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|
# File produced by Kranc
if (other_timelevels == 1)
{
STORAGE: ML_cons_detg[1]
}
if (other_timelevels == 1)
{
STORAGE: ML_cons_Gamma[1]
}
if (other_timelevels == 1)
{
STORAGE: ML_cons_traceA[1]
}
if (other_timelevels == 1)
{
STORAGE: ML_Ham[1]
}
if (other_timelevels == 1)
{
STORAGE: ML_mom[1]
}
if (timelevels == 1)
{
STORAGE: ML_curv[1]
}
if (timelevels == 2)
{
STORAGE: ML_curv[2]
}
if (timelevels == 3)
{
STORAGE: ML_curv[3]
}
if (timelevels == 1)
{
STORAGE: ML_dtlapse[1]
}
if (timelevels == 2)
{
STORAGE: ML_dtlapse[2]
}
if (timelevels == 3)
{
STORAGE: ML_dtlapse[3]
}
if (timelevels == 1)
{
STORAGE: ML_dtshift[1]
}
if (timelevels == 2)
{
STORAGE: ML_dtshift[2]
}
if (timelevels == 3)
{
STORAGE: ML_dtshift[3]
}
if (timelevels == 1)
{
STORAGE: ML_Gamma[1]
}
if (timelevels == 2)
{
STORAGE: ML_Gamma[2]
}
if (timelevels == 3)
{
STORAGE: ML_Gamma[3]
}
if (timelevels == 1)
{
STORAGE: ML_lapse[1]
}
if (timelevels == 2)
{
STORAGE: ML_lapse[2]
}
if (timelevels == 3)
{
STORAGE: ML_lapse[3]
}
if (timelevels == 1)
{
STORAGE: ML_log_confac[1]
}
if (timelevels == 2)
{
STORAGE: ML_log_confac[2]
}
if (timelevels == 3)
{
STORAGE: ML_log_confac[3]
}
if (timelevels == 1)
{
STORAGE: ML_metric[1]
}
if (timelevels == 2)
{
STORAGE: ML_metric[2]
}
if (timelevels == 3)
{
STORAGE: ML_metric[3]
}
if (timelevels == 1)
{
STORAGE: ML_shift[1]
}
if (timelevels == 2)
{
STORAGE: ML_shift[2]
}
if (timelevels == 3)
{
STORAGE: ML_shift[3]
}
if (timelevels == 1)
{
STORAGE: ML_trace_curv[1]
}
if (timelevels == 2)
{
STORAGE: ML_trace_curv[2]
}
if (timelevels == 3)
{
STORAGE: ML_trace_curv[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_curvrhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_curvrhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_curvrhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_dtlapserhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_dtlapserhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_dtlapserhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_dtshiftrhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_dtshiftrhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_dtshiftrhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_Gammarhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_Gammarhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_Gammarhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_lapserhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_lapserhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_lapserhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_log_confacrhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_log_confacrhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_log_confacrhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_metricrhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_metricrhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_metricrhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_shiftrhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_shiftrhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_shiftrhs[3]
