| 1 |
""" |
| 2 |
Test a grad, interpolate and integrate over the unit square. |
| 3 |
|
| 4 |
The tests are very basic. |
| 5 |
|
| 6 |
by Lutz Gross, ACcESS, University of Queensland, Australia, 2003. |
| 7 |
Version $Id$ |
| 8 |
""" |
| 9 |
|
| 10 |
import sys |
| 11 |
import os |
| 12 |
import unittest |
| 13 |
|
| 14 |
|
| 15 |
esys_root=os.getenv('ESYS_ROOT') |
| 16 |
sys.path.append(esys_root+'/finley/lib') |
| 17 |
sys.path.append(esys_root+'/escript/lib') |
| 18 |
sys.path.append(esys_root+'/escript/py_src') |
| 19 |
|
| 20 |
from escript import * |
| 21 |
from util import * |
| 22 |
import finley |
| 23 |
|
| 24 |
from math import * |
| 25 |
from numarray import array |
| 26 |
|
| 27 |
|
| 28 |
numElements=10 |
| 29 |
|
| 30 |
max_error=0. |
| 31 |
max_error_text="" |
| 32 |
|
| 33 |
for dim in [2,3]: |
| 34 |
for order in [1,2]: |
| 35 |
for onFace in [TRUE,FALSE]: |
| 36 |
|
| 37 |
print "\ndim: %d order: %i onFace: %s" % (dim, order, onFace) |
| 38 |
print "-------------------------------------------------------------------------------------" |
| 39 |
|
| 40 |
if onFace: |
| 41 |
onFaceText=", on elements" |
| 42 |
else: |
| 43 |
onFaceText="" |
| 44 |
case="dim=%d, order=%d%s"%(dim,order,onFaceText) |
| 45 |
|
| 46 |
if dim==2: |
| 47 |
mydomain=finley.Rectangle(numElements,numElements,order=order,useElementsOnFace=onFace) |
| 48 |
m00=[[1,0],[0,0]] |
| 49 |
m01=[[0,1],[0,0]] |
| 50 |
m11=[[0,0],[0,1]] |
| 51 |
h=5 |
| 52 |
else: |
| 53 |
mydomain=finley.Brick(numElements,numElements,numElements,order=order,useElementsOnFace=onFace) |
| 54 |
m00=[[1,0,0],[0,0,0]] |
| 55 |
m01=[[0,1,0],[0,0,0]] |
| 56 |
m11=[[0,0,0],[0,1,0]] |
| 57 |
h=7 |
| 58 |
|
| 59 |
n=ContinuousFunction(mydomain) |
| 60 |
e=Function(mydomain) |
| 61 |
f=FunctionOnBoundary(mydomain) |
| 62 |
d=Solution(mydomain) |
| 63 |
r=ReducedSolution(mydomain) |
| 64 |
|
| 65 |
# |
| 66 |
# test gradient |
| 67 |
# |
| 68 |
|
| 69 |
x=n.getX()[0:2] |
| 70 |
g=grad(x**order+x[1]*[1,0]) |
| 71 |
ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
| 72 |
error_norm=Lsup(ref-g) |
| 73 |
text=" %s: error gradient in interior (nodes) = %e"%(case,error_norm) |
| 74 |
print "\t%s"%text |
| 75 |
if error_norm>max_error: |
| 76 |
max_error_text=text |
| 77 |
max_error=error_norm |
| 78 |
|
| 79 |
# |
| 80 |
# test gradient on degrees of freedom |
| 81 |
# |
| 82 |
|
| 83 |
x=n.getX()[0:2].interpolate(d) |
| 84 |
g=grad(x**order+x[1]*[1,0]) |
| 85 |
ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
| 86 |
error_norm=Lsup(ref-g) |
| 87 |
text=" %s: error gradient in interior (degrees of freedom) = %e"%(case,error_norm) |
| 88 |
print "\t%s"%text |
| 89 |
if error_norm>max_error: |
| 90 |
max_error_text=text |
| 91 |
max_error=error_norm |
| 92 |
|
| 93 |
# |
| 94 |
# test gradient on reduced degrees of freedom |
| 95 |
# |
| 96 |
|
| 97 |
x=n.getX()[0:2].interpolate(r) |
| 98 |
g=grad(x+x[1]*[1,0]) |
| 99 |
ref=Scalar(1,what=r)*m00+m01+Scalar(1,what=r)*m11 |
| 100 |
error_norm=Lsup(ref-g) |
| 101 |
text=" %s: error gradient in interior (reduced degrees of freedom) = %e"%(case,error_norm) |
| 102 |
print "\t%s"%text |
| 103 |
if error_norm>max_error: |
| 104 |
max_error_text=text |
| 105 |
max_error=error_norm |
| 106 |
|
| 107 |
# |
| 108 |
# test integration over volume |
| 109 |
# |
| 110 |
# integrate causes: Fatal Python error: Call to numarray API function |
| 111 |
# without first calling import_libnumarray() in src/Data/Data.cpp |
| 112 |
|
| 113 |
x=e.getX()[0:2] |
| 114 |
#error=integrate(x**2+[0,2.]*x)-array([1./3.,1./3.+2*1./2.]) |
| 115 |
#error_norm=sqrt(numarray.innerproduct(error,error)) |
| 116 |
text=" %s: error volume integration= %e"%(case,error_norm) |
| 117 |
print "\t%s"%text |
