fiat team mailing list archive

[Jed Brown <jed@xxxxxxxx>]

Here is a patch which adds LGL and CGL to the possible Lagrange LINE nodes.
Someone else can extend it to simplices if desired.  I didn't add plumbing up to
the user interface, but it's a one line change to choose a different set of
nodes.

Jed

diff -r bf2daae56306 FIAT/shapes.py
--- a/FIAT/shapes.py	Thu Apr 24 09:57:46 2008 -0500
+++ b/FIAT/shapes.py	Mon May 26 10:11:41 2008 +0200
@@ -17,7 +17,7 @@
 from factorial import factorial
 from math import sqrt
 import numbering, reference # UFC vs. FIAT modules.
-
+import jacobi
 
 def strike_col( A , j ):
     m,n = A.shape
@@ -216,7 +216,7 @@
         td = td * ( n + i + 1 )
     return td / factorial( d )
 
-def make_lattice_line( n , interior = 0 ):
+def make_lattice_line_evenly_spaced( n , interior = 0 ):
     if n == 0:
         return tuple( )
     v0 = vertices[ LINE ][0][0]
@@ -224,6 +224,29 @@
     h = abs( v1 - v0 )
     return tuple( [ ( v0 + ( h * jj ) / n , ) \
                     for jj in xrange( interior , n + 1 - interior ) ] )
+
+def compute_lgl_points( n, interior = 0 ):
+    if n == 0:
+        return []
+    xi = jacobi.compute_gauss_jacobi_points(1,1,n-2)
+    return interior and xi or [-1] + xi + [1]
+
+def compute_cgl_points( n, interior = 0 ):
+    if n == 0:
+        return []
+    xi = n == 1 and [] or [ numpy.cos(i * numpy.pi / (n-1)) for i in xrange(1,n-1) ]
+    return interior and xi or [-1] + xi + [1]
+
+def make_lattice_line_gen( n , interior = 0 , pointgen = compute_lgl_points ):
+    if n == 0:
+        return tuple( )
+    v0 = vertices[ LINE ][0][0]
+    v1 = vertices[ LINE ][1][0]
+    h = ( v1 - v0 ) / 2
+    return tuple( [ (v0 + h * (x + 1),) for x in pointgen(n+1, interior) ] )
+
+def make_lattice_line( n , interior = 0 ):
+    return make_lattice_line_gen( n, interior, compute_lgl_points )
 
 def make_lattice_triangle( n , interior = 0 ):
     if n == 0: return tuple( )

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