Table of Contents

Introduction

The Spectral Einstein Code (SpEC) is a flexible infrastructure for solving partial differential equations using multi-domain spectral methods. While SpEC was primarily designed for fully general-relativistic compact object simulations, it can be applied to a wide range of hyperbolic and elliptic equations. Some of its features are:

Binary black holes at t=33 Binary black holes at t=7920 Binary black holes at t=8200 Binary black holes at t=9000

SpEC simulation of inspiral and merger of two black holes

The main application area of SpEC lies in simulating compact binary objects. Specifically, it is one of the most accurate and efficient codes to compute the gravitational waveforms for inspiraling and coalescing binary black holes.

Contributors

SpEC was originally developed by Lawrence Kidder, Harald Pfeiffer, and Mark Scheel, who remain the principal maintainers of the code. Since then, many further individuals have contributed to SpEC. Most especially, Matt Duez and Francois Foucart have developed the hydrodynamics module, and Béla Szilágyi has made numerous valuable additions throughout the code. In addition to these people, Lee Lindblom has contributed significantly to the algorithms used in SpEC.

Further contributions to SpEC were made by Thomas Baumgarte, Andy Bohn, Michael Boyle, Jeandrew Brink, Luisa Buchman, Tony Chu, Michael Cohen, Gregory Cook, Jason Grigsby, Francois Hebert, Dan Hemberger, Frank Herrmann, Jeff Kaplan, Stephen Lau, François Limousin, Geoffrey Lovelace, Keith Matthews, Abdul Mroué, Curran Muhlberger, Rob Owen, Oliver Rinne, Olivier Sarbach, Deirdre Shoemaker, Nick Taylor, Saul Teukolsky, Will Throwe, Manuel Tiglio, Anil Zenginoglu, and Fan Zhang.

Finally, we thank the following undergraduate students for assisting with visualization and improving visualization capabilities: Adam Bartnik, Deshpreet Bedi, Patrick Calhoun, Cameron Cogburn, Bryant Garcia, Daniel Jones, Dave Kotfis, Yor Limkumnerd, Robert McGehee, Dmitry Meyerson, Adam Neumann, Hiroaki Oyaizu, Jennifer Seiler, Alexandre Streicher, Allen Sussman.

Availability

Because of the steep learning curve and complexity of SpEC, new users are typically introduced to SpEC through a collaboration with experienced SpEC users. If interested in using SpEC, please contact Lawrence Kidder, Harald Pfeiffer, or Mark Scheel.

Publications

These publications have made use of SpEC:

2000

  1. Black hole evolution by spectral methods L.E. Kidder, M.A. Scheel, S.A. Teukolsky, E.D. Carlson, G.B. Cook Phys. Rev. D 62, 084032 (2000) [arXiv:gr-qc/0005056]

2001

  1. Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations L.E. Kidder, M.A. Scheel, S.A. Teukolsky Phys. Rev. D 64, 064017 (2001) [arXiv:gr-qc/0105031]

2002

  1. Comparing initial-data sets for binary black holes H.P. Pfeiffer, G.B. Cook, S.A. Teukolsky Phys. Rev. D 66, 024047 (2002) [arXiv:gr-qc/0203085]
  2. Energy norms and the stability of the Einstein evolution equations L. Lindblom, M.A. Scheel Phys. Rev. D 66, 084014 (2002) [arXiv:gr-qc/0206035]
  3. Toward stable 3D numerical evolutions of black-hole spacetimes M.A. Scheel, L.E. Kidder, L. Lindblom, H.P. Pfeiffer, S.A. Teukolsky Phys. Rev. D 66, 124005 (2002) [arXiv:gr-qc/0209115]

2003

  1. A multidomain spectral method for solving elliptic equations H.P. Pfeiffer, L.E. Kidder, M.A. Scheel, S.A. Teukolsky Computer Physics Communications 152, 253-273 (2003) [arXiv:gr-qc/0202096]
  2. Extrinsic curvature and the Einstein constraints H.P. Pfeiffer, J.W. York Phys. Rev. D 67, 044022 (2003) [arXiv:gr-qc/0207095]
  3. Dynamical gauge conditions for the Einstein evolution equations L. Lindblom, M.A. Scheel Phys. Rev. D 67, 124005 (2003) [arXiv:gr-qc/0301120]

