fast multipole boundary element method

Dr. Koen De LangheIr. Peter Segaert Dr. Fuliang Zhan (LMS China 詹福良博士)

Multipole BEMBreaking the High Frequency Barrier

2 copyright LMS International - 2008

Problem statement: Performance Simulation of Engines

Objective Performance simulation stretches over different attributes : Engine performance, Vibration, Noise radiation (acoustics), Durability, …Model is be adapted to provide solutions in different attribute domains.For noise radiation: a FULL FE model of the engine is needed: HUGE FE modelsFrequency target: 3000Hz and higher

Particular issues

Physically large systems resulting in vast structural and acoustic models in the frequency range of interest → efficiency is key

Example model size

Engine: 5 X 2 X 2 meterFrequency target: 3000 HzAround 50 elements / meter

→ 2500 elements / m^2Overall resulting in 125 000 elements


Problem Statement

Vehicle loading

Sound Package Design

BODY

Lower fuel consumptionLower TRIM Cost


Problem StatementVehicle Exterior Acoustics

Objective Vehicle exterior acoustics: simulate the pressure distribution on the exterior of the car up to 5000 Hz and more in view of more accurate sound package optimizationOr in view of simulating pass-by-noise

Particular issues

Complex system:→ Including engine bay, exhaust, wheel house,..

Up to high frequency, resulting in HUGEBEM models

Example model size

Typical dimensions: 5 X 2 X 1.5 m meterFrequency target: 5 000 HzAround 100 elements / meter

→ 10 000 elements / m^2Overall resulting in 410 000 BEM elements


Problem StatementUltrasonic sensors

Objective Detect obstacleDetect intrusion, glass breaking

Particular issues

Very high frequency operating conditions: typically 40 to 50khzPerformance of sensor is dependant up system integration: need to model the full system as wellFull system: bumper, grill, interior

Example model size

Grill: 0. 5 X 0.25 meterFrequency target: 50 kHzAround 1000 elements / meter

→ 1 000 000 elements / m^2Overall resulting in 125 000 elements


Breakthrough technology is needed

Classsical BEMSize of the model System requirements

2000 (mid size)O(minutes) / frequencyRuns on a regular PC; full frequency

10 000 (large size)

O(hour) / frequencyFor full frequency, preferably to run on high end PCs or workstations

50 000 (Huge size)

O(day) / frequencyTypically only few frequencies, runs in parallel on supercomputers

Classical BEM:

For every doubling of frequency:

Times 64

wrt calculation times

Need for new techniques to solver ultra-large scale models


Performance Gains with NEW Multipole BEM solver

DOFs Frequency Doubling Frequency

Conventional BEM 64 more time

needed

NEW Fast Multipole BEM

From 4 to 6 more time

needed

( )6fO( )3nO

( )( )nnO 2log⋅ ( )( )222 log ffO ⋅


Classical BEM versus Multipole BEM

1k 10k

0.1

100

100 000

10 000 000Computation times

Model Size100k 1000k

Conventional BEM

Multipole BEM

>100 times faster


Example speed up conventional BEM versus FMBEM

0,00001

0,0001

0,001

0,01

0,1

1

10

100

1000

50 400

750

1100

1450

1800

2150

2500

2850

3200

3550

3900

4250

4600

4950

For complex models and higher frequencies, the new powerful multipole

BEM solver is faster then FEM acoustics


Radiation process

Vibration Response

Vector Processing

StructuralModes

StructuralLoads

MotionFlexible Body

SimulationPDS

BEM Mesh

Structural Mesh

Field PointMesh ATVs

Acoustic Boundary

Conditions

Pressure Response

structural

acoustical

time

frequency

2 options:-Create “optimal mesh”with mesh coarsening (2 hours)Or-Just create “envelop”. 5 minutes Significant gain

with FMBEM


Benefits of Multipole BEM

1.Faster and less memory requirements for medium to large size problems

O ( N * Log^2 ( N ) )

Versus

O ( N ^ 3 )

2.Opens a range of new applications:

From 50 000 ElementsTo

>> 1 000 000elements

3. Efficiency for meshing: relaxes the meshing constraint


New Range of Applications

1. High frequency self induced pressure loading:

Simulating the pressure loading on vehicles engine, exhaust, tire sources

3. Pass-by-noise:Simulating the noise level at given distance

2. Vehicle Loading for Transparency problems:

Simulating the pressure loading on vehicles when other vehicle passes-by


New Range of Applications

1. Complete system simulation:Modeling of engine bay, covers…

2. Higher frequency noise radiation:Injector ticking..Today: practical up to 2500HzWith Fast Multipole BEM: practical up to 10 000 Hz


Fast Multipole BEM Technology Components

Multilevel Substructuring

“Instead of transporting letters directly from the sender to the receiver, they are dropped in a mailbox. From there they pass through a level hierarchy—post office, distribution center, post office, postman—to finally arrive at their destination in a much more efficient way”

64-bitMulti OS supportParallellized (MPI)

Iterative Solver TechnologyGMRESSPAI preconditionerSVD (to reduce number of RHS)

The Kernel DecompositionClassical evaluation of BEM operator in near fieldClustering of boundary elements and evaluation by multipole expansion in far field.