}
if (rhs_timelevels == 1)
{
STORAGE: ML_trace_curvrhs[1]
}
if (rhs_timelevels == 2)
{
STORAGE: ML_trace_curvrhs[2]
}
if (rhs_timelevels == 3)
{
STORAGE: ML_trace_curvrhs[3]
}
schedule ML_BSSN_MP_Startup at STARTUP
{
LANG: C
OPTIONS: meta
} "create banner"
schedule ML_BSSN_MP_RegisterSymmetries in SymmetryRegister
{
LANG: C
OPTIONS: meta
} "register symmetries"
if (CCTK_EQUALS(my_initial_data, "Minkowski"))
{
schedule ML_BSSN_MP_Minkowski IN ADMBase_InitialData
{
LANG: C
WRITES: ML_BSSN_MP::ML_curv
WRITES: ML_BSSN_MP::ML_dtlapse
WRITES: ML_BSSN_MP::ML_dtshift
WRITES: ML_BSSN_MP::ML_Gamma
WRITES: ML_BSSN_MP::ML_lapse
WRITES: ML_BSSN_MP::ML_log_confac
WRITES: ML_BSSN_MP::ML_metric
WRITES: ML_BSSN_MP::ML_shift
WRITES: ML_BSSN_MP::ML_trace_curv
} "ML_BSSN_MP_Minkowski"
}
if (CCTK_EQUALS(my_initial_data, "ADMBase"))
{
schedule ML_BSSN_MP_convertFromADMBase AT initial AFTER ADMBase_PostInitial
{
LANG: C
READS: ADMBase::curv
READS: ADMBase::lapse
READS: ADMBase::metric
READS: ADMBase::shift
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_trace_curv
WRITES: ML_BSSN_MP::ML_curv
WRITES: ML_BSSN_MP::ML_lapse
WRITES: ML_BSSN_MP::ML_log_confac
WRITES: ML_BSSN_MP::ML_metric
WRITES: ML_BSSN_MP::ML_shift
WRITES: ML_BSSN_MP::ML_trace_curv
} "ML_BSSN_MP_convertFromADMBase"
}
if (CCTK_EQUALS(my_initial_data, "ADMBase"))
{
schedule ML_BSSN_MP_InitGamma AT initial BEFORE ML_BSSN_MP_convertFromADMBaseGamma
{
LANG: C
WRITES: ML_BSSN_MP::ML_dtlapse
WRITES: ML_BSSN_MP::ML_dtshift
WRITES: ML_BSSN_MP::ML_Gamma
} "ML_BSSN_MP_InitGamma"
}
if (CCTK_EQUALS(my_initial_data, "ADMBase"))
{
schedule ML_BSSN_MP_convertFromADMBaseGamma AT initial AFTER ML_BSSN_MP_convertFromADMBase
{
LANG: C
SYNC: ML_dtlapse
SYNC: ML_dtshift
SYNC: ML_Gamma
READS: ADMBase::dtlapse
READS: ADMBase::dtshift
READS: grid::coordinates
READS: Grid::coordinates
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
WRITES: ML_BSSN_MP::ML_dtlapse
WRITES: ML_BSSN_MP::ML_dtshift
WRITES: ML_BSSN_MP::ML_Gamma
} "ML_BSSN_MP_convertFromADMBaseGamma"
}
schedule ML_BSSN_MP_RHS1 IN ML_BSSN_MP_evolCalcGroup
{
LANG: C
READS: grid::coordinates
READS: Grid::coordinates
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_dtlapse
READS: ML_BSSN_MP::ML_dtshift
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
READS: TmunuBase::stress_energy_scalar
READS: TmunuBase::stress_energy_tensor
READS: TmunuBase::stress_energy_vector
WRITES: ML_BSSN_MP::ML_dtlapserhs
WRITES: ML_BSSN_MP::ML_dtshiftrhs
WRITES: ML_BSSN_MP::ML_Gammarhs
WRITES: ML_BSSN_MP::ML_lapserhs
WRITES: ML_BSSN_MP::ML_log_confacrhs
WRITES: ML_BSSN_MP::ML_metricrhs
WRITES: ML_BSSN_MP::ML_shiftrhs
WRITES: ML_BSSN_MP::ML_trace_curvrhs
} "ML_BSSN_MP_RHS1"