2004

  1. 3D simulations of linearized scalar fields in Kerr spacetime M.A. Scheel, A.L. Erickcek, L.M. Burko, L.E. Kidder, H.P. Pfeiffer, S.A. Teukolsky Phys. Rev. D 69, 104006 (2004) [arXiv:gr-qc/0305027]
  2. Controlling the growth of constraints in hyperbolic evolution systems L. Lindblom, M.A. Scheel, L.E. Kidder, H.P. Pfeiffer, D. Shoemaker, S.A. Teukolsky Phys. Rev. D 69, 124025 (2004) [arXiv:gr-qc/0402027]
  3. Optimal constraint projection for hyperbolic evolution systems M. Holst, L. Lindblom, R. Owen, H.P. Pfeiffer, M.A. Scheel, L.E. Kidder Phys. Rev. D 70, 084017 (2004) [arXiv:gr-qc/0407011]
  4. Excision boundary conditions for black-hole initial data G.B. Cook, H.P. Pfeiffer Phys. Rev. D 70, 104016 (2004) [arXiv:gr-qc/0407078]

2005

  1. Initial data for Einstein's equations with superposed gravitational waves H.P. Pfeiffer, L.E. Kidder, M.A. Scheel, D. Shoemaker Phys. Rev. D 71, 024020 (2005) [arXiv:gr-qc/0410016]
  2. Boundary conditions for the Einstein evolution system L.E. Kidder, L. Lindblom, M.A. Scheel, L.T. Buchman, H.P. Pfeiffer Phys. Rev. D 71, 064020 (2005) [arXiv:gr-qc/0412116]
  3. Uniqueness and Nonuniqueness in the Einstein Constraints H.P. Pfeiffer, J.W. York Physical Review Letters 95, 091101 (2005) [arXiv:gr-qc/0504142]

2006

  1. A new generalized harmonic evolution system L. Lindblom, M.A. Scheel, L.E. Kidder, R. Owen, O. Rinne Classical and Quantum Gravity 23, 447 (2006) [arXiv:gr-qc/0512093]
  2. Circular orbits and spin in black-hole initial data M. Caudill, G.B. Cook, J.D. Grigsby, H.P. Pfeiffer Phys. Rev. D 74, 064011 (2006) [arXiv:gr-qc/0605053]
  3. Approximate initial data for binary black holes K.A. Dennison, T.W. Baumgarte, H.P. Pfeiffer Phys. Rev. D 74, 064016 (2006) [arXiv:gr-qc/0606037]
  4. Solving Einstein's equations with dual coordinate frames M.A. Scheel, H.P. Pfeiffer, L. Lindblom, L.E. Kidder, O. Rinne, S.A. Teukolsky Phys. Rev. D 74, 104006 (2006) [arXiv:gr-qc/0607056]

2007

  1. Testing the accuracy and stability of spectral methods in numerical relativity M. Boyle, L. Lindblom, H.P. Pfeiffer, M.A. Scheel, L.E. Kidder Phys. Rev. D 75, 024006 (2007) [arXiv:gr-qc/0609047]
  2. Einstein constraints: Uniqueness and nonuniqueness in the conformal thin sandwich approach T.W. Baumgarte, N.Ó. Murchadha, H.P. Pfeiffer Phys. Rev. D 75, 044009 (2007) [arXiv:gr-qc/0610120]
  3. Reducing orbital eccentricity in binary black hole simulations H.P. Pfeiffer, D.A. Brown, L.E. Kidder, L. Lindblom, G. Lovelace, M.A. Scheel Classical and Quantum Gravity 24, 59 (2007) [arXiv:gr-qc/0702106]
  4. Constraint damping in first-order evolution systems for numerical relativity R. Owen Phys. Rev. D 76, 044019 (2007) [arXiv:gr-qc/0703145]
  5. Testing outer boundary treatments for the Einstein equations O. Rinne, L. Lindblom, M.A. Scheel Classical and Quantum Gravity 24, 4053-4078 (2007) [arXiv:0704.0782]
  6. High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions M. Boyle, D.A. Brown, L.E. Kidder, A.H. Mroué, H.P. Pfeiffer, M.A. Scheel, G.B. Cook, S.A. Teukolsky Phys. Rev. D 76, 124038 (2007) [arXiv:0710.0158]

