Parallel computation techniques for virtual acoustics and physical

191 Pages·2014·7.54 MB·English

by  Craig J. Webb

Parallel computation techniques for virtual
acoustics and physical modelling synthesis
Craig J. Webb
U N I VER
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Doctor of Philosophy
Acoustics and Audio Group
University of Edinburgh
2014
Abstract
The numerical simulation of large-scale virtual acoustics and physical modelling
synthesis is a computationally expensive process. Time stepping methods, such as
finite difference time domain, can be used to simulate wave behaviour in models of
three-dimensional room acoustics and virtual instruments. In the absence of any form
of simplifying assumptions, and at high audio sample rates, this can lead to simula-
tions that require many hours of computation on a standard Central Processing Unit
(CPU). In recent years the video game industry has driven the development of Graph-
icsProcessingUnits(GPUs)thatarenowcapableofmulti-teraflopperformanceusing
highly parallel architectures. Whilst these devices are primarily designed for graphics
calculations,theycanalsobeusedforgeneralpurposecomputing. Thisthesisexplores
theuseofsuchhardwaretoacceleratesimulationsofthree-dimensionalacousticwave
propagation, and embedded systems that create physical models for the synthesis of
sound.
Test case simulations of virtual acoustics are used to compare the performance of
workstationCPUstothatofNvidia’sTeslaGPUhardware. Usingrepresentativemulti-
core CPU benchmarks, such simulations can be accelerated in the order of 5X for
single precision and 3X for double precision floating-point arithmetic. Optimisation
strategies are examined for maximising GPU performance when using single devices,
aswellasformultipledevicecodesthatcancomputesimulationsusingbillionsofgrid
points. This allows the simulation of room models of several thousand cubic metres
at audio rates such as 44.1kHz, all within a useable time scale. The performance of
alternative finite difference schemes is explored, as well as strategies for the efficient
implementationofboundaryconditions.
Creating physical models of acoustic instruments requires embedded systems that
often rely on sparse linear algebra operations. The performance efficiency of various
sparse matrix storage formats is detailed in terms of the fundamental operations that
are required to compute complex models, with an optimised storage system achieving
substantial performance gains over more generalised formats. An integrated instru-
mentmodelofthetimpanidrumisusedtodemonstratetheperformancegainsthatare
possibleusingtheoptimisationstrategiesdevelopedthroughthisthesis.
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Declaration
I declare that this thesis was composed by myself, that the work contained herein is
myownexceptwhereexplicitlystatedotherwiseinthetext,andthatthisworkhasnot
beensubmittedforanyotherdegreeorprofessionalqualificationexceptasspecified.
(CraigJ.Webb)
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Publications
Elements of this thesis have been published in the following papers. The contribution
ofthecurrentauthorisdetailedineachcase.
1. C. Webb and S. Bilbao, “Computing Room Acoustics with CUDA - 3D FDTD
schemes with boundary losses and viscosity”, In Proceedings of the IEEE Interna-
tional Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague,
Czech,2011,pp. 317-320.
Theauthorproducedtheentirepaper,withtheexceptionofSection2whichdetails
thenumericaldesignofthefinitedifferencescheme.
2. C.WebbandS.Bilbao,“VirtualRoomAcoustics: AComparisonoftechniquesfor
computing3D-FDTDschemesusingCUDA”,InProceedingsofthe130thConven-
tionoftheAudioEngineeringSociety,vol. 2,London,UK,2011,pp. 1163-1169.
Theauthorproducedtheentirepaper,withtheexceptionofthenumericaldesignof
thefinitedifferenceschemeasdetailedinthepreviouspaper.
3. C. Webb and S. Bilbao, “Binaural Simulations using audio rate FDTD schemes
andCUDA”,InProceedingsofthe15thInternationalConferenceonDigitalAudio
Effects,York,UK,2012,pp. 97-100.
The author is responsible for the entire paper, with the exception of the numerical
designoftheEnquistMajdaboundarycondition.