schedule ML_BSSN_MP_RHS2 IN ML_BSSN_MP_evolCalcGroup
{
LANG: C
READS: grid::coordinates
READS: Grid::coordinates
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
READS: TmunuBase::stress_energy_scalar
READS: TmunuBase::stress_energy_tensor
READS: TmunuBase::stress_energy_vector
WRITES: ML_BSSN_MP::ML_curvrhs
} "ML_BSSN_MP_RHS2"
if (CCTK_EQUALS(apply_dissipation, "always"))
{
schedule ML_BSSN_MP_Dissipation IN ML_BSSN_MP_evolCalcGroup AFTER (ML_BSSN_MP_RHS1 ML_BSSN_MP_RHS2)
{
LANG: C
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_curvrhs
READS: ML_BSSN_MP::ML_dtlapse
READS: ML_BSSN_MP::ML_dtlapserhs
READS: ML_BSSN_MP::ML_dtshift
READS: ML_BSSN_MP::ML_dtshiftrhs
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_Gammarhs
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_lapserhs
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_log_confacrhs
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_metricrhs
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_shiftrhs
READS: ML_BSSN_MP::ML_trace_curv
READS: ML_BSSN_MP::ML_trace_curvrhs
WRITES: ML_BSSN_MP::ML_curvrhs
WRITES: ML_BSSN_MP::ML_dtlapserhs
WRITES: ML_BSSN_MP::ML_dtshiftrhs
WRITES: ML_BSSN_MP::ML_Gammarhs
WRITES: ML_BSSN_MP::ML_lapserhs
WRITES: ML_BSSN_MP::ML_log_confacrhs
WRITES: ML_BSSN_MP::ML_metricrhs
WRITES: ML_BSSN_MP::ML_shiftrhs
WRITES: ML_BSSN_MP::ML_trace_curvrhs
} "ML_BSSN_MP_Dissipation"
}
schedule ML_BSSN_MP_Advect IN ML_BSSN_MP_evolCalcGroup AFTER (ML_BSSN_MP_RHS1 ML_BSSN_MP_RHS2)
{
LANG: C
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_curvrhs
READS: ML_BSSN_MP::ML_dtlapse
READS: ML_BSSN_MP::ML_dtlapserhs
READS: ML_BSSN_MP::ML_dtshift
READS: ML_BSSN_MP::ML_dtshiftrhs
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_Gammarhs
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_lapserhs
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_log_confacrhs
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_metricrhs
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_shiftrhs
READS: ML_BSSN_MP::ML_trace_curv
READS: ML_BSSN_MP::ML_trace_curvrhs
WRITES: ML_BSSN_MP::ML_curvrhs
WRITES: ML_BSSN_MP::ML_dtlapserhs
WRITES: ML_BSSN_MP::ML_dtshiftrhs
WRITES: ML_BSSN_MP::ML_Gammarhs
WRITES: ML_BSSN_MP::ML_lapserhs
WRITES: ML_BSSN_MP::ML_log_confacrhs
WRITES: ML_BSSN_MP::ML_metricrhs
WRITES: ML_BSSN_MP::ML_shiftrhs
WRITES: ML_BSSN_MP::ML_trace_curvrhs
} "ML_BSSN_MP_Advect"
schedule ML_BSSN_MP_InitRHS AT analysis BEFORE ML_BSSN_MP_evolCalcGroup
{
LANG: C
WRITES: ML_BSSN_MP::ML_curvrhs
WRITES: ML_BSSN_MP::ML_dtlapserhs
WRITES: ML_BSSN_MP::ML_dtshiftrhs
WRITES: ML_BSSN_MP::ML_Gammarhs
WRITES: ML_BSSN_MP::ML_lapserhs
WRITES: ML_BSSN_MP::ML_log_confacrhs
WRITES: ML_BSSN_MP::ML_metricrhs
WRITES: ML_BSSN_MP::ML_shiftrhs
WRITES: ML_BSSN_MP::ML_trace_curvrhs
} "ML_BSSN_MP_InitRHS"
if (CCTK_EQUALS(my_rhs_boundary_condition, "static"))
{
schedule ML_BSSN_MP_RHSStaticBoundary IN MoL_CalcRHS
{
