xx ProcaEvolve

ProcaEvolve

Helvi Witek, Miguel Zilhxo

October 26 2018

1 Notes

This thorn evolves the Proca equations in generic spacetimes, as outlined inx[1]. When setting the mass of the vector field (parameter mu from thorn ProcaBase) to zero, the system reduces to the Maxwell equations in the Lorenz gauge.

“Right-hand-side” variables rhsxAi, rhsxEi, rhsxAphi and rhsxZeta defined in interface.ccl are given by equations (2.12), (2.13), (2.15) and (2.16) respectively inx[1].

References

[1]xxxM.xZilhxo,  H.xWitek  and

V.xCardoso, “Nonlinear interactions between black holes and Proca fields,” Class.xQuant.xGrav.x32 (2015) 234003 doi:10.1088/0264-9381/32/23/234003 [arXiv:1505.00797 [gr-qc]].

2 Parameters

11chixfloor 10Scope: privatex01 REAL

11Description: Minimal value of abs(chi)

11 Range 10 x01 Default: 1.0d-05
11*:*  10Any value possible

11

11confxfacxexponent  10Scope: privatex01  REAL

11Description: Exponent n for hgammaxij = chin̂ gammaxij conformal decomposition

11 Range 10 x01 Default: 1
11(*:*)  101 or 2 are good choices

11

11derivsxorder  10Scope: privatex01  INT

11Description: Order for derivatives

11 Range 10 x01 Default: 4
114  104th order stencils
116  106th order stencils

11

11kappa  10Scope: privatex01  REAL

11Description: Damping parameter for Maxwell equations

11 Range 10 x01 Default: 1
110:*  10non-negative

11

11usexadvectionxstencils  10Scope: privatex01  BOOLEAN

11Description: Use lop-sided stencils for advection derivs

11                              10  x01  Default: yes

11

11zetaxomegaxfac  10Scope: privatex01  REAL

11Description: Set to zero to not evolve Zeta and Omega

11 Range 10 x01 Default: 1
11*:*  10zero or one

11

11procaevolvexmaxnumconstrainedvars 10Scope: restrictedx01  INT

11Description: The maximum number of constrained variables used by ProcaEvolve

11 Range 10 x01 Default: (none)
110:0  10none

11

11procaevolvexmaxnumevolvedvars 10Scope: restrictedx01  INT

11Description: The maximum number of evolved variables used by ProcaEvolve

11 Range 10 x01 Default: 8
118:8  10Just 8: Ex, Axi, Aphi, Zeta

11

11procaevolvexmaxnumsandrvars  10Scope: restrictedx01  INT

11Description: The maximum number of save and restore variables used by ProcaEvolve

11 Range 10 x01 Default: 16
1116:16  10lapse, shift, metric, and extrinsic curvature

11

11a0  10Scope: shared from PROCABASEx01REAL

11

11aphi0  10Scope: shared from PROCABASEx01REAL

11e0  10Scope: shared from PROCABASEx01REAL

11

11evolutionxmethod  10Scope: shared from PROCABASEx01  KEYWORD

11Extends ranges:

