontal acoustic source position and microphone 4 (i.e. the microphone located on the right face of the engine,

figure 3). In general the correlation is quite good and both simulation models are able to properly represent

the ATFs acoustic field reduction when passing from configuration 1 to configuration 3, i.e. when closing some apertures around the engine bay mockup.

Figure 10: ATFs, Config. 1, FS, Mic. 04 Figure 11: ATFs, Config. 3, FS, Mic. 04

Figure 12 and figure 13 show similar ATFs results for configurations 1 and 7, frontal acoustic source position and microphone 5 (i.e. the microphone located on the frontal face of the engine). Both

simulations are able to represent the acoustic field reduction effect due to the acoustic treatments

application even in the case of a microphone positioned acoustically far away from the acoustic source.

Figure 12: ATFs, Config. 1, FS, Mic. 05 Figure 13: ATFs, Config. 7, FS, Mic. 05

The above comparisons have illustrated that both BE and FEM AML methods are able to capture

accurately the effect of both acoustic trim parts and apertures located in the vicinity of the engine bay.

Moreover some general conclusions and remarks can be drawn from the benchmarking activity carried

out:

• Analyses results indicate that both BE and FEM AML methods correlate quite well with testing,

up to 3.5 kHz. Both are able to reproduce not only the absolute values of the ATFs but also their

variation when a certain aperture is open/closed or a certain acoustical treatment is applied/removed;


• In general, both for BE simulations and for FEM AML simulations, the computation times for the

configurations without treatments (i.e. configurations 1 and 3) turned out to be substantially longer

than those for the configurations with treatments (i.e. configurations 7 and 11). It seems then that

the presence of acoustical treatments favors the solution’s convergence;

• BE analysis required developing three independent BE models for three different frequency sub-

ranges. The Fast Multipole accelerator available in LMS Virtual.Lab code was indicated to speed

up solution time for the two higher frequency ranges. FEM AML simulations required one single

model only over all the analyzed frequency range and with a constant frequency step;

• FEM AML simulations are in any case much faster than BE simulations, in spite of the fact that

the model is bigger and the number of calculation frequencies is almost double.

CAE innovative approaches

3.4 H-MATRIX BEM

The use of standard BEM techniques limits either the upper frequency or geometric size of the analysis as six elements per wavelength are required in order to achieve good result accuracy. This rapidly increases

the size of the system with respect to frequency [5]. The H-Matrix Boundary Elements Method (H-Matrix

BEM) computes acoustic radiation using a state-of-the-art Hierarchical Matrix BEM solver. It uses recursive matrix storage and compression, based on the low rank approximation.

Figure 14: The benefits of low rank approximation in H-Matrix BEM

Figure 14 illustrates the advantages of using a low rank approximation. It also explains why H-Matrix

BEM efficiently handles medium to large models, with as key benefits:

• Speed: faster computation as it uses matrix compression technology;

• Efficiency: reduces the memory requirements as it uses hierarchical matrix storage and

compression;

• Scalability: multi-load cases handled efficiently with direct solver approach.

In order to define the (column) rank of the approximations, an octree structure is made in which model is

divided in parts/zones by using boxes with the size depending on the acoustic wavelength for each

frequency. This allows to judge which nodes are lying close to each other (this part of the full system matrix allows for fewer reduction) and which sets of nodes can be seen as lying far away from each other

(the part of the full system matrix capturing the influences between these nodes can be more reduced).


The computational effort is reduced from O(n3) with conventional IBEM to O(n*(log2(n))

2) for H-Matrix

BEM where n is the number of unknown variables as can be seen from the graph below (figure 15). The

FMBEM is still a very competitive solver for very large problems [2].

Figure 15: Comparison between conventional BEM, H-Matrix BEM and FMBEM methods

However, H-Matrix BEM seems to be the optimal solver for the mid-sized acoustic models and frequency

range. In the framework of the current paper, this new H-Matrix BEM approach was not yet tested. This

can be part of future work on the engine mockup case.

3.5 FEM Adaptive Order (FEM AO)

A truly breakthrough FEM solver technology is the Adaptive Order (FEM AO) method [6] implemented in LMS Virtual.Lab R12 [5]. FEM AO sets the order of each element in a FEM model and at each

frequency to ensure accuracy. Higher order hierarchical shape functions are used to represent the pressure

inside each element. At order 10, an element can span more than two acoustic wavelengths. As the solver

increases element order, and therefore also the model’s total DOFs number, with frequency, the key benefits are:

• Important savings on time and memory in lower frequencies;

• Models can be built using coarser elements leading to smaller models which are easy and

fast to pre-processor in LMS Virtual.Lab;

• Discretization only needs refinement in order to capture accurately the geometry and

boundary conditions.

