Chapter 4: Interpolation and update operations

4.1 Interpolation

4.1.1 Main procedures involved

Agrif_Set_BcInterp() : Type of interpolation at boundaries

Agrif_Set_Bc() : Where to interpolate

Agrif_Bc_Variable() : Make a boundary interpolation

Agrif_Set_Interp() : Type of interpolation within the domain

Agrif_Interp_Variable() : Make an interior interpolation

Agrif_Init_Variable() : To interpolate over the whole domain (within the domain and boundaries)

4.1.2 Interpolation: how to specify where to interpolate ?

1. Agrif_Set_Bc

Agrif_Set_Bc(variable_id,point)

with point = (/begin,end/)

Examples:

Centered variables

point=(/0,0/)

_images/grille_T_1D_0_0.png

point=(/-1,-1/)

_images/grille_T_1D_m1_m1.png

point=(/0,1/)

_images/grille_T_1D_01_01.png

Location specification in case of interpolation of centered variable (T) in 1D

Noncentered variables:

point=(/0,0/)

_images/grille_U_1D_0_0.png

point=(/-1,-1/)

_images/grille_U_1D_m1_m1.png

point=(/0,1/)

_images/grille_U_1D_01_01.png

Location specification in case of interpolation of Noncentered variable (U) in 1D

2. Agrif_Set_BcInterp

Agrif_Set_BcInterp(Variable_id,interp=Agrif_Interp_Type)

The default value of agrif_interp_type is agrif_constant .

Interpolation schemes

  Order Conservative Monotone
Agrif_constant 0 X X
Agrif_linear 1    
Agrif_linear_conserv 1 X  
Agrif_linear_conservlim 1 X X
Agrif_lagrange 2    
Agrif_ppm 2 X X
Agrif_eno 2 X  
Agrif_weno 3 X  

Examples:

1D
Call Agrif_Set_BcInterp(u_id,interp = Agrif_linear)

2D
Call Agrif_Set_BcInterp(u_id,interp = Agrif_linear)
or
Call  Agrif_Set_BcInterp(u_id,interp2 = Agrif_PPM)
or
Call Agrif_Set_BcInterp(u_id, interp1 = Agrif_PPM, interp2 = Agrif_PPM)

Note

  • Interp1 indicates interpolation in the first dimension
  • Interp2 indicates interpolation in the second dimension

4.1.3 The call: Agrif_Bc_Variable

1. Agrif_Bc_Variable

Agrif_Bc_Variable(variable_id,procname)

Example: procname Interp_MyTraceur

Call Agrif_Bc_Variable(u_id,procname=Interp_MyTraceur)

Algorithm of procname’s call

  1. AGRIF calls procname on the coarse grid with before = .TRUE. output array : tabres
  2. AGRIF interpolates tabres on the fine grid
  3. AGRIF calls procname on the fine grid with before = .FALSE. input array : tabres
_images/Algorithm_interpolation.png

Algorithm of procname’s call by AGRIF for interpolation

  Subroutine Interp_My_Traceur(tabres,i1,i2,before)

       use module_My_traceur

       real,dimension(i1:i2),intent(out) :: tabres

       Logical :: before

       if (before) then     ! on parent grid

               tabres(i1:i2) = My_traceur(i1:i2)

       else                 ! on child grid

               My_traceur(i1:i2) = tabres(i1:i2)

       endif


End Subroutine Interp_MyTraceur

4.1.4 Time interpolation

1. How are time interpolations handle ?

_images/ngridstep_counter.png

Grid step counters Agrif_Nb_Step() and Agrif_Nbstepint() with a time refinement factor of 2

_images/ngridstep_counter_2.png

Description of time interpolation

2. Agrif_Bc_Variable

Agrif_Bc_Variable (variable_id,procname,calledweight= \(\alpha\))

Inside AGRIF, the spatial interpolation is done only when the time index of the parent grid changes. So, the spatial interpolation is done at the first call of Agrif_Bc_Variable inside a parent grid time step.

_images/ngridstep_counter_3.png

Description of Agrif_Nbstepint

Note

  • In order to interpolate the very first parent field, a call to Agrif_Bc_Variable() in the Agrif_Initvalues procedure is mandatory.
  • To force an interpolation (even if the parent grid index has not changed)

Call Agrif_Set_Bc(variable_id,point,Interpolationshouldbemade=.TRUE.)

4.1.5 Interpolation over the whole domain

The interpolation over the whole domain is done through the subroutine Agrif_Init_Variable() .

In fact, Agrif_Init_Variable() represents an addition of interpolation within the domain made through a call to the subroutine Agrif_Interp_Variable() and interpolation at boundaries made through a call to Agrif_Bc_Variable() . Interpolation with the subroutine Agrif_Interp_Variable() is made from the first point within the domain to the last point within the domain.

It is important to notice that for boundary interpolation we use the subroutine Agrif_Set_bcinterp to indicate the type of interpolation and the subroutine Agrif_Set_interp() in case of interpolation within the domain. All those two subroutines use the same arguments.

Agrif_Init_Variable() = call to Agrif_Interp_Variable() + call to Agrif_Bc_Variable()

Example :

  • Centered points (T):
_images/grille_T_update_1D.png

Interpolation of centered point (T)

  • NonCentered points (U):
_images/grille_U_update_1D.png

Interpolation of non-centered point (U)

4.1.6 Treatment of masked fields

Agrif_SpecialValue: replacement of masked values by neighboring values.

