## Interpatch Interpolation

April 20, 2017

Abstract

The Interpolate2 thorn provides interpatch interpolation.

### 1 Overview

The interpolator works in several steps.

In the ﬁrst step, during startup, it decides which points need to be set via interpolation. This is usually a layer N grid points deep at the boundaries of the patches, excluding ghost zones, and also excluding the outer boundaries.

After each regridding, the Coordinates thorn iterates over these grid points, converts their locations to global coordinates, and ﬁnds out which patch “owns” each location. It then assumes that this location is suﬃciently far in the interior of the patch that one can apply a full interpolation stencil there. That is, the interpolation source must be surrounded by suﬃciently many ghost zones, outer boundary points, or additional overlap points that the stencil does not include any other inter-patch boundary points. This condition depends, among other things, on the grid spacings in the patches, and thus there is no generic rule. It is tested each time via a dummy interpolation.

At this point, Interpolate2 also calculates and stores the weights for the interpolation stencils, because calculating them is somewhat expensive. If the interpolation point is on a 2D plane, 1D line, or on a grid point (with a small tolerance of about $1{0}^{-12}$), then the interpolation dimension is reduced, so that either 2D or 1D interpolation is performed whenever possible, or even “0D” interpolation (i.e. copying of grid points).

Finally, each time the symmetry boundary conditions are applied, these stencils are evaluated and the result transferred (via MPI) to the target process.

Interpolate2 provides the same interface as Interpolate, but it uses the CarpetInterp2 thorn to perform the actual interpolation instead of CarpetInterp. This is more eﬃcient.

### 2 Parameters

 continue_if_selftest_fails Scope: private BOOLEAN Description: Continue if the self test fails – this is only for debugging Default: no

 ﬁll_patch0_radius_max Scope: private REAL Description: Interpolate to patch 0 up to this radius Range Default: 1e+30 0.0:*

 ﬁll_patch0_radius_min Scope: private REAL Description: Interpolate to patch 0 from this radius on Range Default: 1e+30 0.0:*

 ﬁll_patch0_xyradius_max Scope: private REAL Description: Interpolate to patch 0 up to this cylindrical radius in the x-y plane Range Default: 1e+30 0.0:*

 ﬁll_patch0_xyradius_min Scope: private REAL Description: Interpolate to patch 0 from this cylindrical radius in the x-y plane on Range Default: 1e+30 0.0:*

 interpolate_zero Scope: private BOOLEAN Description: Set interpolation result to zero – this is only for debugging Default: no

 interpolator_order Scope: private INT Description: Interpolation order Range Default: 4 0:*

 interpolator_order_matter Scope: private INT Description: Interpolation order for those variables having an ’interpolator=matter’ tag Range Default: -1 -1 Don’t use special matter interpolator 1 1st-order Lagrange 2 2nd order ENO

 poison Scope: private REAL Description: Poison value to detect uninitialised variables Range Default: -4.2e+20 *:*

 shift_edges Scope: private BOOLEAN Description: Artiﬁcially shift coordinates of grid function edges (use this for DGFE) Default: no

 verbose Scope: private BOOLEAN Description: Produce debug output Default: no

### 3 Interfaces

Implements:

interpolate

Inherits:

coordinates

grid

#### Grid Variables

##### 3.0.1 PRIVATE GROUPS
 Group Names Variable Names Details test compact 0 test description Test grid function dimensions 3 distribution DEFAULT group type GF tags tensortypealias=”Scalar” Checkpoint=”no” Prolongation=”none” timelevels 1 variable type REAL

##### 3.0.2 PUBLIC GROUPS
 Group Names Variable Names Details source_patch compact 0 Sn description source patch number description -1 for interior points Sn description -2 for outer boundary points Sn description -3 for inter-processor ghost points dimensions 3 distribution DEFAULT group type GF tags Checkpoint=”no” Prolongation=”none” timelevels 1 variable type INT

tensortypes.h

loopcontrol.h

carpetinterp2.hh

### 4 Schedule

This section lists all the variables which are assigned storage by thorn Llama/Interpolate2. 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: Conditional: source_patch test

#### Scheduled Functions

CCTK_BASEGRID

interpolate2init

initialise interpolating inter-patch boundaries

 After: choosepatchsystem correctcoordinates spatialcoordinates coordinates_setglobalcoords_group Language: c Type: function

CCTK_BASEGRID

interpolate2test

test interpolating inter-patch boundaries

 After: interpolate2init Storage: test Type: group

Interpolate2Test

interpolate2testinit

test: initialise test grid function

 Language: c Type: function

Interpolate2Test

interpolate2testselectbcs

test: interpolate test grid function

 After: interpolate2testinit Language: c Options: level Sync: test Type: function

Interpolate2Test

applybcs

test: interpolate test grid function

 After: interpolate2testselectbcs Options: level Type: group

Interpolate2Test

interpolate2testcheck

test: check test grid function

 After: interpolate2testapplybcs Language: c Type: function

BoundaryConditions

interpolate2applybc

apply interpolating inter-patch boundaries

 Language: c Options: level Type: function

#### Aliased Functions

 Alias Name: Function Name: ApplyBCs Interpolate2TestApplyBCs