Changes between Version 1 and Version 2 of SubSampling

Timestamp:

06/27/13 22:46:28 (12 years ago)

Author:

Jonathan

Comment:

—

SubSampling

@@ -1 +1 @@
 = Sub Sampling =
-AstroBEAR stores most fluid quantities as volume averages in the {{{q}}} array.  That is
+
+== Cell centered quantities ==
+* AstroBEAR stores most fluid quantities as volume averages in the array {{{Info%q(i,j,k,:)}}}
+* Each cell is a cube with a side {{{dx=levels(Info%level)%dx}}}
+* The 'lower' corner of the cube is located at {{{Info%xbounds(:,1) + ((/i,j,k/)-1)*dx}}}
+* The 'upper' corner of the cube is located at {{{Info%xbounds(:,1) + ((/i,j,k/))*dx}}}
+* The 'center' of the cube is located at {{{Info%xbounds(:,1) + (REAL(/i,j,k/)-.5)*dx}}}
+=== Sub-sampling ===
+* If we break each cube into NxNxN sub-pieces, and set {{{ddx=dx/N}}} then the center of the [ii,jj,kk] sub piece will be at {{{Info%xBounds(:,1)+(/i-1,j-1,k-1/)*dx + (REAL(/ii,jj,kk/)-.5)*ddx}}}
+* So we could use the following routine to initialize cell centered quantities in q.  Here is a routine for density.
+{{{
+dx=levels(Info%level)%dx
+ddx=dx/N
+DO i=1,Info%mX(1)
+  DO j=1,Info%mx(2)
+    DO k=1,Info%mx(3)
+      new_rho=0d0
+      DO ii=1,N
+        DO jj=1,N
+          DO kk=1,N
+            pos=Info%xBounds(:,1)+(/i-1,j-1,k-1/)*dx + (REAL(/ii,jj,kk/)-.5)*ddx
+            new_rho=new_rho+rho_func(pos)
+          END DO
+        END DO
+      END DO
+      Info%q(i,j,k,1)=new_rho/N**nDim
+    END DO
+  END DO
+END DO
+}}}
+
+ or we could try to speed it up by reducing some repeated computations.
+{{{
+dx=levels(Info%level)%dx
+ddx=dx/N
+DO i=1,Info%mX(1)
+  pos(1)=Info%xBbounds(1,1)+(i-1)*dx
+  DO j=1,Info%mx(2)
+    pos(2)=Info%xBbounds(1,1)+(i-1)*dx
+    DO k=1,Info%mx(3)
+      pos(3)=Info%xBbounds(1,1)+(i-1)*dx
+      new_rho=0d0
+      DO ii=1,N
+        ppos(1)=pos(1)+(REAL(ii)-.5)*ddx
+        DO jj=1,N
+          ppos(2)=pos(2)+(REAL(jj)-.5)*ddx
+          DO kk=1,N
+            ppos(3)=pos(3)+(REAL(kk)-.5)*ddx
+            new_rho=new_rho+rho_func(pos)
+          END DO
+        END DO
+      END DO
+      Info%q(i,j,k,1)=new_rho/N**nDim
+    END DO
+  END DO
+END DO
+}}}
+
+ and sometimes we may be implementing a function that is only defined for a certain region (like a clump object etc...) where the value for q outside of a given radius is unknown.  In that case, we just want to add up changes to q for subcells within the region.  So for example to calculate the x component of the potential along a given edge we would
+{{{
+dx=levels(Info%level)%dx
+ddx=dx/N
+DO i=1,Info%mX(1)+1
+  pos(1)=Info%xBbounds(1,1)+(i-1)*dx
+  DO j=1,Info%mx(2)+1
+    pos(2)=Info%xBbounds(1,1)+(i-1)*dx
+    DO k=1,Info%mx(3)+1
+      pos(3)=Info%xBbounds(1,1)+(i-1)*dx
+      drho=0d0
+      DO ii=1,N
+        ppos(1)=pos(1)+(REAL(ii)-.5)*ddx
+        DO jj=1,N
+          ppos(2)=pos(2)+(REAL(jj)-.5)*ddx
+          DO kk=1,N
+            ppos(3)=pos(3)+(REAL(kk)-.5)*ddx
+            drho=(rho_func(ppos)-Info%q(i,j,k,1))
+          END DO
+        END DO
+      END DO
+      Info%q(i,j,k,1)=Info%q(i,j,k,1)+drho/N**nDim
+    END DO
+  END DO
+END DO
+}}}
+
+For face centered fields we could also subsample, but their is the divergence criterion to consider for B-fields.  We could calculate the potential on a subgrid, and then take a bunch of curls on each face and add them up, but Stoke's theorem lets us just do the integral around the outside.  So we really just need to subsample along the appropriate edge for each component of the vector potential.
+{{{
+dx=levels(Info%level)%dx
+ddx=dx/N
+DO i=1,Info%mX(1)
+  pos(1)=Info%xBbounds(1,1)+(i-1)*dx
+  DO j=1,Info%mx(2)
+    pos(2)=Info%xBbounds(1,1)+(i-1)*dx
+    DO k=1,Info%mx(3)
+      pos(3)=Info%xBbounds(1,1)+(i-1)*dx
+      drho=0d0
+      DO ii=1,N
+        ppos(1)=pos(1)+(REAL(ii)-.5)*ddx
+        DO jj=1,N
+          ppos(2)=pos(2)+(REAL(jj)-.5)*ddx
+          DO kk=1,N
+            ppos(3)=pos(3)+(REAL(kk)-.5)*ddx
+            drho=(rho_func(ppos)-Info%q(i,j,k,1))
+          END DO
+        END DO
+      END DO
+      Info%q(i,j,k,1)=Info%q(i,j,k,1)+drho/N**nDim
+    END DO
+  END DO
+END DO
+}}}
+