11ProcaEvolve  10Use ProcaEvolve to evolve Proca variables

11

11mu  10Scope: shared from PROCABASEx01REAL

11

11nxa  10Scope: shared from PROCABASEx01INT

11

11nxaphi  10Scope: shared from PROCABASEx01INT

11

11nxe  10Scope: shared from PROCABASEx01INT

11

11nxzeta  10Scope: shared from PROCABASEx01INT

11

3 Interfaces

General Implements: procaevolve

Inherits: admbase tmunubase procabase boundary

Grid Variables 3.0.1 PUBLIC GROUPS

11x Group Names x10x Variable Names xx01 Details x11x
11  rhsxei  10  x01  compact110
11                 10  rhsxEx  x01 description11right hand sides for Ex evolution equations
11                 10  rhsxEy  x01 dimensions113
11                 10  rhsxEz  x01 distribution11DEFAULT
11                 10  x01 group type11GF
11 10 x01 tags11tensortypealias=”U” tensorweight=0 prolongation=”none” Checkpoint=”no”
11                 10  x01 timelevels111
11                 10  x01variable type11REAL
11  rhsxai  10  x01  compact110
11                 10  rhsxAx  x01 description11right hand sides for Axi evolution equations
11                 10  rhsxAy  x01 dimensions113
11                 10  rhsxAz  x01 distribution11DEFAULT
11                 10  x01 group type11GF
11 10 x01 tags11tensortypealias=”D” tensorweight=0 prolongation=”none” Checkpoint=”no”
11                 10  x01 timelevels111
11                 10  x01variable type11REAL
11 rhsxaphi 10 rhsxAphi x01 compact110
11                 10  x01 description11right hand sides for Aphi evolution equation
11                 10  x01 dimensions113
11                 10  x01 distribution11DEFAULT
11                 10  x01 group type11GF
11 10 x01 tags11tensortypealias=”Scalar” tensorweight=0 prolongation=”none” Checkpoint=”no”
11                 10  x01 timelevels111
11                 10  x01variable type11REAL
11 rhsxzeta 10 rhsxZeta x01 compact110
11                 10  x01 description11right hand sides for Zeta evolution equation
11                 10  x01 dimensions113
11                 10  x01 distribution11DEFAULT
11                 10  x01 group type11GF
11 10 x01 tags11tensortypealias=”Scalar” tensorweight=0 prolongation=”none” Checkpoint=”no”
11                 10  x01 timelevels111
11                 10  x01variable type11REAL
11  hmetric  10  x01  compact110
11                 10  hxx  x01 description11\tilde gammaxij
11                 10  hxy  x01 dimensions113
11                 10  hxz  x01 distribution11DEFAULT
11                 10  hyy  x01 group type11GF
11                 10  hyz  x01  tags11tensortypealias=”DDxsym” tensorweight=-0.66666666666666666667 prolongation=”none” Checkpoint=”no”
11                 10  hzz  x01 timelevels111
11                 10  x01variable type11REAL
11 confxfacxchi 10  x01  compact110
11                 10  chi  x01 description11conformal factor \chi
11                 10  x01 dimensions113
11                 10  x01 distribution11DEFAULT
11                 10  x01 group type11GF
11 10 x01 tags11tensortypealias=”Scalar” tensorweight=-0.66666666666666666667 prolongation=”none” Checkpoint=”no”
11                 10  x01 timelevels111
11                 10  x01variable type11REAL

11

11x Group Names x10x Variable Names xx01 Details x11x
11  trk  10  x01  compact110
11                 10  tracek  x01 description11Tr(K)
11                 10  x01 dimensions113
11                 10  x01 distribution11DEFAULT
11                 10  x01 group type11GF
11 10 x01 tags11tensortypealias=”Scalar” tensorweight=0 prolongation=”none” Checkpoint=”no”
11                 10  x01 timelevels111
11                 10  x01variable type11REAL

4 Schedule This section lists all the variables which are assigned storage by thorn Proca/ProcaEvolve. Storage can either last for the duration of the run (Always means that if this thorn is activated storage will be assigned, Conditional means that if this thorn is activated storage will be assigned for the duration of the run if some condition is met), or can be turned on for the duration of a schedule function.

Storage x

11x11Conditional:
11x 11rhsxEi rhsxAi rhsxAphi rhsxZeta
11x 11hmetric confxfacxchi trk

11x 11x

11

Scheduled Functions

CCTKxBASEGRID (conditional) x procaxinitsymbound x schedule symmetries x

11x11Language:11fortran
11 x 11Options: 11meta
11 x 11Type: 11function

11

CCTKxBASEGRID (conditional) x procaxzeroxrhs x set all rhs functions to zero to prevent spurious nans x

11x11After: 11procaxinitsymbound
11 x 11Language:11fortran
11 x 11Type: 11function

11

MoLxRegister (conditional) x procaxregistervars x register variables for mol x

11x11Language:11c
11 x 11Options: 11meta
11 x 11Type: 11function

MoLxCalcRHS (conditional) x procaxcalcxrhs x mol rhs calculation for proca variables x

11x11Language:11fortran
11 x 11Type: 11function

11

MoLxCalcRHS (conditional) x procaxcalcxrhsxbdry x mol boundary rhs calculation for proca variables x

11x11After: 11procaxcalcrhs
11 x 11Language:11fortran
11 x 11Type: 11function

11

MoLxPostStep (conditional) x procaxboundaries x mol boundary enforcement for proca variables x

11x11Language:11fortran
11 x 11Options: 11level
11 x 11Sync:  11procabase::ei
11 x 11x  11procabase::ai
11 x 11x  11procabase::aphi
11 x 11x  11procabase::zeta
11 x 11Type: 11function

11

MoLxPostStep (conditional) x applybcs x apply boundary conditions x

11x11After:11procaxboundaries
11 x 11Type:11group

11

AddToTmunu (conditional) x procaxcalcxtmunu x compute the energy-momentum tensor x

11x11Language:11fortran
11 x 11Type: 11function

11

Aliased Functions

11Alias Name: xxxxxxx11Function Name:
11ApplyBCs  11ProcaxApplyBCs
11ProcaxcalcxTmunu  11ProcaxAddToTmunu
11Procaxcalcxrhs  11ProcaxCalcRHS
11Procaxcalcxrhsxbdry 11ProcaxCalcRHSxBdry