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390 Numerical relativitynumerics and computer science) and because of the geographical distribution ofthe people and computer resources involved in simulation and data analysis.The name Cactus comes from the design of a central core (or flesh) whichconnects to application modules (or thorns) through an extensible interface.Thorns can implement custom developed scientific or engineering applications,such as the Einstein solvers, or other applications such as computational fluiddynamics. Other thorns from a standard computational toolkit provide a range ofcapabilities, such as parallel I/O, data distribution, or checkpointing.Cactus runs on many architectures. Applications, developed on standardworkstations or laptops, can be seamlessly run on clusters or supercomputers.Parallelism and portability are achieved by hiding the driver layer and featuressuch as the I/O system and calling interface under a simple abstraction API. TheCactus API supports C/C++ and F77/F90 programming languages for the thorns.Thus, thorn programmers can work in the language they find most convenient,and are not required to master the latest and greatest computing paradigms. Thismakes it easier for scientists to turn existing codes into thorns which can thenmake use of the complete Cactus infrastructure, and in turn be used by otherthorns within Cactus.Cactus provides easy access to many cutting edge software technologies beingdeveloped in the academic research community, such as the Globus MetacomputingToolkit, HDF5 parallel file I/O, the PETSc scientific computing library,adaptive mesh refinement, web interfaces, and advanced visualization tools.So, how does a user use the code? A detailed user guide is available withthe code (see http://www.cactuscode.org), but in a nutshell, one specifies whichphysics modules, and which computational/parallelism modules, are desired in aconfiguration file, and makes the code on the desired architecture, which can beany one of a number of machines from SGI/Cray Origin or T3E, Dec Alpha, Linuxworkstations or clusters, NT clusters, and others. The make system automaticallydetects the architecture and configures the code appropriately. Control of runparameters is then provided through an input file. Additional modules can beselected from a large community-developed library, or new modules may bewritten and used in conjunction with the pre-developed modules.Our experiences with Cactus up to now suggest that these techniques areeffective. It allows a code of many tens of thousands of lines, but with acompact flesh that is possible to maintain despite the large number of peoplecontributing to it. The common code base has enhanced the collaborativeprocess, having important and beneficial effects on the flow of ideas betweenremote groups. This flexible, open code architecture allows, for example, arelativity expert to contribute to the code without knowing the details of, say,the computational layers (e.g., message passing or AMR libraries) or othercomponents (e.g., hydrodynamics). We encourage users from throughout therelativity and astrophysics communities to make use of this freely downloadablecode infrastructure and physics modules, either for their own use, or as acollaborative tool to work with other groups in the community.
Cactus computational toolkit 39118.6.1 Adaptive mesh refinement3D simulations of Einstein’s equations are very demanding computationally. Inthis section we outline the computational needs, and techniques designed toreduce them. We will need to resolve waves with wavelengths of order 5M or less,where M is the mass of the BH or the neutron star. Although for Schwarzschildblack holes, the fundamental l = 2 quasinormal mode wavelength is 16.8M,higher modes, such as l = 4 and above, have wavelengths of 8M and below. TheBH itself has a radius of 2M. More importantly, for very rapidly rotating KerrBHs, which are expected to be formed in realistic astrophysical BH coalescence,the modes are shifted down to significantly shorter wavelengths [3, 4]. As we
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GRAVITATIONAL WAVES
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c IOP Publishing Ltd 2001All righ
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viContents4 Astrophysics of gravita
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viiiContents11.3 Gravitational wave
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xContents16.5 Cosmological perturba
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PrefaceGravitational waves today re
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2 Gravitational waves, theory and e
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10 Gravitational waves, theory and
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SynopsisGravitational waves and the
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Chapter 2Elements of gravitational
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Using the TT gauge to understand gr
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Interaction of gravitational waves
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Analysis of beam detectors 21This d
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Exercises for chapter 2 232. Show t
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Gravitational-wave detectors 25indi
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Gravitational-wave observables 27th
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The physics of interferometers 29
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The physics of interferometers 31Dr
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The physics of interferometers 33Fi
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The physics of resonant mass detect
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The physics of resonant mass detect
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A detector in space 39LISA has been
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Gravitational and electromagnetic w
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Chapter 4Astrophysics of gravitatio
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Sources detectable from ground and
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Variational principles and the ener
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Variational principles and the ener
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Practical applications of the Isaac
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Exercises for chapter 5 57(f)This s
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Expansion for the far field of a sl
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Application of the TT gauge to the
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6.4.1 Mass-quadrupole radiationEner
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Chapter 7Source calculationsNow tha
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The r-modes 73As we mentioned in ch
