Added 6-3 minimal bandwidth 2nd derivative operators. Added 4-2 minimal

bandwidth 2nd derivative operators. Moved the 4-2 optimised operators.
Fixed missing break statements get_up_coeffs.c.


git-svn-id: https://svn.cct.lsu.edu/repos/numrel/LSUThorns/SummationByParts/trunk@89 f69c4107-0314-4c4f-9ad4-17e986b73f4a

10 files changed, 591 insertions, 13 deletions

diff --git a/src/All_Coeffs_mod.F90 b/src/All_Coeffs_mod.F90
index 76dfcc9..69e58a9 100644
--- a/src/All_Coeffs_mod.F90
+++ b/src/All_Coeffs_mod.F90
@@ -497,6 +497,7 @@ module All_Coeffs_mod
       q2(7,1) = zero
       q2(8,1) = zero
       q2(9,1) = zero
+
       q2(1,2) = -0.4261090852993166609415800254745304380753_wp
       q2(2,2) = -0.1198701406809289935902771997003246482977_wp
       q2(3,2) = 0.4312121105197350491616311601533345702699_wp
@@ -506,6 +507,7 @@ module All_Coeffs_mod
       q2(7,2) = zero
       q2(8,2) = zero
       q2(9,2) = zero
+
       q2(1,3) = -0.008331409049041400793408941823041323547141_wp
       q2(2,3) = -0.3179917159117626605641230407454828831892_wp
       q2(3,3) = -0.5046108447067502766506824050165990409443_wp
@@ -515,6 +517,7 @@ module All_Coeffs_mod
       q2(7,3) = zero
       q2(8,3) = zero
       q2(9,3) = zero
+
       q2(1,4) = 0.1280751399324364352167190636169803213668_wp
       q2(2,4) = -0.3704544846040473075364791079948980171701_wp
       q2(3,4) = -0.1053961094122492652071919749185808657060_wp
@@ -524,6 +527,7 @@ module All_Coeffs_mod
       q2(7,4) = 0.02687068482925919014741556260496361261429_wp
       q2(8,4) = zero
       q2(9,4) = zero
+
       q2(1,5) = -0.03614399304268576976452921364705641609825_wp
       q2(2,5) = 0.1234319378557362297361923714125920669065_wp
       q2(3,5) = -0.09358865464680026772155005029274896720786_wp
@@ -533,6 +537,7 @@ module All_Coeffs_mod
       q2(7,5) = -0.2742160721086708137615843595277389869240_wp
       q2(8,5) = 0.03656214294782277516821124793703186492319_wp
       q2(9,5) = zero
+
       q2(1,6) = -0.01141318406360863692889821914555232596651_wp
       q2(2,6) = 0.02049729840293952857599941220163960606616_wp
       q2(3,6) = 0.02756893105132916059596754912522489034598_wp
@@ -545,6 +550,78 @@ module All_Coeffs_mod
 
     end subroutine coeffs_up_6_3_opt
 
+    subroutine coeffs_2_6_3 ( a, q )
+
+      CCTK_REAL, dimension(4), intent(OUT) :: a
+      CCTK_REAL, dimension(9,6), intent(OUT) :: q
+
+      a(1) = -2.722222222222222222222222222222222222222_wp
+      a(2) = 1.500000000000000000000000000000000000000_wp
+      a(3) = -0.1500000000000000000000000000000000000000_wp
+      a(4) = 0.01111111111111111111111111111111111111111_wp
+
+      q(1,1) = 2.788238454587637677973966346740908979901_wp
+      q(2,1) = -8.024525606271521723203165067037878232838_wp
+      q(3,1) = 8.215717879209710113072996800742423132342_wp
+      q(4,1) = -3.382384545876376779739663467409089799008_wp
+      q(5,1) = 0.2745256062715217232031650670378782328376_wp
+      q(6,1) = 0.1284282120790289886927003199257576867658_wp
+      q(7,1) = 0_wp
+      q(8,1) = 0_wp
+      q(9,1) = 0_wp
+
+      q(1,2) = 1.053412969283276450511945392491467576792_wp
+      q(2,2) = -2.350398179749715585893060295790671217292_wp
+      q(3,2) = 1.867463026166097838452787258248009101251_wp
+      q(4,2) = -1.034129692832764505119453924914675767918_wp
+      q(5,2) = 0.6003981797497155858930602957906712172924_wp
+      q(6,2) = -0.1367463026166097838452787258248009101251_wp
+      q(7,2) = 0_wp
+      q(8,2) = 0_wp
+      q(9,2) = 0_wp
+
+      q(1,3) = -0.6441780400836099840157383499323742776343_wp
+      q(2,3) = 4.137556867084716586745358416328538054838_wp
+      q(3,3) = -8.108447067502766506824050165990409443010_wp
+      q(4,3) = 6.941780400836099840157383499323742776343_wp
+      q(5,3) = -2.887556867084716586745358416328538054838_wp
+      q(6,3) = 0.5608447067502766506824050165990409443010_wp
+      q(7,3) = 0_wp
+      q(8,3) = 0_wp
+      q(9,3) = 0_wp
+
+      q(1,4) = 0.2133575915904708589911053057162405921503_wp
+      q(2,4) = -1.159078186228774025004665049449524164956_wp
+      q(3,4) = 3.511693723953473906823412328170678609193_wp
+      q(4,4) = -4.723144865335572557069104932512284630217_wp
+      q(5,4) = 2.489690240716551595446911737264415002799_wp
+      q(6,4) = -0.3414753996392361759034645767245132798408_wp
+      q(7,4) = 0.008956894943086396715805187534987870871431_wp
+      q(8,4) = 0_wp
+      q(9,4) = 0_wp
+
+      q(1,5) = -0.1790783293131903008759680081249206550717_wp
+      q(2,5) = 0.9156510515847827006897719097795268926410_wp
+      q(3,5) = -1.987601032541999915365409843002835258770_wp
+      q(4,5) = 3.387647581566586263806017519360162498413_wp
+      q(5,5) = -3.719859506580339384706529558630612331260_wp
+      q(6,5) = 1.735582497566755532986331513689644957894_wp
+      q(7,5) = -0.1645296432652024882569506157166433921544_wp
+      q(8,5) = 0.01218738098260759172273708264567728830773_wp
+      q(9,5) = 0_wp
+
+      q(1,6) = 0.04002001476374207590389869333272451922711_wp
+      q(2,6) = -0.1875223548929628699496967344733377472356_wp
+      q(3,6) = 0.3471267779274445788908929019885390744504_wp
+      q(4,6) = -0.4177910702190969764769449708149737829426_wp
+      q(5,6) = 1.560601736642238000654475164189554271972_wp
+      q(6,6) = -2.684870208442729618045250108445012670944_wp
+      q(7,6) = 1.479418278121504075249423529143170247255_wp
+      q(8,6) = -0.1479418278121504075249423529143170247255_wp
+      q(9,6) = 0.01095865391201114129814387799365311294263_wp
+
+    end subroutine coeffs_2_6_3
+
     subroutine coeffs_1_8_4 ( a, q )
 