4. S.BilbaoandC.Webb,“TimpaniDrumSynthesisin3DonGPGPUs”,InProceed-
ingsofthe15thInternationalConferenceonDigitalAudioEffects,York,UK,2012,
pp. 269-276.
InthispaperthenumericaldesignandinitialprototypemodellingisbyBilbao. The
authorisresponsiblefortheGPUimplementationandoptimisationtechniques,and
theresultingperformancedata.
5. J. Sheaffer, C. Webb and B. Fazenda, “Modeling Binaural Receivers in Finite Dif-
ferenceSimulationofRoomAcoustics”,InProceedingsofMeetingsonAcoustics:
InternationalCongressonAcoustics,vol. 19,Montreal,Canada,2013,p. 15098.
The theoretical and analysis sections of this paper are by Sheaffer. The author
contributed the large-scale GPU testing data on which the results are based, having
implementedthecomputationalmodels.
6. C. Webb and A. Gray, “Large-scale virtual acoustics simulation at audio rates us-
ing three-dimensional finite difference time domain and multiple GPUs”, In Pro-
ceedings of Meetings on Acoustics: International Congress on Acoustics, vol .19,
Montreal,Canada,2013,p. 70092.
Theauthorproducedtheentirepaper,withmanuscripteditingbyGray.
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7. S. Bilbao, B. Hamilton, A. Torin, C. Webb, P. Graham, A. Gray, K. Kavoussanakis
and J. Perry, “Large scale physical modeling sound synthesis”, In Proceedings of
the Stockholm Music Acoustics Conference, Stockholm, Sweden, 2013, pp. 593-
600.
Forthisreviewpaper,theauthorcontributedSection5onGPUimplementation,and
elementsofSection6.4showingbenchmarkCPUandGPUperformanceanalysis.
8. C. Webb, “Computing virtual acoustics using the 3D finite difference time domain
method and Kepler architecture GPUs” , In Proceedings of the Stockholm Music
AcousticsConference,Stockholm,Sweden,2013,pp. 648-653.
Theauthorisresponsiblefortheentirepaper.
9. B.HamiltonandC.Webb,“RoomacousticsmodellingusingGPUacceleratedfinite
differenceandfinitevolumemethodsonaface-centeredcubicgrid”,InProceedings
of the 16th International Conference on Digital Audio Effects, Maynooth, Ireland,
2013,pp. 336-343.
For this paper, the author produced GPU implementations of the various finite
schemesthataretested,andtheperformancedatausedinSection8.
10. S. Bilbao and C. Webb, “Physical modeling of timpani drums in 3D on GPGPUs”,
JournaloftheAudioEngineeringSociety,vol. 61,no. 10,pp. 737-748,2013.
InthispaperthenumericaldesignandinitialprototypemodellingisbyBilbao. The
authoris responsiblefor theGPUimplementation andoptimisationtechniques, the
resultingperformancedata,andtheabstractedmulti-instrumentmodel.
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Acknowledgements
ThisresearchhasbeensupportedbyUniversityofEdinburghscholarshipsawardedby
the College of Humanities and Social Science and the Edinburgh College of Art, and
bytheEuropeanResearchCouncilunderGrantStG-2011-279068-NESS.
The NESS project (Next generation sound synthesis) began in the second year of
myPhDstudies,andIamveryfortunatetohavebeenapartofitfromtheoutset. When
I began my PhD as the only student working with Stefan I had no idea that I would
verysoonbepartofalarge,dedicated,researchgroup.
IwouldliketothankthemanycolleaguesthatIhavemetalongtheway,bothfrom
the MSc course and the NESS project group, that really made my time at Edinburgh
theexperiencethatitwas. InparticularIhavetothankBrianHamilton,AlbertoTorin,
and Dr. Michele Ducceschi for their collaboration on various papers and elements of
mywork.
IwouldalsoliketothankmyfamilyandElenifortheircontinuedsupportthrough-
out my four and half years of MSc and then PhD study. Finally I wish to thank my
excellentsupervisorsDr. StefanBilbaoandDr. AlanGray,withoutwhomnoneofthis
wouldhavebeenpossible.
