TestDerivs

Liwei Ji <ljsma@rit.edu>

July 27 2023

Abstract

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


deriv_order	Scope: private	INT

Description: Order of spatial finite differencing

Range		Default: 4
2	Second order finite difference
4	Fourth order finite difference
6	Sixth order finite difference
8	Eighth order finite difference


kxx	Scope: private	REAL

Description: par for polynomial

Range		Default: 0.0
:


kxy	Scope: private	REAL

Description: par for polynomial

Range		Default: 0.0
:


kyz	Scope: private	REAL

Description: par for polynomial

Range		Default: 0.0
:


refined_radius	Scope: private	REAL

Description: size of the refined region at the center

Range		Default: 0.25
(0:*	any positive size

7 Interfaces

General

Implements:

testderivs

Inherits:

carpetxregrid

Grid Variables

7.0.1 PRIVATE GROUPS


Group Names	Variable Names	Details

chi	chi	centering	centering={0 0 0}
		compact	0
		description	Test grid function
		dimensions	3
		distribution	DEFAULT
		group type	GF
		timelevels	1
		variable type	REAL

dchi		centering	centering={0 0 0}
	dxchi	compact	0
	dychi	description	1st derivs of test grid function
	dzchi	dimensions	3
		distribution	DEFAULT
		group type	GF
		tags	checkpoint=”no”
		timelevels	1
		variable type	REAL

ddchi		centering	centering={0 0 0}
	dxxchi	compact	0
	dxychi	description	2nd derivs of test grid function
	dxzchi	dimensions	3
	dyychi	distribution	DEFAULT
	dyzchi	group type	GF
	dzzchi	tags	checkpoint=”no”
		timelevels	1
		variable type	REAL

chi_diss	chi_diss	centering	centering={0 0 0}
		compact	0
		description	dissipation term
		dimensions	3
		distribution	DEFAULT
		group type	GF
		tags	checkpoint=”no”
		timelevels	1
		variable type	REAL

beta		centering	centering={0 0 0}
	betax	compact	0
	betay	description	velocity function used for calculating upwind term
	betaz	dimensions	3
		distribution	DEFAULT
		group type	GF
		timelevels	1
		variable type	REAL

chi_upwind	chi_upwind	centering	centering={0 0 0}
		compact	0
		description	upwind term
		dimensions	3
		distribution	DEFAULT
		group type	GF
		tags	checkpoint=”no”
		timelevels	1
		variable type	REAL


Group Names	Variable Names	Details

dchi_error		centering	centering={0 0 0}
	dxchi_error	compact	0
	dychi_error	description	error of 1st derivs of test grid function
	dzchi_error	dimensions	3
		distribution	DEFAULT
		group type	GF
		tags	checkpoint=”no”
		timelevels	1
		variable type	REAL

ddchi_error		centering	centering={0 0 0}
	dxxchi_error	compact	0
	dxychi_error	description	error of 2nd derivs of test grid function
	dxzchi_error	dimensions	3
	dyychi_error	distribution	DEFAULT
	dyzchi_error	group type	GF
	dzzchi_error	tags	checkpoint=”no”
		timelevels	1
		variable type	REAL

chi_diss_error	chi_diss_error	centering	centering={0 0 0}
		compact	0
		description	error in dissipation term
		dimensions	3
		distribution	DEFAULT
		group type	GF
		tags	checkpoint=”no”
		timelevels	1
		variable type	REAL

chi_upwind_error	chi_upwind_error	centering	centering={0 0 0}
		compact	0
		description	error in upwind term
		dimensions	3
		distribution	DEFAULT
		group type	GF
		tags	checkpoint=”no”
		timelevels	1
		variable type	REAL

Uses header:

defs.hxx

loop_device.hxx

simd.hxx

vect.hxx

derivs.hxx

8 Schedule

This section lists all the variables which are assigned storage by thorn CarpetX/TestDerivs. 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:
chi
dchi
ddchi

Scheduled Functions

CCTK_POSTINITIAL

testderivs_seterror

set up test grid

	Language:	c
	Type:	function
	Writes:	carpetxregrid::regrid_error(interior)

CCTK_INITIAL

testderivs_set

set up test data

	Language:	c
	Sync:	chi
		beta
	Type:	function
	Writes:	chi(interior)
		beta(interior)

CCTK_POSTREGRID

testderivs_sync

synchronize

	Language:	c
	Options:	global
	Sync:	chi
	Type:	function

CCTK_POSTSTEP

testderivs_calcderivs

calculate derivs

	Language:	c
	Reads:	chi(everywhere)
		beta(interior)
	Sync:	dchi
		ddchi
		chi_diss
		chi_upwind
	Type:	function
	Writes:	dchi(interior)
		ddchi(interior)
		chi_diss(interior)
		chi_upwind(interior)

CCTK_POSTSTEP

testderivs_calcerror

calculate derivs error

	After:	testderivs_calcderivs
	Language:	c
	Reads:	dchi(interior)
		ddchi(interior)
		chi_diss(interior)
		chi_upwind(interior)
	Sync:	dchi_error
		ddchi_error
		chi_diss_error
		chi_upwind_error
	Type:	function
	Writes:	dchi_error(interior)
		ddchi_error(interior)
		chi_diss_error(interior)
		chi_upwind_error(interior)