       CCTK_REAL, dimension(4), intent(OUT) :: a
diff --git a/src/Coefficients2_4_2.F90 b/src/Coefficients2_4_2.F90
index 14a1cec..5883b02 100644
--- a/src/Coefficients2_4_2.F90
+++ b/src/Coefficients2_4_2.F90
@@ -36,14 +36,14 @@ subroutine set_coeff2_4_2 ( nsize, loc_order, bb, gsize, imin, imax, dd )
   if ( bb(1) == 0 ) then
     il = 1 + gsize
   else
-    dd(1:6,1) = q(1:6,1)
-    imin(1) = 1; imax(1) = 6
+    dd(1:4,1) = q(1:4,1)
+    imin(1) = 1; imax(1) = 4
 
-    dd(1:6,2) = q(1:6,2)
-    imin(2) = 1; imax(2) = 6
+    dd(1:3,2) = q(1:3,2)
+    imin(2) = 1; imax(2) = 3
 
-    dd(1:6,3) = q(1:6,3)
-    imin(3) = 1; imax(3) = 6
+    dd(1:5,3) = q(1:5,3)
+    imin(3) = 1; imax(3) = 5
 
     dd(1:6,4) = q(1:6,4)
     imin(4) = 1; imax(4) = 6
@@ -56,14 +56,14 @@ subroutine set_coeff2_4_2 ( nsize, loc_order, bb, gsize, imin, imax, dd )
     dd(nsize-5:nsize,nsize-3) = q(6:1:-1,4)
     imin(nsize-3) = nsize-5; imax(nsize-3) = nsize
 
-    dd(nsize-5:nsize,nsize-2) = q(6:1:-1,3)
-    imin(nsize-2) = nsize-5; imax(nsize-2) = nsize
+    dd(nsize-4:nsize,nsize-2) = q(5:1:-1,3)
+    imin(nsize-2) = nsize-4; imax(nsize-2) = nsize
 
-    dd(nsize-5:nsize,nsize-1) = q(6:1:-1,2)
-    imin(nsize-1) = nsize-5; imax(nsize-1) = nsize
+    dd(nsize-2:nsize,nsize-1) = q(3:1:-1,2)
+    imin(nsize-1) = nsize-2; imax(nsize-1) = nsize
 
-    dd(nsize-5:nsize,nsize) = q(6:1:-1,1)
-    imin(nsize) = nsize-5; imax(nsize) = nsize
+    dd(nsize-3:nsize,nsize) = q(4:1:-1,1)
+    imin(nsize) = nsize-3; imax(nsize) = nsize
 
