CalcK — Calculate \(K_{ij}\)

Erik Schnetter <schnetter@aei.mpg.de>

\( \)Date\( \)

Abstract

Calculate the extrinsic curvature \(K_{ij}\) from several time levels of the three-metric \(\gamma _{ij}\), lapse \(\alpha \), and shift \(\beta ^i\).

1 Introduction

2 Physical System

3 Numerical Implementation

4 Using This Thorn

4.1 Obtaining This Thorn

4.2 Basic Usage

4.3 Special Behaviour

4.4 Interaction With Other Thorns

4.5 Examples

4.6 Support and Feedback

5 History

5.1 Thorn Source Code

5.2 Thorn Documentation

5.3 Acknowledgements

References

6 Parameters

calc_extcurv
 Scope: private BOOLEAN
Description: Calculate extrinsic curvature
Default: no

copy_to_next
 Scope: private BOOLEAN
Description: Copy ADMBase::metric to CalcK::metric_next
Default: no

copy_to_prev
 Scope: private BOOLEAN
Description: Copy ADMBase::metric to CalcK::metric_prev
Default: no

copy_to_prev2
 Scope: private BOOLEAN
Description: Copy ADMBase::metric to CalcK::metric_prev2
Default: no

extcurv_boundary
 Scope: private STRING
Description: Boundary condition for the extrinsic curvature
Range Default: Robin
.*
must be a registered boundary condition

extcurv_boundary_options
 Scope: private STRING
Description: Options for the boundry condition for the extrinsic curvature
Range Default: decay_power=2.0
.*
must have the options table syntax

metric_type
 Scope: shared from ADMBASEKEYWORD

7 Interfaces

General

Implements:

calck

Inherits:

admbase

staticconformal

Grid Variables

7.0.1 PRIVATE GROUPS

  Group Names     Variable Names   Details    
metric_prev compact 0
gxx_prev description ADM 3-metric
  description previous time
gxy_prev dimensions 3
gxz_prev distribution DEFAULT
gyy_prev group type GF
gyz_prev timelevels 1
gzz_prev variable type REAL
metric_prev2 compact 0
gxx_prev2 description ADM 3-metric
  description pre-previous time
gxy_prev2 dimensions 3
gxz_prev2 distribution DEFAULT
gyy_prev2 group type GF
gyz_prev2 timelevels 1
gzz_prev2 variable type REAL
metric_next compact 0
gxx_next description ADM 3-metric
  description next time
gxy_next dimensions 3
gxz_next distribution DEFAULT
gyy_next group type GF
gyz_next timelevels 1
gzz_next variable type REAL

8 Schedule

This section lists all the variables which are assigned storage by thorn EinsteinAnalysis/CalcK. 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

 

Always:  
metric_prev metric_prev2 metric_next  
   

Scheduled Functions

CCTK_POSTINITIAL (conditional)

  calck_copy_to_prev

  copy admbase::metric to calck::metric_prev

 

  Language: fortran
  Type: function

CCTK_POSTINITIAL (conditional)

  calck_copy_to_prev2

  copy admbase::metric to calck::metric_prev2

 

  Language: fortran
  Type: function

CCTK_POSTINITIAL (conditional)

  calck_copy_to_next

  copy admbase::metric to calck::metric_next

 

  Language: fortran
  Type: function

CCTK_POSTINITIAL (conditional)

  calck

  calculate k_ij from gamma_ij, alpha, and betaî

 

  Language: fortran
  Sync: admbase::curv
  Type: function

CCTK_POSTINITIAL (conditional)

  applybcs

  apply boundary conditions

 

  After: calck
  Type: group

Aliased Functions

 

Alias Name:         Function Name:
ApplyBCs CalcK_ApplyBCs