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Table of Contents
I Introduction and background theory 1
1 Introduction 2
1.1 Introductoryremarks . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Thesisobjectivesandoutline . . . . . . . . . . . . . . . . . . . . . . 3
2 Backgroundtheoryandliterature 6
2.1 Virtualacousticsimulations . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Principlesofacousticsandthewaveequation . . . . . . . . . 7
2.1.2 Geometricmethods . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 Wave-basedmethods . . . . . . . . . . . . . . . . . . . . . . 11
2.1.4 3Dfinitedifferencetimedomainmethod . . . . . . . . . . . 14
2.1.5 Hybridandalternativemethods . . . . . . . . . . . . . . . . 19
2.2 Physicalmodellingsynthesis . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Modalsynthesis . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Digitalwaveguides . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 Finitedifferencetimedomainmethod . . . . . . . . . . . . . 23
2.3 Parallelcomputingusinggraphicsprocessingunits . . . . . . . . . . 24
2.3.1 Parallelcomputing . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 EvolutionofGPUcomputing . . . . . . . . . . . . . . . . . 27
2.3.3 GPUarchitectures . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.4 CUDAdevicememory . . . . . . . . . . . . . . . . . . . . . 29
2.3.5 CUDAthreadmodel . . . . . . . . . . . . . . . . . . . . . . 30
2.3.6 Performanceoptimisation . . . . . . . . . . . . . . . . . . . 31
2.3.7 GPUsand3DFDTDsimulations . . . . . . . . . . . . . . . 32
2.3.8 GPUsforaudioprocessing . . . . . . . . . . . . . . . . . . . 33
2.4 Sparselinearalgebra . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
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2.4.2 Sparsematrices . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.3 Solutiontosystemsoflinearequations . . . . . . . . . . . . 39
2.4.4 SparselinearalgebraandGPUs . . . . . . . . . . . . . . . . 43
2.5 Timingmethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
II Accelerating virtual acoustics 46
3 Computingsolutionstothe3Dwaveequation 47
3.1 Thebasic3Dscheme . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Testsimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Lineardecompositionofthree-dimensionaldata . . . . . . . . . . . . 49
3.4 CPUbenchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.1 Singlethreadcode . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.2 Multi-threadedcode . . . . . . . . . . . . . . . . . . . . . . 51
3.4.3 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 52
3.5 GPUkerneldesignandoptimisation . . . . . . . . . . . . . . . . . . 55
3.5.1 OverviewoftheCUDAprogramdesign . . . . . . . . . . . . 55
3.5.2 Mappingthreadstothedataset . . . . . . . . . . . . . . . . 56
3.5.3 Useofsharedmemory . . . . . . . . . . . . . . . . . . . . . 57
3.5.4 Cacheoptimisation . . . . . . . . . . . . . . . . . . . . . . . 59
3.5.5 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 60
3.6 TheuseofmultipleGPUswithCUDA . . . . . . . . . . . . . . . . . 63
3.6.1 DatapartitioningovermultipleGPUs . . . . . . . . . . . . . 64
3.6.2 Non-asynchronousimplementation . . . . . . . . . . . . . . 65
3.6.3 Asynchronousimplementation . . . . . . . . . . . . . . . . . 65
3.6.4 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 66
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4 Performanceofalternativeschemes 70
4.1 Benchmarksimulation . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Staggeredgridformation . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.1 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.2.2 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 74
4.3 Interpolatedwidebandandface-centredcubic . . . . . . . . . . . . . 75
4.3.1 Descriptionofschemes . . . . . . . . . . . . . . . . . . . . . 75
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4.3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3.3 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 78
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5 Virtualacousticsimulations 83