2008

  1. Gauge drivers for the generalized harmonic Einstein equations L. Lindblom, K.D. Matthews, O. Rinne, M.A. Scheel Phys. Rev. D 77, 084001 (2008) [arXiv:0711.2084]
  2. Initial data for black hole neutron star binaries: A flexible, high-accuracy spectral method F. Foucart, L.E. Kidder, H.P. Pfeiffer, S.A. Teukolsky Phys. Rev. D 77, 124051 (2008) [arXiv:0804.3787]
  3. High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants M. Boyle, A. Buonanno, L.E. Kidder, A.H. Mroué, Y. Pan, H.P. Pfeiffer, M.A. Scheel Phys. Rev. D 78, 104020 (2008) [arXiv:0804.4184]
  4. Ineffectiveness of Padé resummation techniques in post-Newtonian approximations A.H. Mroué, L.E. Kidder, S.A. Teukolsky Phys. Rev. D 78, 044004 (2008) [arXiv:0805.2390]
  5. Binary-black-hole initial data with nearly extremal spins G. Lovelace, R. Owen, H.P. Pfeiffer, T. Chu Phys. Rev. D 78, 084017 (2008) [arXiv:0805.4192]
  6. Evolving black hole-neutron star binaries in general relativity using pseudospectral and finite difference methods M.D. Duez, F. Foucart, L.E. Kidder, H.P. Pfeiffer, M.A. Scheel, S.A. Teukolsky Phys. Rev. D 78, 104015 (2008) [arXiv:0809.0002]

2009

  1. IMEX evolution of scalar fields on curved backgrounds S.R. Lau, H.P. Pfeiffer, J.S. Hesthaven Commun. Comput. Phys. 6, 1063--1094 (2009) [arXiv:0808.2597]
  2. Revisiting event horizon finders M.I. Cohen, H.P. Pfeiffer, M.A. Scheel Classical and Quantum Gravity 26, 035005 (2009) [arXiv:0809.2628]
  3. High-accuracy waveforms for binary black hole inspiral, merger, and ringdown M.A. Scheel, M. Boyle, T. Chu, L.E. Kidder, K.D. Matthews, H.P. Pfeiffer Phys. Rev. D 79, 024003 (2009) [arXiv:0810.1767]
  4. Implementation of higher-order absorbing boundary conditions for the Einstein equations O. Rinne, L.T. Buchman, M.A. Scheel, H.P. Pfeiffer Classical and Quantum Gravity 26, 075009 (2009) [arXiv:0811.3593]
  5. Reducing spurious gravitational radiation in binary-black-hole simulations by using conformally curved initial data G. Lovelace Classical and Quantum Gravity 26, 114002 (2009) [arXiv:0812.3132]
  6. Comparison of high-accuracy numerical simulations of black-hole binaries with stationary-phase post-Newtonian template waveforms for initial and advanced LIGO M. Boyle, D.A. Brown, L. Pekowsky Classical and Quantum Gravity 26, 114006 (2009) [arXiv:0901.1628]
  7. Samurai project: Verifying the consistency of black-hole-binary waveforms for gravitational-wave detection M. Hannam et al. Phys. Rev. D 79, 084025 (2009) [arXiv:0901.2437]
  8. Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project B. Aylott et al. Classical and Quantum Gravity 26, 165008 (2009) [arXiv:0901.4399]
  9. Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonspinning, equal-mass black holes A. Buonanno, Y. Pan, H.P. Pfeiffer, M.A. Scheel, L.T. Buchman, L.E. Kidder Phys. Rev. D 79, 124028 (2009) [arXiv:0902.0790]
  10. Orbiting binary black hole evolutions with a multipatch high order finite-difference approach E. Pazos, M. Tiglio, M.D. Duez, L.E. Kidder, S.A. Teukolsky Phys. Rev. D 80, 024027 (2009) [arXiv:0904.0493]
  11. Improved gauge driver for the generalized harmonic Einstein system L. Lindblom, B. Szilágyi Phys. Rev. D 80, 084019 (2009) [arXiv:0904.4873]
  12. Extrapolating gravitational-wave data from numerical simulations M. Boyle, A.H. Mroué Phys. Rev. D 80, 124045 (2009) [arXiv:0905.3177]
  13. Status of NINJA: the Numerical INJection Analysis project L. Cadonati et al. Classical and Quantum Gravity 26, 114008 (2009) [arXiv:0905.4227]
  14. Final remnant of binary black hole mergers: Multipolar analysis R. Owen Phys. Rev. D 80, 084012 (2009) [arXiv:0907.0280]
  15. Black hole initial data on hyperboloidal slices L.T. Buchman, H.P. Pfeiffer, J.M. Bardeen Phys. Rev. D 80, 084024 (2009) [arXiv:0907.3163]
  16. High accuracy simulations of black hole binaries: Spins anti-aligned with the orbital angular momentum T. Chu, H.P. Pfeiffer, M.A. Scheel Phys. Rev. D 80, 124051 (2009) [arXiv:0909.1313]
  17. Simulations of binary black hole mergers using spectral methods B. Szilágyi, L. Lindblom, M.A. Scheel Phys. Rev. D 80, 124010 (2009) [arXiv:0909.3557]