Technology components: The Kernel Decomposition

Interaction between “well-separated” set of points can be treated in one timeLess CPU timeLess memory requirements

Single level FMBEM:The object is cut into piecesMultipole Expansion is used to treat interaction between distant boxes

M1 M2

M1 M2

BEM

FMBEM


Technology components: Multilevel Substructuring

Level 1

Level 2

Level 3

Level 4


Number of DOFs

CP

U T

ime

(s)

Technology components: CPU Time Trend

Break even point.The break even point depends on complexity of model:Below this point, Classical BEM is preferred•More accurate•No convergence problems•More performant


Technology components: RAM Trend

0

1000

2000

3000

4000

5000

6000

7000

0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 55000


Application example of Multi-pole BEM for high frequency vehicle loading


Example 1: Vehicle exterior acoustics

Vehicle loading

Sound Package Design

BODY

Lower fuel consumptionLower TRIM Cost


Simulation Process

Step 1:Creation of Vehicle Mesh valid up to > 5 000 HzVirtual.Lab Mesh CoarseningAcoustic mesh of about 366k NodesTiming: ~ 3hrs

Step 2:Acoustic pre (source definition, response points etc.)30 minutes

Step 3:Run the analysis (parallel machine)“1 day”

Step 4:Post-process results1 hour


ResultsPredicted versus Measured

Test results obtained by GM


Computational Requirements

Hardware configuration:64 node LINUX cluster

• 2 processors: Intel Xeon 5160 dual core at 3 GHz

• 16GB RAM / node• 100GB hard disc / node

Considered for this study:4 node configuration (4 x 4 = 16 CPUs)8 node configuration (4 x 8 = 32 CPUs)16 node configuration 94 x 16 = 64 CPUs)


Example: Vehicle Acoustic Load

250 000 unknowns FMBEM BEM

RAM requirements (Gb) 0.5 200CPU time (hours) 10 8000


Example 2: exterior acoustics of skidsteer

Hydraulic noise

Powertrain and gear

noise

Cooling noise

Intake noise Exhaust

noise

Enclosure modeling

Cab noise treatment


Problem statement and solution

Problem Statement:Simulate the exterior noise and driver ear noise from exhaust noise source.Accurate prediction of diffraction around the structureUp to 2000Hz: resulting in detailed exterior acoustics model

Solution: VL AcousticsAcoustic meshing: envelope of the structural mesh. Created in Virtual.LabMultipole BEM for exterior acoustics


Comparison Classical BEM versus Multipole BEM

Coarse model:8.6 kNodes9 kElementsUp to 500Hz

Fine model:86 kNodes; 171kTRIA elementsMesh creation: 5 minutes (envelope of the

structural mesh)Up to 2000hz


Example 4: Powertrain radiationProblem statement

Pain of the Powertrain NVH manager:Accurately and efficiently predict the radiation noise of an engine in operating conditions, identify critical areas, and provide a fundamental solution

Pain of the Engineer:Pressure on timeVast amount of data:

• Huge FEM structural models: up to 3M Nodes• Large number of load conditions• Every higher frequencies, ever larger models

Finding a solution to the problem

Solution: LMS Virtual.Lab Numerical Engine AcousticsAnd multipole BEM acousitic

#1 solution



Fine model:60 kNodes120 kTRIA elementsUp to 10000Hz

Coarse model:4.5 kNodes9 k TRIA elementsUp to 1500Hz


Example 5: Horn designProblem statement

Objectives:Frequency responseSensitivity versus efficiencyDirectivityDistortionFrequency range

ConstraintsMaximum sizeManufacturingPleasing design

With Classical BEM: computational resources allow the calculation of small horns up to about 10kHz with high accuracy.

For large horns: too huge models in full audible frequency range

Solution: LMS Virtual.Lab Multipole BEM




Coarse model:4.2 kNodes8.2 k TRIA elementsUp to 2000Hz


Example 7: Acoustic scattering Problem statement

Objective Optimize the passive acoustic signature of the systemMake the ship or submarine more ‘stealth like’Analyze the scattered field:

-Minimize the reflected fieldDesign proper countermeasures:

-Fitting of anechoic tiles to the hull-Shape

From low to mid frequency sonar wave excitation


Acoustic Signature: Scattering

Solution Virtual.Lab Fast Multipole BEM

Benefits Analyze the scattered field from different angles efficientlyThrough the previous, creates insightsEfficiently run and analyze different designs and different loading conditions

BEM analysis

BEM Mesh

Incident wave



Coarse model:5 kNodes10 k TRIA elementsUp to 400Hz



Thank you

fast multipole boundary element method

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