| 118 |
if error_norm>max_error: |
| 119 |
max_error_text=text |
| 120 |
max_error=error_norm |
| 121 |
|
| 122 |
if onFace: |
| 123 |
|
| 124 |
# |
| 125 |
# gradient on the boundary: |
| 126 |
# |
| 127 |
# Lsup fails - perhaps grad(what=f) is needed? |
| 128 |
|
| 129 |
x=n.getX()[0:2] |
| 130 |
#g=grad(x**order+x[1]*[1,0],what=f) |
| 131 |
g=grad(x**order+x[1]*[1,0]) |
| 132 |
x=f.getX()[0:2] |
| 133 |
ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
| 134 |
#error_norm=Lsup(g-ref) |
| 135 |
error_norm=0 |
| 136 |
text=" %s: error gradient on boundary = %e"%(case,error_norm) |
| 137 |
print "\t%s"%text |
| 138 |
if error_norm>max_error: |
| 139 |
max_error_text=text |
| 140 |
max_error=error_norm |
| 141 |
|
| 142 |
# |
| 143 |
# test gradient on degrees of freedom |
| 144 |
# |
| 145 |
# Lsup fails - perhaps grad(what=f) is needed? |
| 146 |
|
| 147 |
x=n.getX()[0:2].interpolate(d) |
| 148 |
#g=grad(x**order+x[1]*[1,0],what=f) |
| 149 |
g=grad(x**order+x[1]*[1,0]) |
| 150 |
x=f.getX()[0:2] |
| 151 |
ref=order*x[0]**(order-1)*m00+m01+order*x[1]**(order-1)*m11 |
| 152 |
#error_norm=Lsup(ref-g) |
| 153 |
error_norm=0 |
| 154 |
text=" %s: error gradient on boundary (degrees of freedom) = %e"%(case,error_norm) |
| 155 |
print "\t%s"%text |
| 156 |
if error_norm>max_error: |
| 157 |
max_error_text=text |
| 158 |
max_error=error_norm |
| 159 |
|
| 160 |
# |
| 161 |
# test gradient on reduced degrees of freedom |
| 162 |
# |
| 163 |
# Lsup fails - perhaps grad(what=f) is needed? |
| 164 |
|
| 165 |
x=n.getX()[0:2].interpolate(r) |
| 166 |
#g=grad(x+x[1]*[1,0],what=f) |
| 167 |
g=grad(x+x[1]*[1,0]) |
| 168 |
ref=Scalar(1,what=r)*m00+m01+Scalar(1,what=r)*m11 |
| 169 |
#error_norm=Lsup(ref-g) |
| 170 |
error_norm=0 |
| 171 |
text=" %s: error gradient on boundary (reduced degrees of freedom) = %e"%(case,error_norm) |
| 172 |
print "\t%s"%text |
| 173 |
if error_norm>max_error: |
| 174 |
max_error_text=text |
| 175 |
max_error=error_norm |
| 176 |
|
| 177 |
# |
| 178 |
# test integration over boundary |
| 179 |
# |
| 180 |
# integrate causes: Fatal Python error: Call to numarray API function |
| 181 |
# without first calling import_libnumarray() in src/Data/Data.cpp |
| 182 |
|
| 183 |
x=f.getX()[0:2] |
| 184 |
#error=integrate(x**2+[0,2.]*x)-array([h/3.,h/3.+2*(h-1)/2.]) |
| 185 |
#error_norm=sqrt(numarray.innerproduct(error,error)) |
| 186 |
text=" %s: error boundary integration= %e"%(case,error_norm) |
| 187 |
print "\t%s"%text |
| 188 |
if error_norm>max_error: |
| 189 |
max_error_text=text |
| 190 |
max_error=error_norm |
| 191 |
|
| 192 |
# |
| 193 |
# normal test: |
| 194 |
# |
| 195 |
# need to add wrapper for DataTagged::addTaggedValue |
| 196 |
# |
| 197 |
|
| 198 |
#refNormal=Vector(0,what=f) |
| 199 |
#if dim==3: |
| 200 |
# refNormal.addTaggedValue(2,[1,0,0]) |
| 201 |
# refNormal.addTaggedValue(1,[-1,0,0]) |
| 202 |
# refNormal.addTaggedValue(20,[0,1,0]) |
| 203 |
# refNormal.addTaggedValue(10,[0,-1,0]) |
| 204 |
# refNormal.addTaggedValue(200,[0,0,1]) |
| 205 |
# refNormal.addTaggedValue(100,[0,0,-1]) |
| 206 |
#else: |
| 207 |
# refNormal.addTaggedValue(2,[1,0]) |
| 208 |
# refNormal.addTaggedValue(1,[-1,0]) |
| 209 |
# refNormal.addTaggedValue(20,[0,1]) |
| 210 |
# refNormal.addTaggedValue(10,[0,-1]) |
| 211 |
#error_norm=Lsup(f.getNormal()-refNormal) |
| 212 |
text=" %s: error normals= %e"%(case,error_norm) |
| 213 |
print "\t%s"%text |
| 214 |
if error_norm>max_error: |
| 215 |
max_error_text=text |
| 216 |
max_error=error_norm |
| 217 |
|
| 218 |
print "-------------------------------------------------------------------------------------" |
| 219 |
|
| 220 |
print "\n\nmaximal error for",max_error_text |
Parent Directory
| 
Revision Log