2010

  1. Momentum flow in black-hole binaries. II. Numerical simulations of equal-mass, head-on mergers with antiparallel spins G. Lovelace, Y. Chen, M. Cohen, J.D. Kaplan, D. Keppel, K.D. Matthews, D.A. Nichols, M.A. Scheel, U. Sperhake Phys. Rev. D 82, 064031 (2010) [arXiv:0907.0869]
  2. Effective-one-body waveforms calibrated to numerical relativity simulations: Coalescence of nonprecessing, spinning, equal-mass black holes Y. Pan, A. Buonanno, L.T. Buchman, T. Chu, L.E. Kidder, H.P. Pfeiffer, M.A. Scheel Phys. Rev. D 81, 084041 (2010) [arXiv:0912.3466]
  3. Equation of state effects in black hole\ndashneutron star mergers M.D. Duez, F. Foucart, L.E. Kidder, C.D. Ott, S.A. Teukolsky Classical and Quantum Gravity 27, 114106 (2010) [arXiv:0912.3528]
  4. Hyperboloidal evolution of test fields in three spatial dimensions A. Zenginoglu, L.E. Kidder Phys. Rev. D 81, 124010 (2010) [arXiv:1004.0760]
  5. Degeneracy measures for the algebraic classification of numerical spacetimes R. Owen Phys. Rev. D 81, 124042 (2010) [arXiv:1004.3768]
  6. Measuring orbital eccentricity and periastron advance in quasicircular black hole simulations A.H. Mroué, H.P. Pfeiffer, L.E. Kidder, S.A. Teukolsky Phys. Rev. D 82, 124016 (2010) [arXiv:1004.4697]
  7. Spectral methods for the wave equation in second-order form N.W. Taylor, L.E. Kidder, S.A. Teukolsky Phys. Rev. D 82, 024037 (2010) [arXiv:1005.2922]

2011

  1. Black hole-neutron star mergers: Effects of the orientation of the black hole spin F. Foucart, M.D. Duez, L.E. Kidder, S.A. Teukolsky Phys. Rev. D 83, 024005 (2011) [arXiv:1007.4203]
  2. Hyperboloidal layers for hyperbolic equations on unbounded domains A. Zenginoğlu Journal of Computational Physics 230, 2286-2302 (2011) [arXiv:1008.3809]
  3. Simulating merging binary black holes with nearly extremal spins G. Lovelace, M.A. Scheel, B. Szilágyi Phys. Rev. D 83, 024010 (2011) [arXiv:1010.2777]
  4. Horizon dynamics of distorted rotating black holes T. Chu, H.P. Pfeiffer, M.I. Cohen Phys. Rev. D 83, 104018 (2011) [arXiv:1011.2601]
  5. Reducing orbital eccentricity of precessing black-hole binaries A. Buonanno, L.E. Kidder, A.H. Mroué, H.P. Pfeiffer, A. Taracchini Phys. Rev. D 83, 104034 (2011) [arXiv:1012.1549]
  6. Frame-Dragging Vortexes and Tidal Tendexes Attached to Colliding Black Holes: Visualizing the Curvature of Spacetime R. Owen et al. Physical Review Letters 106, 151101 (2011) [arXiv:1012.4869]
  7. Suitability of post-Newtonian/numerical-relativity hybrid waveforms for gravitational wave detectors I. MacDonald, S. Nissanke, H.P. Pfeiffer Classical and Quantum Gravity 28, 134002 (2011) [arXiv:1102.5128]
  8. Implicit-explicit (IMEX) evolution of single black holes S.R. Lau, G. Lovelace, H.P. Pfeiffer [arXiv:1105.3922]
  9. Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism Y. Pan, A. Buonanno, M. Boyle, L.T. Buchman, L.E. Kidder, H.P. Pfeiffer, M.A. Scheel [arXiv:1106.1021]
  10. Periastron Advance in Black Hole Binaries A. Le Tiec, A.H. Mroué, L. Barack, A. Buonanno, H.P. Pfeiffer, N. Sago, A. Taracchini [arXiv:1106.3278]
  11. Visualizing Spacetime Curvature via Frame-Drag Vortexes and Tidal Tendexes I. General Theory and Weak-Gravity Applications D.A. Nichols et al. [arXiv:1108.5486]

External Software

SpEC benefits from the years of work put into the following general-purpose scientific software packages: