Issues and Methods in Numerical General Relativity| Issues and Methods in Numerical General Relativity |
In General > s.a. computational
physics; numerical relativity [gauge choice, constraints].
* Form of the equations:
2008, The two main formulations used to produce well-posed initial-value
problems are the BSSN and the harmonic formulations.
@ General references: Alcubierre et al CQG(04)gq/03 [testbeds];
Neilsen et al LNP(06)gq/04 [examples];
Shinkai JKPS(09)-a0805-ln;
Zumbusch CQG(09)-a0901;
Bona et al PRD(10)-a1008 [action principle].
@ Boundary conditions: Sarbach JPCS(07)-a0708 [absorbing];
> s.a. numerical relativity.
@ Characteristic problem:
Stewart & Friedrich PRS(82);
Corkill & Stewart PRS(83) [2 Killing vectors, vacuum];
Bishop CQG(93);
Winicour PTPS(99)gq [binary black holes],
gq/00-proc [waves];
Barreto et al PRD(05)gq/04 [Einstein-Klein-Gordon];
Winicour LRR(05)gq,
LRR(09),
LRR(12) [rev];
Kreiss & Winicour CQG(11)-a1010 [null-timelike boundary problem];
van der Walt & Bishop PRD(12) [and observational cosmology].
@ Cauchy + characteristic:
Clarke & d'Inverno CQG(94);
Clarke et al PRD(95);
d'Inverno & Vickers PRD(96),
PRD(97) [axial symmetry];
Papadopoulos & Laguna PRD(97)gq/96 [Einstein-Klein-Gordon];
Dubal et al PRD(98) [spherical + fluid];
Bishop et al gq/98-in;
d'Inverno et al CQG(00)gq;
Szilágyi PhD(00)gq;
Winicour LRR(01)gq.
@ Cauchy + boundary: Stewart CQG(98);
Szilágyi & Winicour PRD(03)gq/02;
Frittelli & Gómez PRD(03) [boundary conditions];
Nagy & Sarbach CQG(06)gq [variational problem for lapse];
Babiuc et al PRD(06) [harmonic];
Winicour CQG(12) [boundary conditions, rev].
> Related topics:
see initial-value formulation; models
[collapse, binaries, cosmology, astrophysics]; regge calculus.
Stability and Hyperbolicity > s.a. einstein's equation [various forms].
* Idea: To ensure stability
of the evolution, a common strategy involves using symmetric hyperbolic
formulations of Einstein's equation.
@ Stability: Alcubierre et al PRD(00)gq/99 [ADM];
Szilágyi et al PRD(00)gq/99;
Frittelli & Gómez JMP(00)gq [ill-posedness];
Miller gq/00/PRD [ADM vs CT];
Laguna & Shoemaker CQG(02)gq [conformal-traceless];
Calabrese et al PRD(02)gq,
PRD(02)gq,
JCP(06)gq/05;
O'Shaughnessy PRD(03)gq;
Lehner et al CQG(06)gq/05 [higher accuracy].
@ Hyperbolic form: Bona et al PRL(95)gq/94,
PRD(97)gq [first-order];
Scheel et al PRD(97)gq [black holes];
Yoneda & Shinkai CQG(01)gq/00;
Shinkai & Yoneda gq/01-proc [connection variables];
Buchman & Bardeen PRD(03)gq [tetrad variables];
Bona & Palenzuela PRD(04)gq [and dynamical shift].
@ Symmetric hyperbolicity: Tiglio et al PRD(04)gq/03 [3D simulations].
Other Approaches and Methods
> s.a. Symplectic Integrators.
@ Conformal form:
Shibata & Nakamura PRD(95);
Frauendiener PRD(98)gq/97,
PRD(98)gq/97;
Baumgarte & Shapiro PRD(99)gq/98;
Alcubierre et al PRD(00)gq;
Lehner et al gq/00 [causal differencing excision];
Gourgoulhon & Novak IJMPA(02).
@ BSSN formulation: Sarbach et al PRD(02)gq;
Yoneda & Shinkai PRD(02)gq;
Beyer & Sarbach PRD(04)gq;
Brown CQG(08)-a0705 [spherical];
Gentle IJMPD(10)-a0707 [nature of equations].
@ In higher dimensions: Yoshino & Shibata PRD(09)-a0907;
Zilhão a1301-PhD;
Sperhake IJMPD(13)-a1301;
Witek IJMPA(13)-a1308-ln;
Witek et al PRD(14)-a1406 [comparison of two codes].
@ Algebraic computing: Husa & Lechner gq/03-proc;
> s.a. computation.
@ Connection variables: Salisbury et al CQG(94)gq;
Shinkai & Yoneda gq/97-MG8,
PRD(99)gq,
CQG(00)gq [Ashtekar variables].
@ Spectral methods: Grandclément & Novak LRR(09)-a0706;
Amorim et al CQG(09) [Gowdy spacetimes].
@ Other formulations and techniques: Teukolsky PRD(00)gq/99 [iterated Crank-Nicholson method];
Sperhake PhD(01)gq/02 [non-linear techniques];
Jansen et al PRD(06)gq/03 [stability, AA vs ADM & BSSN formulations];
Calabrese PRD(05)gq/04 [first- vs second-order, black holes];
Alic et al PRD(07)-a0706 [finite-volume methods];
Paschalidis PRD(08) [mixed hyperbolic–second-order-parabolic];
Garrett a0902 [direct finite differencing];
Mongwane GRG(15)-a1504 [mesh refinement algorithms];
Hamilton PRD(17)-a1611 [covariant Hamiltonian tetrad approach];
Bieri et al CQG(20)-a1905 [with no outer boundary condition].
@ Related topics: Stewart PRS(89) [Bondi mass];
Arbona et al PRD(99)gq;
Papadopoulos & Sopuerta PRD(02)gq/01 [background geometry];
Bona et al PRD(02)gq [evolution systems],
gq/02/PRL [extended constraint-free system];
Cordero-Carrión et al PRD(08);
Jasiulek CQG(09)-a0906 [quasilocal invariants];
> s.a. differential forms [discrete]; models
in numerical relativity [including adaptive mesh].
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