LANG: C
WRITES: ML_BSSN_MP::ML_curvrhs
WRITES: ML_BSSN_MP::ML_dtlapserhs
WRITES: ML_BSSN_MP::ML_dtshiftrhs
WRITES: ML_BSSN_MP::ML_Gammarhs
WRITES: ML_BSSN_MP::ML_lapserhs
WRITES: ML_BSSN_MP::ML_log_confacrhs
WRITES: ML_BSSN_MP::ML_metricrhs
WRITES: ML_BSSN_MP::ML_shiftrhs
WRITES: ML_BSSN_MP::ML_trace_curvrhs
} "ML_BSSN_MP_RHSStaticBoundary"
}
schedule ML_BSSN_MP_enforce IN MoL_PostStepModify
{
LANG: C
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_metric
WRITES: ML_BSSN_MP::ML_curv
WRITES: ML_BSSN_MP::ML_lapse
} "ML_BSSN_MP_enforce"
if (CCTK_EQUALS(my_boundary_condition, "Minkowski"))
{
schedule ML_BSSN_MP_boundary IN MoL_PostStep
{
LANG: C
WRITES: ML_BSSN_MP::ML_curv
WRITES: ML_BSSN_MP::ML_dtlapse
WRITES: ML_BSSN_MP::ML_dtshift
WRITES: ML_BSSN_MP::ML_Gamma
WRITES: ML_BSSN_MP::ML_lapse
WRITES: ML_BSSN_MP::ML_log_confac
WRITES: ML_BSSN_MP::ML_metric
WRITES: ML_BSSN_MP::ML_shift
WRITES: ML_BSSN_MP::ML_trace_curv
} "ML_BSSN_MP_boundary"
}
schedule ML_BSSN_MP_convertToADMBase IN ML_BSSN_MP_convertToADMBaseGroup
{
LANG: C
READS: ADMBase::metric
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
WRITES: ADMBase::curv
WRITES: ADMBase::lapse
WRITES: ADMBase::metric
WRITES: ADMBase::shift
} "ML_BSSN_MP_convertToADMBase"
if (CCTK_EQUALS(dt_lapse_shift_method, "correct"))
{
schedule ML_BSSN_MP_convertToADMBaseDtLapseShift IN ML_BSSN_MP_convertToADMBaseGroup
{
LANG: C
SYNC: ADMBase::dtlapse
SYNC: ADMBase::dtshift
READS: grid::coordinates
READS: Grid::coordinates
READS: ML_BSSN_MP::ML_dtlapse
READS: ML_BSSN_MP::ML_dtshift
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
WRITES: ADMBase::dtlapse
WRITES: ADMBase::dtshift
} "ML_BSSN_MP_convertToADMBaseDtLapseShift"
}
if (CCTK_EQUALS(dt_lapse_shift_method, "correct"))
{
schedule ML_BSSN_MP_convertToADMBaseDtLapseShiftBoundary IN ML_BSSN_MP_convertToADMBaseGroup
{
LANG: C
READS: grid::coordinates
READS: Grid::coordinates
READS: ML_BSSN_MP::ML_dtlapse
READS: ML_BSSN_MP::ML_dtshift
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
WRITES: ADMBase::dtlapse
WRITES: ADMBase::dtshift
} "ML_BSSN_MP_convertToADMBaseDtLapseShiftBoundary"
}
if (CCTK_EQUALS(dt_lapse_shift_method, "noLapseShiftAdvection"))
{
schedule ML_BSSN_MP_convertToADMBaseFakeDtLapseShift IN ML_BSSN_MP_convertToADMBaseGroup
{
LANG: C
READS: grid::coordinates
READS: Grid::coordinates
READS: ML_BSSN_MP::ML_dtlapse
READS: ML_BSSN_MP::ML_dtshift
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
WRITES: ADMBase::dtlapse
WRITES: ADMBase::dtshift
} "ML_BSSN_MP_convertToADMBaseFakeDtLapseShift"
}
schedule group ML_BSSN_MP_constraints1_group in MoL_PseudoEvolution after MoL_PostStep
{
# no language specified
} "ML_BSSN_MP_constraints1"
schedule ML_BSSN_MP_constraints1 in ML_BSSN_MP_constraints1_group
{
LANG: C
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
READS: TmunuBase::stress_energy_scalar
READS: TmunuBase::stress_energy_tensor
READS: TmunuBase::stress_energy_vector