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The r-modes 75instability. In an id
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The r-modes 77Table 7.1. Gravitatio
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The r-modes 79evolution turns out t
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ReferencesWe have divided the refer
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References 83[19] van der Klis M 19
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Solutions to exercises 85For this p
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Solutions to exercises 87The gauge
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Chapter 8Resonant detectors for gra
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Sensitivity and bandwidth of resona
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8.2 Sensitivity for various GW sign
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Sensitivity for various GW signals
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Recent results obtained with the re
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Discussion and conclusions 101Figur
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Chapter 9The Earth-based large inte
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Introduction 105Figure 9.1. The sim
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h(sqrt(1/Hz))10 −610 −810 −10
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18.5 cmThe SA suspension and requir
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A few words about the Low Frequency
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Conclusion 113Figure 9.7. The R and
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Chapter 10LISA: A proposed joint ES
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Description of the LISA mission 117
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Expected gravitational-wave results
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References 149[8] Folkner W M 1998
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References 151[68] Miralda-Escuda J
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Introduction 153detect GWs with a s
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Testing theories of gravity 155•
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0Testing theories of gravity 157the
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Taking the scalar product we findGr
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Gravitational wave radiation in the
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The hollow sphere 169and introduced
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Scalar-tensor cross sections 171mon
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Scalar-tensor cross sections 173Tab
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Scalar-tensor cross sections 175Tab
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References 177Frossati G and Coccia
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Chapter 12Generalities on the stoch
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Introduction 183contribution to the
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Definitions 185The value of H 0 is
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Definitions 18712.2.2 The character
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Definitions 189or, dividing by the
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The overlap reduction function 191O
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The overlap reduction function 193T
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The overlap reduction function 195F
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Achievable sensitivities to the SGW
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Observational bounds 207Table 12.10
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equation gives immediately(ρgwρ
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Chapter 13Sources of SGWBHere we re
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Topological defects 213This correla
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Topological defects 215It can be sh
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Topological defects 217(i)A loop ra
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Topological defects 219• A peak n
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Topological defects 22113.1.2 Hybri
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Inflation 223Hubble radius and when
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Inflation 225as a first approximati
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Inflation 227the lower bound to the
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String cosmology 22913.3 String cos
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String cosmology 231HPre-big bangPo
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String cosmology 233Figure 13.6. h
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First-order phase transitions 23580
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Astrophysical sources 237which is t
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References 239of [71]). However, fo
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References 241[39] Liddle A R 2000
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PART 4THEORETICAL DEVELOPMENTSHerma
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246 Infinite-dimensional symmetries
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Chapter 15Gyroscopes and gravitatio
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270 Gyroscopes and gravitational wa
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Chapter 16Elementary introduction t
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282 Elementary introduction to pre-
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Page 349 and 350: Chapter 17Post-Newtonian computatio
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Page 369: PART 5NUMERICAL RELATIVITYEdward Se
Page 372 and 373: 362 Numerical relativityspite of mo
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Page 376 and 377: 366 Numerical relativityHere we hav
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Page 380 and 381: 370 Numerical relativityThe Palma,
Page 382 and 383: 372 Numerical relativityHyperbolic
Page 384 and 385: 374 Numerical relativityEinstein di
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Page 390 and 391: 380 Numerical relativityFigure 18.1
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Page 396 and 397: 386 Numerical relativityto a very a
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Page 412 and 413: 402 Numerical relativity18.9.5.2 Co
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Page 416 and 417: 406 Numerical relativity[101] Shapi
Page 418 and 419: 408 Numerical relativity(Singapore:
Page 420 and 421: 410 IndexEhlers Lagrangian, 254Eins
Page 422: 412 Indexscalarspherical harmonics,
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