Essentially, higher orders are used at high frequencies and/or for large elements and low orders will be

employed at low frequencies and/or for small elements. A conformity rule is applied at the interface

between two FEM AO elements in order to guarantee a variable field continuity through the mesh.

The FEM AO method allows different possible ‘accuracy settings’ in order to control the speed of

incrementing elements order versus frequency. A more accurate result is obtained by a faster increment

even if the additional DOFs make the model slower in the solution phase. The ‘standard’ and ‘coarse’ settings have been considered in this analysis.

The FEM AO method has been applied to the FEM AML model above described (figure 8) and a first

comparative study was carried out for different FEM models created to simulate test configurations 1 and 7 (table 1) with a source in front of the engine bay mockup [4]. A first goal was to see if the computation

time could be further optimized by reducing the meshed fluid volume, the second objective was to find

how much improvement in performance can be obtained by applying the FEM AO method.


All computations referred to FEM AO were setup in LMS Virtual.Lab Acoustics R12 and carried out on a

Windows 7 Desktop, having 16 cores (2 Intel Xeon processors, 3.1 GHz with each 8 cores) and 256 GB

RAM in total.

3.5.1 Conventional FEM AML models comparison

Figure 16 shows the two meshed volumes used. A first volume is identical to the one used in the FEM

AML models tested for comparison with BEM models, the second one follows the mockup surface more closely in order to minimize the meshed volume and hence reduce the model size. Also note the positions

of the microphones in Figure 16, presented by highlighted yellow dots.

Figure 16: Same FEM AML model as in figure 8 and compared to BEM model (left) ;

FEM AML mesh with smaller optimized volume (right)

Table 3 presents the quantitative overview of the two FEM AML models (left) and computation

performance (right) to be referred to the analyses carried out. We learn from table 3 that optimizing the

FEM AML meshed volume yields 20 GB RAM reduction in memory and shaves off about 20% of the

required computation time. Moreover, no significant loss of accuracy can be noted in the analysis results for the smaller optimized model. As can be seen indeed from figure 17 the deviations from the reference

model results remain within limits (max 3 dB on the peaks) for the full frequency range.

Table 3: Model sizes of the two conventional FEM AML models (left) and computation performance (right)

FEM AML Reference

FEM AML Optimized Volume

Solver Direct Solver Direct Solver

# processes 4 4

# threads/process 4 4

# load cases 1 1

# freqs 1651 (2 Hz � 3500 Hz)

1651 (2 Hz � 3500 Hz)

Peak Memory (Mb all procs)

56800 34600

Time (h) 24.09 18.89

FEM AML (1st order)

16 mm ref. model FEM AML (1

st order)

16 mm smaller volume

# nodes (excl AML) 721589 543920

# elements 4002490 3045251

# field points 6 6

# nr DOFs total 934079 684315


Figure 17: ATFs comparison between reference and smaller optimized FEM AML models

3.5.2 Conventional FEM AML and FEM AO models comparison

Table 4, left lists the sizes of the three FEM AML AO models which were compared in search of a right

balance between reduced computation time and maintained accuracy. For all FEM AO models, the same volume was meshed, albeit each time with a different discretisation. Table 4 mentions the edge sizes

chosen as boundary conditions for a tetrahedron filler meshing algorithm. ‘FEM AO, 35 mm inner, 48 mm

outer’ for instance means that the surfaces representing the mockup, including engine and engine bay

surfaces, have an edge size of 35 mm and the AML and ground surface use a 48 mm edge size.

Table 4: Three FEM AO models characteristics (left) and computation performance (right)

First order elements were used for the meshing and as can be seen from table 4, left the FEM AO models are small in number of nodes used for discretization. Note however that this does not provide information

on the actual number of DOFs used at each frequency. Indeed, FEM Adaptive Order will adjust per

frequency the order of each element to guarantee a given accuracy. This will define the total number of DOFs used for each frequency. Table 4, left lists the maximum model size in its last row when using a

‘standard’ setting for FEM AO accuracy. All models show a maximum number of DOFs higher than that

of the conventional FEM AML model (about 685k DOFs). Note however that this maximum is only reached at the highest frequency. At lower frequencies the FEM AO model will have a lot less DOFs

compared to the conventional FEM AML model. This way we expect most gains in performance.