     ir = nsize - 4
   end if
diff --git a/src/Coefficients2_4_2_min_err_coeff.F90 b/src/Coefficients2_4_2_min_err_coeff.F90
new file mode 100644
index 0000000..9720d05
--- /dev/null
+++ b/src/Coefficients2_4_2_min_err_coeff.F90
@@ -0,0 +1,74 @@
+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine set_coeff2_4_2_opt ( nsize, loc_order, bb, gsize, imin, imax, dd )
+
+  use All_Coeffs_mod
+
+  implicit none
+
+  DECLARE_CCTK_FUNCTIONS
+  DECLARE_CCTK_PARAMETERS
+
+  CCTK_INT, intent(IN) :: nsize, loc_order
+  CCTK_INT, dimension(2), intent(IN) :: bb
+  CCTK_INT, intent(IN) :: gsize
+  CCTK_INT, dimension(nsize), intent(OUT) :: imin, imax
+  CCTK_REAL, dimension(nsize,nsize), intent(OUT) :: dd
+
+  CCTK_REAL, dimension(3), save :: a
+  CCTK_REAL, dimension(6,4), save :: q 
+
+  CCTK_INT :: i, il, ir
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    call coeffs_2_4_2_opt ( a, q )
+    first = .false.
+  end if
+
+  dd = zero
+  imin = 0
+  imax = 0
+
+  if ( bb(1) == 0 ) then
+    il = 1 + gsize
+  else
+    dd(1:6,1) = q(1:6,1)
+    imin(1) = 1; imax(1) = 6
+
+    dd(1:6,2) = q(1:6,2)
+    imin(2) = 1; imax(2) = 6
+
+    dd(1:6,3) = q(1:6,3)
+    imin(3) = 1; imax(3) = 6
+
+    dd(1:6,4) = q(1:6,4)
+    imin(4) = 1; imax(4) = 6
+
+    il = 5
+  end if
+  if ( bb(2) == 0 ) then
+    ir = nsize - gsize
+  else
+    dd(nsize-5:nsize,nsize-3) = q(6:1:-1,4)
+    imin(nsize-3) = nsize-5; imax(nsize-3) = nsize
+
+    dd(nsize-5:nsize,nsize-2) = q(6:1:-1,3)
+    imin(nsize-2) = nsize-5; imax(nsize-2) = nsize
+
+    dd(nsize-5:nsize,nsize-1) = q(6:1:-1,2)
+    imin(nsize-1) = nsize-5; imax(nsize-1) = nsize
+
+    dd(nsize-5:nsize,nsize) = q(6:1:-1,1)
+    imin(nsize) = nsize-5; imax(nsize) = nsize
+
+    ir = nsize - 4
+  end if
+  do i = il, ir
+    dd(i-2:i-1,i) = a(3:2:-1); dd(i:i+2,i) = a(1:3)
+    imin(i) = i-2; imax(i) = i+2
+  end do
+end subroutine set_coeff2_4_2_opt
diff --git a/src/Coefficients2_6_3.F90 b/src/Coefficients2_6_3.F90
new file mode 100644
index 0000000..3563c48
--- /dev/null
+++ b/src/Coefficients2_6_3.F90
@@ -0,0 +1,86 @@
+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine set_coeff2_6_3 ( nsize, loc_order, bb, gsize, imin, imax, dd )
+
+  use All_Coeffs_mod
+
+  implicit none
+
+  DECLARE_CCTK_FUNCTIONS
+  DECLARE_CCTK_PARAMETERS
+
+  CCTK_INT, intent(IN) :: nsize, loc_order
+  CCTK_INT, dimension(2), intent(IN) :: bb
+  CCTK_INT, intent(IN) :: gsize
+  CCTK_INT, dimension(nsize), intent(OUT) :: imin, imax
+  CCTK_REAL, dimension(nsize,nsize), intent(OUT) :: dd
+
+  CCTK_REAL, dimension(4), save :: a
+  CCTK_REAL, dimension(9,6), save :: q 
+
+  CCTK_INT :: i, il, ir
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    call coeffs_2_6_3 ( a, q )
+    first = .false.
+  end if
+
+  dd = zero
+  imin = 0
+  imax = 0
+
+  if ( bb(1) == 0 ) then
+    il = 1 + gsize
+  else
+    dd(1:6,1) = q(1:6,1)
+    imin(1) = 1; imax(1) = 6
+
+    dd(1:6,2) = q(1:6,2)
+    imin(2) = 1; imax(2) = 6
+
+    dd(1:6,3) = q(1:6,3)
+    imin(3) = 1; imax(3) = 6
+
+    dd(1:7,4) = q(1:7,4)
+    imin(4) = 1; imax(4) = 7
+
+    dd(1:8,5) = q(1:8,5)
+    imin(5) = 1; imax(5) = 8
+
+    dd(1:9,6) = q(1:9,6)
+    imin(6) = 1; imax(6) = 9
+
+    il = 7
+  end if
+  if ( bb(2) == 0 ) then
+    ir = nsize - gsize
+  else
+    dd(nsize-8:nsize,nsize-5) = q(9:1:-1,6)
+    imin(nsize-5) = nsize-8; imax(nsize-5) = nsize
+
+    dd(nsize-7:nsize,nsize-4) = q(8:1:-1,5)
+    imin(nsize-4) = nsize-7; imax(nsize-4) = nsize
+
+    dd(nsize-6:nsize,nsize-3) = q(7:1:-1,4)
+    imin(nsize-3) = nsize-6; imax(nsize-3) = nsize
+
+    dd(nsize-5:nsize,nsize-2) = q(6:1:-1,3)
+    imin(nsize-2) = nsize-5; imax(nsize-2) = nsize
+
+    dd(nsize-5:nsize,nsize-1) = q(6:1:-1,2)
+    imin(nsize-1) = nsize-5; imax(nsize-1) = nsize
+
+    dd(nsize-5:nsize,nsize) = q(6:1:-1,1)
+    imin(nsize) = nsize-5; imax(nsize) = nsize
+
+    ir = nsize - 6
+  end if
+  do i = il, ir
+    dd(i-3:i-1,i) = a(4:2:-1); dd(i:i+3,i) = a(1:4)
+    imin(i) = i-3; imax(i) = i+3
+  end do
+end subroutine set_coeff2_6_3
diff --git a/src/Derivatives2_6_3.F90 b/src/Derivatives2_6_3.F90
new file mode 100644
index 0000000..63bf6b8
--- /dev/null
+++ b/src/Derivatives2_6_3.F90
@@ -0,0 +1,294 @@
+#include "cctk.h"
+#include "cctk_Functions.h"
+#include "cctk_Parameters.h"
+
+subroutine deriv2_gf_6_3 ( var, ni, nj, nk, dir, bb, gsize, delta, dvar2 )
+
+  use All_Coeffs_mod
+
+  implicit none
+
+  DECLARE_CCTK_FUNCTIONS
+  DECLARE_CCTK_PARAMETERS
+
+  CCTK_INT, intent(IN) :: ni, nj, nk
+  CCTK_REAL, dimension(ni,nj,nk), intent(IN) :: var
+  CCTK_INT, intent(IN) :: dir
+  CCTK_INT, intent(IN) :: bb(2)
+  CCTK_INT, intent(IN) :: gsize
+  CCTK_REAL, intent(IN) :: delta
+  CCTK_REAL, dimension(ni,nj,nk), intent(OUT) :: dvar2
+
+  CCTK_REAL, dimension(4), save :: a
+  CCTK_REAL, dimension(9,6), save :: q 
+  CCTK_REAL :: idel2
+
+  CCTK_INT :: il, ir, jl, jr, kl, kr
+
+  logical, save :: first = .true.
+
+  if ( first ) then
+    call coeffs_2_6_3 ( a, q )
+    first = .false.
+  end if
+
+  idel2 = 1.0_wp / delta**2
+
+  direction: select case (dir)
+  case (0) direction
+    if ( bb(1) == 0 ) then
+      il = 1 + gsize
+    else
+      dvar2(1,:,:) = ( q(1,1) * var(1,:,:) + q(2,1) * var(2,:,:)  + &
+                       q(3,1) * var(3,:,:) + q(4,1) * var(4,:,:) + &
+                       q(5,1) * var(4,:,:) + q(6,1) * var(6,:,:) ) * idel2
+      dvar2(2,:,:) = ( q(1,2) * var(1,:,:) + q(2,2) * var(2,:,:) + &
+                       q(3,2) * var(3,:,:) + q(4,2) * var(4,:,:) + &
+                       q(5,2) * var(5,:,:) + q(6,2) * var(6,:,:) ) * idel2
+      dvar2(3,:,:) = ( q(1,3) * var(1,:,:) + q(2,3) * var(2,:,:) + &
+                       q(3,3) * var(3,:,:) + q(4,3) * var(4,:,:) + &
+                       q(5,3) * var(5,:,:) + q(6,3) * var(6,:,:) ) * idel2
+      dvar2(4,:,:) = ( q(1,4) * var(1,:,:) + q(2,4) * var(2,:,:) + &
+                       q(3,4) * var(3,:,:) + q(4,4) * var(4,:,:) + &
+                       q(5,4) * var(5,:,:) + q(6,4) * var(6,:,:) + &
+                       q(7,4) * var(7,:,:) ) * idel2
+      dvar2(5,:,:) = ( q(1,5) * var(1,:,:) + q(2,5) * var(2,:,:) + &
+                       q(3,5) * var(3,:,:) + q(4,5) * var(4,:,:) + &
+                       q(5,5) * var(5,:,:) + q(6,5) * var(6,:,:) + &
+                       q(7,5) * var(7,:,:) + q(8,6) * var(8,:,:) ) * idel2
+      dvar2(6,:,:) = ( q(1,6) * var(1,:,:) + q(2,6) * var(2,:,:) + &
+                       q(3,6) * var(3,:,:) + q(4,6) * var(4,:,:) + &
+                       q(5,6) * var(5,:,:) + q(6,6) * var(6,:,:) + &
+                       q(7,6) * var(7,:,:) + q(8,6) * var(8,:,:) + &
+                       q(9,6) * var(9,:,:) ) * idel2
+      il = 7
+    end if
+    if ( bb(2) == 0 ) then
+      ir = ni - gsize
+    else
+      dvar2(ni-5,:,:) = ( q(1,6) * var(ni,:,:) + &
+                          q(2,6) * var(ni-1,:,:) + &
+                          q(3,6) * var(ni-2,:,:) + &
+                          q(4,6) * var(ni-3,:,:) + &
+                          q(5,6) * var(ni-4,:,:) + &
+                          q(6,6) * var(ni-5,:,:) + &
+                          q(7,6) * var(ni-6,:,:) + &
+                          q(8,6) * var(ni-7,:,:) + &
+                          q(9,6) * var(ni-8,:,:) ) * idel2
+      dvar2(ni-4,:,:) = ( q(1,5) * var(ni,:,:) + &
+                          q(2,5) * var(ni-1,:,:) + &
+                          q(3,5) * var(ni-2,:,:) + &
+                          q(4,5) * var(ni-3,:,:) + &
+                          q(5,5) * var(ni-4,:,:) + &
+                          q(6,5) * var(ni-5,:,:) + &
+                          q(7,5) * var(ni-6,:,:) + &
+                          q(8,5) * var(ni-7,:,:) ) * idel2
+      dvar2(ni-3,:,:) = ( q(1,4) * var(ni,:,:) + &
+                          q(2,4) * var(ni-1,:,:) + &
+                          q(3,4) * var(ni-2,:,:) + &
+                          q(4,4) * var(ni-3,:,:) + &
+                          q(5,4) * var(ni-4,:,:) + &
+                          q(6,4) * var(ni-5,:,:) + &
+                          q(7,4) * var(ni-6,:,:) ) * idel2
+      dvar2(ni-2,:,:) = ( q(1,3) * var(ni,:,:) + &
+                          q(2,3) * var(ni-1,:,:) + &
+                          q(3,3) * var(ni-2,:,:) + &
+                          q(4,3) * var(ni-3,:,:) + &
+                          q(5,3) * var(ni-4,:,:) + &
+                          q(6,3) * var(ni-5,:,:) ) * idel2
+      dvar2(ni-1,:,:) = ( q(1,2) * var(ni,:,:) + &
+                          q(2,2) * var(ni-1,:,:) + &
+                          q(3,2) * var(ni-2,:,:) + &
+                          q(4,2) * var(ni-3,:,:) + &
+                          q(5,2) * var(ni-4,:,:) + &
+                          q(6,2) * var(ni-5,:,:) ) * idel2
+      dvar2(ni,:,:)   = ( q(1,1) * var(ni,:,:) + &
+                          q(2,1) * var(ni-1,:,:) + &
+                          q(3,1) * var(ni-2,:,:) + &
+                          q(4,1) * var(ni-3,:,:) + &
+                          q(5,1) * var(ni-4,:,:) + &
+                          q(6,1) * var(ni-5,:,:) ) * idel2
+      ir = ni - 6
+    end if
+    dvar2(il:ir,:,:) = ( a(1) * var(il:ir,:,:) + &
+                         a(2) * ( var(il+1:ir+1,:,:) + &
+                                  var(il-1:ir-1,:,:) ) + &
+                         a(3) * ( var(il+2:ir+2,:,:) + &
+                                  var(il-2:ir-2,:,:) ) + &
+                         a(4) * ( var(il+3:ir+3,:,:) + &
+                                  var(il-3:ir-3,:,:) ) ) * idel2
+  case (1) direction
+    if ( zero_derivs_y /= 0 ) then
+      dvar2 = zero
+    else
+      if ( bb(1) == 0 ) then
+        jl = 1 + gsize
+      else
+        dvar2(:,1,:) = ( q(1,1) * var(:,1,:) + q(2,1) * var(:,2,:)  + &
+                         q(3,1) * var(:,3,:) + q(4,1) * var(:,4,:) + &
+                         q(5,1) * var(:,4,:) + q(6,1) * var(:,6,:) ) * idel2
+        dvar2(:,2,:) = ( q(1,2) * var(:,1,:) + q(2,2) * var(:,2,:) + &
+                         q(3,2) * var(:,3,:) + q(4,2) * var(:,4,:) + &
+                         q(5,2) * var(:,5,:) + q(6,2) * var(:,6,:) ) * idel2
+        dvar2(:,3,:) = ( q(1,3) * var(:,1,:) + q(2,3) * var(:,2,:) + &
+                         q(3,3) * var(:,3,:) + q(4,3) * var(:,4,:) + &
+                         q(5,3) * var(:,5,:) + q(6,3) * var(:,6,:) ) * idel2
+        dvar2(:,4,:) = ( q(1,4) * var(:,1,:) + q(2,4) * var(:,2,:) + &
+                         q(3,4) * var(:,3,:) + q(4,4) * var(:,4,:) + &
+                         q(5,4) * var(:,5,:) + q(6,4) * var(:,6,:) + &
+                         q(7,4) * var(:,7,:) ) * idel2
+        dvar2(:,5,:) = ( q(1,5) * var(:,1,:) + q(2,5) * var(:,2,:) + &
+                         q(3,5) * var(:,3,:) + q(4,5) * var(:,4,:) + &
+                         q(5,5) * var(:,5,:) + q(6,5) * var(:,6,:) + &
+                         q(7,5) * var(:,7,:) + q(8,6) * var(:,8,:) ) * idel2
+        dvar2(:,6,:) = ( q(1,6) * var(:,1,:) + q(2,6) * var(:,2,:) + &
+                         q(3,6) * var(:,3,:) + q(4,6) * var(:,4,:) + &
+                         q(5,6) * var(:,5,:) + q(6,6) * var(:,6,:) + &
+                         q(7,6) * var(:,7,:) + q(8,6) * var(:,8,:) + &
+                         q(9,6) * var(:,9,:) ) * idel2
+        jl = 7
+      end if
+      if ( bb(2) == 0 ) then
+        jr = nj - gsize
+      else
+        dvar2(:,nj-5,:) = ( q(1,6) * var(:,nj,:) + &
+                            q(2,6) * var(:,nj-1,:) + &
+                            q(3,6) * var(:,nj-2,:) + &
+                            q(4,6) * var(:,nj-3,:) + &
+                            q(5,6) * var(:,nj-4,:) + &
+                            q(6,6) * var(:,nj-5,:) + &
+                            q(7,6) * var(:,nj-6,:) + &
+                            q(8,6) * var(:,nj-7,:) + &
+                            q(9,6) * var(:,nj-8,:) ) * idel2
+        dvar2(:,nj-4,:) = ( q(1,5) * var(:,nj,:) + &
+                            q(2,5) * var(:,nj-1,:) + &
+                            q(3,5) * var(:,nj-2,:) + &
+                            q(4,5) * var(:,nj-3,:) + &
+                            q(5,5) * var(:,nj-4,:) + &
+                            q(6,5) * var(:,nj-5,:) + &
+                            q(7,5) * var(:,nj-6,:) + &
+                            q(8,5) * var(:,nj-7,:) ) * idel2
+        dvar2(:,nj-3,:) = ( q(1,4) * var(:,nj,:) + &
+                            q(2,4) * var(:,nj-1,:) + &
+                            q(3,4) * var(:,nj-2,:) + &
+                            q(4,4) * var(:,nj-3,:) + &
+                            q(5,4) * var(:,nj-4,:) + &
+                            q(6,4) * var(:,nj-5,:) + &
+                            q(7,4) * var(:,nj-6,:) ) * idel2
+        dvar2(:,nj-2,:) = ( q(1,3) * var(:,nj,:) + &
+                            q(2,3) * var(:,nj-1,:) + &
+                            q(3,3) * var(:,nj-2,:) + &
+                            q(4,3) * var(:,nj-3,:) + &
+                            q(5,3) * var(:,nj-4,:) + &
+                            q(6,3) * var(:,nj-5,:) ) * idel2
+        dvar2(:,nj-1,:) = ( q(1,2) * var(:,nj,:) + &
+                            q(2,2) * var(:,nj-1,:) + &
+                            q(3,2) * var(:,nj-2,:) + &
+                            q(4,2) * var(:,nj-3,:) + &
+                            q(5,2) * var(:,nj-4,:) + &
+                            q(6,2) * var(:,nj-5,:) ) * idel2
+        dvar2(:,nj,:)   = ( q(1,1) * var(:,nj,:) + &
+                            q(2,1) * var(:,nj-1,:) + &
+                            q(3,1) * var(:,nj-2,:) + &
+                            q(4,1) * var(:,nj-3,:) + &
+                            q(5,1) * var(:,nj-4,:) + &
+                            q(6,1) * var(:,nj-5,:) ) * idel2
+        jr = nj - 6
+      end if
+      dvar2(:,jl:jr,:) = ( a(1) * var(:,jl:jr,:) + &
+                           a(2) * ( var(:,jl+1:jr+1,:) + &
+                                    var(:,jl-1:jr-1,:) ) + &
+                           a(3) * ( var(:,jl+2:jr+2,:) + &
+                                    var(:,jl-2:jr-2,:) ) + &
+                           a(4) * ( var(:,jl+3:jr+3,:) + &
+                                    var(:,jl-3:jr-3,:) ) ) * idel2
+
+    end if
+  case (2) direction
+    if ( zero_derivs_z /= 0 ) then
+      dvar2 = zero
+    else
+      if ( bb(1) == 0 ) then
+        kl = 1 + gsize
+      else
+        dvar2(:,:,1) = ( q(1,1) * var(:,:,1) + q(2,1) * var(:,:,2)  + &
+                         q(3,1) * var(:,:,3) + q(4,1) * var(:,:,4) + &
+                         q(5,1) * var(:,:,4) + q(6,1) * var(:,:,6) ) * idel2
+        dvar2(:,:,2) = ( q(1,2) * var(:,:,1) + q(2,2) * var(:,:,2) + &
+                         q(3,2) * var(:,:,3) + q(4,2) * var(:,:,4) + &
+                         q(5,2) * var(:,:,5) + q(6,2) * var(:,:,6) ) * idel2
+        dvar2(:,:,3) = ( q(1,3) * var(:,:,1) + q(2,3) * var(:,:,2) + &
+                         q(3,3) * var(:,:,3) + q(4,3) * var(:,:,4) + &
+                         q(5,3) * var(:,:,5) + q(6,3) * var(:,:,6) ) * idel2
+        dvar2(:,:,4) = ( q(1,4) * var(:,:,1) + q(2,4) * var(:,:,2) + &
+                         q(3,4) * var(:,:,3) + q(4,4) * var(:,:,4) + &
+                         q(5,4) * var(:,:,5) + q(6,4) * var(:,:,6) + &
+                         q(7,4) * var(:,:,7) ) * idel2
+        dvar2(:,:,5) = ( q(1,5) * var(:,:,1) + q(2,5) * var(:,:,2) + &
+                         q(3,5) * var(:,:,3) + q(4,5) * var(:,:,4) + &
+                         q(5,5) * var(:,:,5) + q(6,5) * var(:,:,6) + &
+                         q(7,5) * var(:,:,7) + q(8,6) * var(:,:,8) ) * idel2
+        dvar2(:,:,6) = ( q(1,6) * var(:,:,1) + q(2,6) * var(:,:,2) + &
+                         q(3,6) * var(:,:,3) + q(4,6) * var(:,:,4) + &
+                         q(5,6) * var(:,:,5) + q(6,6) * var(:,:,6) + &
+                         q(7,6) * var(:,:,7) + q(8,6) * var(:,:,8) + &
+                         q(9,6) * var(:,:,9) ) * idel2
+        kl = 7
+      end if
+      if ( bb(2) == 0 ) then
+        kr = nk - gsize
+      else 
+        dvar2(:,:,nk-5) = ( q(1,6) * var(:,:,nk) + &
+                            q(2,6) * var(:,:,nk-1) + &
+                            q(3,6) * var(:,:,nk-2) + &
+                            q(4,6) * var(:,:,nk-3) + &
+                            q(5,6) * var(:,:,nk-4) + &
+                            q(6,6) * var(:,:,nk-5) + &
+                            q(7,6) * var(:,:,nk-6) + &
+                            q(8,6) * var(:,:,nk-7) + &
+                            q(9,6) * var(:,:,nk-8) ) * idel2
+        dvar2(:,:,nk-4) = ( q(1,5) * var(:,:,nk) + &
+                            q(2,5) * var(:,:,nk-1) + &
+                            q(3,5) * var(:,:,nk-2) + &
+                            q(4,5) * var(:,:,nk-3) + &
+                            q(5,5) * var(:,:,nk-4) + &
+                            q(6,5) * var(:,:,nk-5) + &
+                            q(7,5) * var(:,:,nk-6) + &
+                            q(8,5) * var(:,:,nk-7) ) * idel2
+        dvar2(:,:,nk-3) = ( q(1,4) * var(:,:,nk) + &
+                            q(2,4) * var(:,:,nk-1) + &
+                            q(3,4) * var(:,:,nk-2) + &
+                            q(4,4) * var(:,:,nk-3) + &
+                            q(5,4) * var(:,:,nk-4) + &
+                            q(6,4) * var(:,:,nk-5) + &
+                            q(7,4) * var(:,:,nk-6) ) * idel2
+        dvar2(:,:,nk-2) = ( q(1,3) * var(:,:,nk) + &
+                            q(2,3) * var(:,:,nk-1) + &
+                            q(3,3) * var(:,:,nk-2) + &
+                            q(4,3) * var(:,:,nk-3) + &
+                            q(5,3) * var(:,:,nk-4) + &
+                            q(6,3) * var(:,:,nk-5) ) * idel2
+        dvar2(:,:,nk-1) = ( q(1,2) * var(:,:,nk) + &
+                            q(2,2) * var(:,:,nk-1) + &
+                            q(3,2) * var(:,:,nk-2) + &
+                            q(4,2) * var(:,:,nk-3) + &
+                            q(5,2) * var(:,:,nk-4) + &
+                            q(6,2) * var(:,:,nk-5) ) * idel2
+        dvar2(:,:,nk)   = ( q(1,1) * var(:,:,nk) + &
+                            q(2,1) * var(:,:,nk-1) + &
+                            q(3,1) * var(:,:,nk-2) + &
+                            q(4,1) * var(:,:,nk-3) + &
+                            q(5,1) * var(:,:,nk-4) + &
+                            q(6,1) * var(:,:,nk-5) ) * idel2
+        kr = nk - 6
+      end if
+      dvar2(:,:,kl:kr) = ( a(1) * var(:,:,kl:kr) + &
+                           a(2) * ( var(:,:,kl+1:kr+1) + &
+                                    var(:,:,kl-1:kr-1) ) + &
+                           a(3) * ( var(:,:,kl+2:kr+2) + &
+                                    var(:,:,kl-2:kr-2) ) + &
+                           a(4) * ( var(:,:,kl+3:kr+3) + &
+                                    var(:,:,kl-3:kr-3) ) ) * idel2
+    end if
+  end select direction
+end subroutine deriv2_gf_6_3
diff --git a/src/call_derivs2.c b/src/call_derivs2.c
index 5ec2100..67f33f8 100644
--- a/src/call_derivs2.c
+++ b/src/call_derivs2.c
@@ -50,6 +50,15 @@ void DiffGv2 ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir1,
                                        const CCTK_INT *gsize,
                                        const CCTK_REAL *delta,
                                        CCTK_REAL *dvar2);
+  void CCTK_FCALL CCTK_FNAME(deriv2_gf_6_3)(const CCTK_REAL *var,
+                                       const CCTK_INT *ni,
+                                       const CCTK_INT *nj,
+                                       const CCTK_INT *nk,
+                                       const CCTK_INT *dir,
+                                       const CCTK_INT *bb,
+                                       const CCTK_INT *gsize,
+                                       const CCTK_REAL *delta,
+                                       CCTK_REAL *dvar2);
   void CCTK_FCALL CCTK_FNAME(deriv2_mixed)(const CCTK_POINTER_TO_CONST *cctkGH,
                                        const CCTK_INT *dir1,
                                        const CCTK_INT *dir2,
@@ -120,6 +129,10 @@ void DiffGv2 ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir1,
         CCTK_FNAME(deriv2_gf_4_2)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar2);
         break;
       }
+      case 6: {
+        CCTK_FNAME(deriv2_gf_6_3)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar2);
+        break;
+      }
       default:
       CCTK_WARN (0, "Unknown 2nd derivative stencil specified");
       }
@@ -133,6 +146,10 @@ void DiffGv2 ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir1,
         CCTK_FNAME(deriv2_gf_4_2_opt)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar2);
         break;
       }
+      case 6: {
+        CCTK_FNAME(deriv2_gf_6_3)(var,&ni,&nj,&nk,&dir,bb,&gsize,&delta,dvar2);
+        break;
+      }
       default:
         CCTK_WARN (0, "Unknown stencil specified");
       }
diff --git a/src/get_coeffs2.c b/src/get_coeffs2.c
index 9d2a0ea..9d13dec 100644
--- a/src/get_coeffs2.c
+++ b/src/get_coeffs2.c
@@ -39,6 +39,20 @@ void DiffCoeff2 ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir,
                                              CCTK_INT *imin,
                                              CCTK_INT *imax,
                                              CCTK_REAL *q);
+  void CCTK_FCALL CCTK_FNAME(set_coeff2_4_2_opt)(const CCTK_INT *nsize,
+                                             const CCTK_INT *loc_order,
+                                             const CCTK_INT *bb,
+                                             const CCTK_INT *gsize,
+                                             CCTK_INT *imin,
+                                             CCTK_INT *imax,
+                                             CCTK_REAL *q);
+  void CCTK_FCALL CCTK_FNAME(set_coeff2_6_3)(const CCTK_INT *nsize,
+                                             const CCTK_INT *loc_order,
+                                             const CCTK_INT *bb,
+                                             const CCTK_INT *gsize,
+                                             CCTK_INT *imin,
+                                             CCTK_INT *imax,
+                                             CCTK_REAL *q);
 