It must be set before the call to Agrif_Bc_Variable() , Agrif_Interp_Variable() .

Agrif_UseSpecialValue= .true.

Agrif_SpecialValue = Val

Examples:

Agrif_UseSpecialValue=.true.

Agrif_SpecialValue=0.

Call Agrif_Bc_Variable(variable_Id,procname)

Agrif_UseSpecialValue=.false.

Note

  • Setting maximum lookup of masked values (since it may affect performance).

    Call Agrif_Set_MaskMaxSearch ( mymaxsearch )

    Defaut Value: MaxSearch = 5

4.2 Updates

4.2.1 Main procedures involved

Agrif_Set_UpdateType() : Type of update

Agrif_Update_Variable() : Make the restriction and specify where to update

4.2.2 Update: how to specify the type of update ?

The type of update has to be indicated through the subroutine Agrif_Set_UpdateType().

1. Agrif_Set_UpdateType

Agrif_Set_UpdateType(variable_id,update = Agrif_Update_Type)

The keyword Agrif_Update_Type should be either Agrif_Update_Copy, Agrif_Update_Average or Agrif_Update_Full_Weighting .

2. Update schemes

Examples:

1D
Call Agrif_Set_UpdateType(variable_id,update = Agrif_average)

2D
Call Agrif_Set_UpdateType(variable_id,update = Agrif_average) ! same update scheme in all directions
Call Agrif_Set_UpdateType(variable_id,update1 = Agrif_Copy, update2 = Agrif_Average)

Example with the space refinement of 3

_images/relative_position_1D_update.png

Relative positions of coarse and fine points with space refinement of 3

copy: \(T^c = T^f(0)\)

Average: \(T^c = \frac{1}{3}[T^f(-1)+T^f(0)+T^f(1)]\)

FW: \(T^c = \frac{1}{9}[T^f(-2)+2T^f(-1)+3T^f(0)+2T^f(1)+T^f(2)]\)

4.2.3 The call: Agrif_Update_Variable

Agrif_Update_Variable(variable_id,locupdate,procname)

Example:

Call Agrif_Update_Variable(u_id,locupdate=(/0,0/), procname=Update_MyTraceur)

Note

  • locupdate is an optional keyword that indicates the location where the update takes place.

4.2.4 Specify locations you want to update

1. Without locupdate keyword

Agrif_Update_Variable(variable_id,procname)

Note

Default location without locupdate keyword is interior of the reference grid

Examples:

  • Centered variable:
_images/grille_T_update_1D.png

Update the centered variable without locupdate keyword

  • Noncentered variable:
_images/grille_U_update_1D.png

Update the Noncentered variable without locupdate keyword

2. With locupdate keyword

Agrif_Update_Variable(variable_id,locupdate,procname)

Note

  • Update is done on limited areas

  • For multidimension we set the keyword as:

    locupdate1=... , locupdate2 = ...

Examples

  • Centered points:

locupdate=(/0,0/)

_images/grille_T_update_1D_0_0.png

locupdate=(/1,1/)

_images/grille_T_update_1D_1_1.png

locupdate=(/0,1/)

_images/grille_T_update_1D_0_1.png

locupdate=(/1,0/)

_images/grille_T_update_1D_1_0.png

Update of centered points(T) with locupdate keyword

  • Non centered points:

locupdate=(/0,0/)

_images/grille_U_update_1D_0_0.png

locupdate=(/1,1/)

_images/grille_U_update_1D_1_1.png

locupdate=(/0,1/)

_images/grille_U_update_1D_0_1.png

locupdate=(/1,0/)

_images/grille_U_update_1D_1_0.png

Update of non-centered points (U) with locupdate keyword

4.2.5 The use of procnames

1. Agrif_Update_Variable

Agrif_Update_Variable(variable_id,procname)

Call Agrif_Update_Variable(variable_id,procname=Update_MyTraceur)

Algorithm of procname’s call

  1. AGRIF calls procname on the child grid with before = .TRUE. output array : tabres
  2. AGRIF updates tabres on the parent grid
  3. AGRIF calls procname on the coarse grid with before = .FALSE. input array : tabres
_images/Algorithm_update.png

Algorithm of procname’s call by AGRIF for update

Subroutine Update_My_Traceur(tabres,i1,i2,before)

        use module_My_traceur

        real,dimension(i1:i2),intent(inout) :: tabres

        logical :: before

        If (before) then      ! on the child grid

                tabres(i1:i2) = My_traceur(i1:i2)

        Else                  ! on the parent grid

                My_traceur(i1:i2) = tabres(i1:i2)

        Endif

End Subroutine Update_My_Traceur

4.2.6 Treatment of masked fields

Agrif_SpecialValue_InfineGrid: the masked values are not taken into account in the restriction operation

Agrif_UseSpecialValueInUpdate = .true.

Agrif_SpecialValueFineGrid = Val

must be set before the call to Agrif_Update_Variable()

Examples:

Agrif_UseSpecialValueInUpdate=.true.

Agrif_SpecialValueFineGrid=0.

Call Agrif_Update_Variable(variable_id,procname=Update_MyTraceur)

Agrif_UseSpecialValueInUpdate=.false.