Table 4, right provides the computational performance for the engine bay mockup configuration 1 (table 1). The time required to cover the full frequency range with FEM AO is about half of the time needed with

conventional FEM AML. The peak memory required to run in-core is significantly higher, but note that

FEM AO 16 mm inner, 48 mm outer

FEM AO 35 mm inner, 48 mm outer

FEM AO 20 mm eng, 40 mm bay, 70 mm outer

# nodes (no AML) 142182 32259 22943

# elements 702753 152516 104098

# field points 6 6 6

# nr DOFs total Max 1581712 Max 940051 Max 743155

Solver FEM AML FEM AO (32k) Standard

FEM AO (32k) Coarse

# procs 4 4 4

# threads/procs 4 4 4

# load cases 1 1 1

# freqs 1651 (2 Hz � 3500 Hz)

1651 (2 Hz � 3500 Hz)

1651 (2 Hz � 3500 Hz)


34600 66000 29200

Time (h) 18.89 9.47 2.39


this memory requirement is dependent on the number of DOFs and therefore frequency dependent for

FEM AO. In other words, this memory is only required at the highest frequencies.

As far as method accuracy is concerned, test and simulations results are again overlaid in figure 18, showing the results for microphone 3 in configuration 1. The FEM AO model reported is the one

containing 32259 nodes for its mesh (table 3, left & right). This model turned out to bring the right

balance between computational performance gains and accuracy. The match between FEM AO and FEM AML results is prominent. Only in few frequency bands there is a small 2 to 3 dB difference. Also the

match with test results is clearly present for both approaches.

Figure 18: ATFs comparison, FEM AML and FEM AO ‘standard’ models with measurements,

microphone 3 in configuration 1 (left); FEM AO ‘standard’ model considered (right)

Analogous results have been obtained referring to the engine bay mockup configuration 7, being the case

with all the acoustic treatments applied (table 1). Figure 19 presents the results for the same microphone

and source but for this configuration. The results allow drawing similar conclusions as for configuration 1.

Here the model with the mesh containing 32259 nodes was again used.

Figure 19: ATFs comparison, FEM AML and FEM AO ‘standard’ models with measurements,

microphone 3 in configuration 7

For the same mesh, again in order to reduce computation time, another ‘coarser’ setting was used as far as

FEM AO model accuracy is concerned. As the accuracy now needs to be relatively less, the order of each

element will be increased at higher frequencies only compared to the ‘standard’ accuracy setting, meaning

that the FEM AO model will have even less DOFs at all frequencies and will be even faster. The results can be seen in figure 20. Up to 1.25 kHz a very good match is kept with the FEM AO ‘standard’


(accuracy) results, but afterwards deviations were judged to be too large to justify the use of the ‘coarse’

setting for this specific engine mockup scenario.

Figure 20: ATFs comparison, FEM AO ‘coarse’ and FEM AO ‘standard’ models with measurements,

microphone 3 in configuration 7

Table 5 reports the computation performance between FEM AML model and the two FEM AO models for

configuration 7 to be compared with table 4, right and configuration 1. As can be seen, the memory

requirements were of course the same. The gains in computational performance are also clearly there, yet

a bit less prominent compared to configuration 1. Why this seems to be the case can represent a subject of further investigation. The ‘coarse’ accuracy setting even divides the computation time needed with a

factor 4, but as discussed above, this FEM AO model yielded accurate enough results up to 1.25 kHz only.

Solver FEM AML FEM AML AO (32k) Standard

FEM AML AO (32k) Coarse

# processes 4 4 4

# threads/process 4 4 4

# load cases 1 1 1

# freqs 1651 (2 Hz � 3500 Hz)

1651 (2 Hz � 3500 Hz)

1651 (2 Hz � 3500 Hz)


34600 66000 29200

Time (h) 18.95 13.75 3.02

Table 5: Computation performance for FEM AML optimized volume model vs two FEM AO models

with different accuracy, configuration 7

The conclusion clearly still holds, that FEM AO approach reduces simulation time significantly.

3.5.3 Some considerations about FEM direct and iterative solvers

The iterative and direct solver results are overlaid for microphone 3 in configuration 1 in figure 21 for

using a conventional (no adaptive order) FEM approach. At most frequencies a very good match is obtained. It should be noted that the iterative solution did not converge for quite some frequencies. This of

course depends on the convergence criterion used and, as the results between direct and iterative

approaches are very close, we can state that at almost all frequencies the results were close to being


converged. But this call can only be made by having the comparison with the direct results available or by

monitoring the stabilisation of results for different values of the residue error used in the convergence

criterion.