WRITES: ML_BSSN_MP::ML_Ham
} "ML_BSSN_MP_constraints1"
schedule ML_BSSN_MP_constraints1_SelectBCs in ML_BSSN_MP_constraints1_bc_group
{
LANG: C
OPTIONS: level
SYNC: ML_Ham
} "ML_BSSN_MP_constraints1_SelectBCs"
schedule group ApplyBCs as ML_BSSN_MP_constraints1_ApplyBCs in ML_BSSN_MP_constraints1_bc_group after ML_BSSN_MP_constraints1_SelectBCs
{
# no language specified
} "Apply BCs for groups set in ML_BSSN_MP_constraints1"
schedule group ML_BSSN_MP_constraints1_bc_group in ML_BSSN_MP_constraints1_group after ML_BSSN_MP_constraints1
{
# no language specified
} "ML_BSSN_MP_constraints1"
schedule group ML_BSSN_MP_constraints1_bc_group in MoL_PseudoEvolutionBoundaries after MoL_PostStep
{
# no language specified
} "ML_BSSN_MP_constraints1"
schedule group ML_BSSN_MP_constraints2_group in MoL_PseudoEvolution after MoL_PostStep
{
# no language specified
} "ML_BSSN_MP_constraints2"
schedule ML_BSSN_MP_constraints2 in ML_BSSN_MP_constraints2_group
{
LANG: C
READS: ML_BSSN_MP::ML_curv
READS: ML_BSSN_MP::ML_Gamma
READS: ML_BSSN_MP::ML_lapse
READS: ML_BSSN_MP::ML_log_confac
READS: ML_BSSN_MP::ML_metric
READS: ML_BSSN_MP::ML_shift
READS: ML_BSSN_MP::ML_trace_curv
READS: TmunuBase::stress_energy_scalar
READS: TmunuBase::stress_energy_tensor
READS: TmunuBase::stress_energy_vector
WRITES: ML_BSSN_MP::ML_cons_detg
WRITES: ML_BSSN_MP::ML_cons_Gamma
WRITES: ML_BSSN_MP::ML_cons_traceA
WRITES: ML_BSSN_MP::ML_mom
} "ML_BSSN_MP_constraints2"
schedule ML_BSSN_MP_constraints2_SelectBCs in ML_BSSN_MP_constraints2_bc_group
{
LANG: C
OPTIONS: level
SYNC: ML_cons_detg
SYNC: ML_cons_Gamma
SYNC: ML_cons_traceA
SYNC: ML_mom
} "ML_BSSN_MP_constraints2_SelectBCs"
schedule group ApplyBCs as ML_BSSN_MP_constraints2_ApplyBCs in ML_BSSN_MP_constraints2_bc_group after ML_BSSN_MP_constraints2_SelectBCs
{
# no language specified
} "Apply BCs for groups set in ML_BSSN_MP_constraints2"
schedule group ML_BSSN_MP_constraints2_bc_group in ML_BSSN_MP_constraints2_group after ML_BSSN_MP_constraints2
{
# no language specified
} "ML_BSSN_MP_constraints2"
schedule group ML_BSSN_MP_constraints2_bc_group in MoL_PseudoEvolutionBoundaries after MoL_PostStep
{
# no language specified
} "ML_BSSN_MP_constraints2"
schedule ML_BSSN_MP_SelectBoundConds in MoL_PostStep
{
LANG: C
OPTIONS: level
SYNC: ML_curv
SYNC: ML_dtlapse
SYNC: ML_dtshift
SYNC: ML_Gamma
SYNC: ML_lapse
SYNC: ML_log_confac
SYNC: ML_metric
SYNC: ML_shift
SYNC: ML_trace_curv
} "select boundary conditions"
schedule ML_BSSN_MP_CheckBoundaries at BASEGRID
{
LANG: C
OPTIONS: meta
} "check boundaries treatment"
schedule ML_BSSN_MP_RegisterVars in MoL_Register
{
LANG: C
OPTIONS: meta
} "Register Variables for MoL"
schedule group ApplyBCs as ML_BSSN_MP_ApplyBCs in MoL_PostStep after ML_BSSN_MP_SelectBoundConds
{
# no language specified
} "Apply boundary conditions controlled by thorn Boundary"
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