   ni = cctk_lsh[0]; nj = cctk_lsh[1]; nk = cctk_lsh[2];
 
@@ -89,6 +103,10 @@ void DiffCoeff2 ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir,
         CCTK_FNAME(set_coeff2_4_2)(&nsize,&loc_order,bb,&gsize,imin,imax,q);
         break;
       }
+      case 6: {
+        CCTK_FNAME(set_coeff2_6_3)(&nsize,&loc_order,bb,&gsize,imin,imax,q);
+        break;
+      }
       default:
         CCTK_WARN (0, "Unknown stencil specified");
       }
@@ -102,6 +120,10 @@ void DiffCoeff2 ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir,
         CCTK_FNAME(set_coeff2_4_2)(&nsize,&loc_order,bb,&gsize,imin,imax,q);
         break;
       }
+      case 6: {
+        CCTK_FNAME(set_coeff2_6_3)(&nsize,&loc_order,bb,&gsize,imin,imax,q);
+        break;
+      }
       default:
         CCTK_WARN (0, "Unknown stencil specified");
       }
diff --git a/src/get_up_coeffs.c b/src/get_up_coeffs.c
index 77226cc..3a78f6a 100644
--- a/src/get_up_coeffs.c
+++ b/src/get_up_coeffs.c
@@ -124,9 +124,11 @@ void DiffUpCoeff ( const CCTK_POINTER_TO_CONST cctkGH_, const CCTK_INT dir,
       }
       case 6: {
         CCTK_FNAME(set_coeff_up_6_3_opt)(&nsize,&up,&loc_order,bb,&gsize,imin,imax,q);
+        break;
       }
       case 8: {
         CCTK_FNAME(set_coeff_up_8_4_opt)(&nsize,&up,&loc_order,bb,&gsize,imin,imax,q);
+        break;
       }
       default:
         CCTK_WARN (0, "Unknown upwinding stencil specified");
diff --git a/src/make.code.defn b/src/make.code.defn
index 7c20a83..5c9b052 100644
--- a/src/make.code.defn
+++ b/src/make.code.defn
@@ -13,6 +13,7 @@ SRCS =  call_derivs.c \
         Derivatives2_4_2.F90 \
         Derivatives2_4_2_min_err_coeff.F90 \
         Derivatives_6_3.F90 \
+        Derivatives2_6_3.F90 \
         Derivatives_6_3_min_err_coeff.F90 \
         Derivatives_8_4.F90 \
         Derivatives_8_4_min_err_coeff.F90 \
@@ -46,7 +47,9 @@ SRCS =  call_derivs.c \
         Coefficients2_2_1.F90 \
         Coefficients_4_2.F90 \
         Coefficients2_4_2.F90 \
+        Coefficients2_4_2_min_err_coeff.F90 \
         Coefficients_6_3.F90 \
+        Coefficients2_6_3.F90 \
         Coefficients_6_3_min_err_coeff.F90 \
         Coefficients_8_4.F90 \
         Coefficients_8_4_min_err_coeff.F90 \
diff --git a/src/make.code.deps b/src/make.code.deps
index 6091656..523b8bf 100644
--- a/src/make.code.deps
+++ b/src/make.code.deps
@@ -5,8 +5,9 @@ Coefficients2_2_1.o:	All_Coeffs_mod.F90.o
 Derivatives_4_2.o:	All_Coeffs_mod.F90.o
 Coefficients_4_2.o:	All_Coeffs_mod.F90.o
 Derivatives2_4_2.o:	All_Coeffs_mod.F90.o
-Derivatives2_4_2_min_err_coeff.o:	All_Coeffs_mod.F90.o
 Coefficients2_4_2.o:	All_Coeffs_mod.F90.o
+Derivatives2_4_2_min_err_coeff.o:	All_Coeffs_mod.F90.o
+Coefficients2_4_2_min_err_coeff.o:	All_Coeffs_mod.F90.o
 Derivatives_4_3.o:	All_Coeffs_mod.F90.o
 Coefficients_4_3.o:	All_Coeffs_mod.F90.o
 Derivatives_4_3_min_err_coeff.o:	All_Coeffs_mod.F90.o
@@ -15,6 +16,8 @@ Derivatives_6_3.o:	All_Coeffs_mod.F90.o
 Coefficients_6_3.o:	All_Coeffs_mod.F90.o
 Derivatives_6_3_min_err_coeff.o:	All_Coeffs_mod.F90.o
 Coefficients_6_3_min_err_coeff.o:	All_Coeffs_mod.F90.o
+Derivatives2_6_3.o:	All_Coeffs_mod.F90.o
+Coefficients2_6_3.o:	All_Coeffs_mod.F90.o
 Derivatives_6_5.o:	All_Coeffs_mod.F90.o
 Coefficients_6_5.o:	All_Coeffs_mod.F90.o
 Derivatives_6_5_min_err_coeff.o:	All_Coeffs_mod.F90.o