Figure 21: ATFs comparison between Iterative and Direct solvers, same reference FEM AML model,

front source and microphone 3

On this purpose, one further point that it is worth mentioning here and that, for brevity reasons, could not be detailed in the paper is the importance of the choice of the proper solver, in particular for the FEM

AML simulations. There are several boundary conditions to be considered which will influence the choice

for the right solver:

• One important constraint can come from the hardware available for running the solver. LMS

Virual.Lab SYSNOISE solvers support solving on multiple cores in parallel. In case a run for a

single frequency requires only a limited amount of memory, this means the total simulation time

can be decreased by in parallel solving other frequencies, as many as the number of cores available. With this respect it should be noted that a direct solver requires typically much more

memory compared to an iterative solver, as the direct solvers will factorize the sparsely populated

acoustic system matrix to compute its inverse which is much more populated. This constraint can

favor using an iterative approach when the hardware available has relatively limited in-core memory;

• On the other hand, the number of load cases should be considered as well. In the abovementioned

examples, only one source at a time was used. However, for some applications, like Pass-By Noise for instance, the ATFs need to be computed typically for a number of source or microphone

positions, resulting in a multi load case problem. Whereas an iterative solver will have to restart

for every new load case, a direct solver needs to compute the acoustic system matrix inverse only

once. Therefore an increase in number of loadcases will deteriorate the performance of an iterative solver much more than that of a direct solver.

For now, FEM AO is only available in combination with a direct solver. From above explained reasons it

may be clear an interesting extension for the FEM AO approach would be to enable using an iterative solver. This is currently being investigated.


4 Conclusions

Topic of the present paper consisted, on the one hand on giving an overview of the benchmarking activity carried out between commercially available and validated deterministic simulation methods, namely BEM

and FEM and their implementation, on the other hand on informing the reader about the latest

improvements available in LMS Virtual.Lab R12 code, i.e. H-Matrix BEM and FEM AML Adaptive

Order (FEM AO). All these methods were compared in terms of results accuracy and computation performance and used to simulate the exterior ATFs measured on an engine bay mockup. Such mockup,

while being simple in its external shape, presents all features that generally challenge deterministic

simulation methods and that can be summarized in the coupling between a rather complicated bounded acoustical environment (with small air-gaps and discontinuous acoustical treatments) and an external

unbounded acoustical environment through localized apertures. On top of this, a further complication is

given by the width of the frequency range to be addressed (up to 3.5 kHz).

Results indicate that both the FEM AML method and the BE method correlate quite well with test results,

up to 3.5 kHz. Both are able to reproduce not only the absolute values of the ATFs, but also their variation

when a certain aperture is open/closed or a certain acoustical treatment is applied/removed. Moreover, the methods computational efficiency has been evaluated and compared in detail, mainly for

what concerns result quality, experimental data correlation and run time in order to single out the best

analysis and simulation tool.

Overall, one can conclude that for the simulation of external ATFs the FEM AML method looks more

attractive than the BE method: similar accuracy and much better computational efficiency. In particular,

the very last approach FEM Adaptive Order (FEM AO) developed in LMS Virtual.Lab R12 code shows

very promising results and proves itself to be the best balance between computational performance gains and accuracy. Further investigations can concern testing the promising H-Matrix BEM on the engine

mockup model, as well as an iterative solver with the FEM AO method, whenever it will become

available.

As a final important conclusion we can say that we can rely on the computational methods as being

valuable and efficient tools in the automotive industry in order to face the more challenging targets for

PBN tests and/or optimize power-train exterior acoustic field reduction.

References

[1] A. Bihhadi, C. Bertolini, G. Miccoli, Simulation of exterior powertrain Acoustic Transfer Functions

using IFEM and other deterministic simulation methods, ATZ Automotive Acoustics Conference, Zurigo (2013).

[2] G. Miccoli, G. Parise, C. Bertolini, F. Tinti, Vehicle Exterior Noise Field Analysis Methods &

Simulation Models, ICSV18, Rio de Janeiro (2011).

[3] G. Miccoli, C. Bertolini, A. Bihhadi, Comparative analysis of different deterministic methods for the

simulation of exterior noise acoustic transfer functions, AIA-DAGA Conference, Merano (2013).

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Documents

A validation of some recent BEM and FEM techniques for ...past.isma-isaac.be/downloads/isma2014/papers/isma2014_0543.pdf · available in LMS Virtual.Lab and other acoustic met hodologies