5.1 State-freeboundaryconditions . . . . . . . . . . . . . . . . . . . . . 83
5.1.1 Frequency-independentlossyboundary . . . . . . . . . . . . 84
5.1.2 Implementationmethods . . . . . . . . . . . . . . . . . . . . 85
5.1.3 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 86
5.2 Boundariesrequiringstatememory . . . . . . . . . . . . . . . . . . . 87
5.2.1 EngquistMajdaboundarycondition . . . . . . . . . . . . . . 87
5.2.2 Implementationmethods . . . . . . . . . . . . . . . . . . . . 87
5.2.3 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 90
5.3 Attenuationofsoundinair . . . . . . . . . . . . . . . . . . . . . . . 91
5.3.1 Descriptionofschemewithviscosity . . . . . . . . . . . . . 91
5.3.2 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 92
5.4 Large-scalemodels . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.4.1 MaximumGPUmemoryusage . . . . . . . . . . . . . . . . 93
5.4.2 Singleprecisionissues . . . . . . . . . . . . . . . . . . . . . 94
5.4.3 Dispersioninthestandardscheme . . . . . . . . . . . . . . . 96
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
III Integrated physical models of instruments 99
6 Basiclinearalgebraoperations 100
6.1 Sparsematrixstorageformats . . . . . . . . . . . . . . . . . . . . . 101
6.1.1 CSRandCSCformats . . . . . . . . . . . . . . . . . . . . . 101
6.1.2 DIAgonalformat . . . . . . . . . . . . . . . . . . . . . . . . 102
6.1.3 ELLPACKformat . . . . . . . . . . . . . . . . . . . . . . . 103
6.2 Vectoraddition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.2.1 CPUperformanceevaluation . . . . . . . . . . . . . . . . . . 104
6.2.2 GPUperformanceevaluation . . . . . . . . . . . . . . . . . . 105
6.3 Thedotproduct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.3.1 Parallelalgorithmdesign . . . . . . . . . . . . . . . . . . . . 106
6.3.2 Performanceevaluation . . . . . . . . . . . . . . . . . . . . . 106
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6.4 Matrixbyvectormultiplication . . . . . . . . . . . . . . . . . . . . . 107
6.4.1 Performancecomparisonofmatrixstorageformats . . . . . . 107
6.4.2 Singleandmulti-threadedCPUperformanceofDIAformat . 110
6.4.3 GPUperformancecomparisonofDIAformat . . . . . . . . . 111
6.5 Matrixvsnon-matrixforms . . . . . . . . . . . . . . . . . . . . . . . 112
6.5.1 Categoriesofschemes . . . . . . . . . . . . . . . . . . . . . 112
6.5.2 2Dwaveequationsystem . . . . . . . . . . . . . . . . . . . 113
6.5.3 CPUperformanceevalutaion . . . . . . . . . . . . . . . . . . 113
6.5.4 GPUperformanceevalutaion . . . . . . . . . . . . . . . . . . 114
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7 Anintegratedmodelofthetimpanidrum 116
7.1 Overviewofthemodel . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2 Computationalelements . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2.1 Simulationsetup . . . . . . . . . . . . . . . . . . . . . . . . 120
7.2.2 Timeiterationmatrices . . . . . . . . . . . . . . . . . . . . . 122
7.2.3 Timeiterationoperations . . . . . . . . . . . . . . . . . . . . 125
7.3 Implementationdesigns . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.3.1 Parallelimplementationofthetimeiterationstages . . . . . . 129
7.3.2 CSCformatusingCSparse . . . . . . . . . . . . . . . . . . . 131
7.3.3 CSRformatandCUSPARSE . . . . . . . . . . . . . . . . . . 132
7.3.4 DIAandELLPACKformat . . . . . . . . . . . . . . . . . . 132
7.3.5 Unrolledmatrix-freeoperations . . . . . . . . . . . . . . . . 133
7.4 Performanceanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.4.1 Testsimulation . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.4.2 Summarycomparisons . . . . . . . . . . . . . . . . . . . . . 136
7.4.3 Analysisofasingleiterationintime . . . . . . . . . . . . . . 137
7.5 Amulti-instrumentmodelinavirtualroom . . . . . . . . . . . . . . 140
7.5.1 Systemabstraction . . . . . . . . . . . . . . . . . . . . . . . 140
7.5.2 Examplesimulation . . . . . . . . . . . . . . . . . . . . . . 141
7.5.3 Furtherparallelimplementations . . . . . . . . . . . . . . . . 142
7.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
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