| 1 |
|
| 2 |
############################################################################## |
| 3 |
# |
| 4 |
# Copyright (c) 2003-2018 by The University of Queensland |
| 5 |
# http://www.uq.edu.au |
| 6 |
# |
| 7 |
# Primary Business: Queensland, Australia |
| 8 |
# Licensed under the Apache License, version 2.0 |
| 9 |
# http://www.apache.org/licenses/LICENSE-2.0 |
| 10 |
# |
| 11 |
# Development until 2012 by Earth Systems Science Computational Center (ESSCC) |
| 12 |
# Development 2012-2013 by School of Earth Sciences |
| 13 |
# Development from 2014 by Centre for Geoscience Computing (GeoComp) |
| 14 |
# |
| 15 |
############################################################################## |
| 16 |
|
| 17 |
from __future__ import print_function, division |
| 18 |
|
| 19 |
__copyright__="""Copyright (c) 2003-2018 by The University of Queensland |
| 20 |
http://www.uq.edu.au |
| 21 |
Primary Business: Queensland, Australia""" |
| 22 |
__license__="""Licensed under the Apache License, version 2.0 |
| 23 |
http://www.apache.org/licenses/LICENSE-2.0""" |
| 24 |
__url__="https://launchpad.net/escript-finley" |
| 25 |
|
| 26 |
from esys.escript import * |
| 27 |
from esys.escript.linearPDEs import Poisson |
| 28 |
from esys import finley |
| 29 |
|
| 30 |
ne_list=[10,15,22,33,50,75] |
| 31 |
height_list=[0.25,0.5,1.] |
| 32 |
|
| 33 |
|
| 34 |
def getDomain(dim,ne,height): |
| 35 |
|
| 36 |
if dim==2: |
| 37 |
ne1=int(ne*height+0.5) |
| 38 |
mydomain=finley.Rectangle(n0=ne,n1=ne1,l1=height,order=1) |
| 39 |
totne=ne1*ne |
| 40 |
else: |
| 41 |
ne2=int(ne*height+0.5) |
| 42 |
mydomain=finley.Brick(n0=ne,n1=ne,n2=ne2,l2=height,order=2) |
| 43 |
totne=ne2*ne*ne |
| 44 |
print("%d -dimensional domain generated."%dim) |
| 45 |
print("height of the domain is ",height) |
| 46 |
print("total number of elements is ",totne) |
| 47 |
return mydomain |
| 48 |
|
| 49 |
|
| 50 |
def Solve1(mydomain,height): |
| 51 |
print("Fully constraint solution") |
| 52 |
l=[1.,1.,1.] |
| 53 |
l[mydomain.getDim()-1]=height |
| 54 |
cf=ContinuousFunction(mydomain) |
| 55 |
x=cf.getX() |
| 56 |
#construct exact solution: |
| 57 |
u_ex=Scalar(1.,cf) |
| 58 |
for i in range(mydomain.getDim()): |
| 59 |
u_ex*=x[i]*(x[i]-l[i]) |
| 60 |
#construct mask: |
| 61 |
msk=Scalar(0.,cf) |
| 62 |
for i in range(mydomain.getDim()): |
| 63 |
msk+=whereZero(x[i])+whereZero(x[i]-l[i]) |
| 64 |
#construct right hand side |
| 65 |
f=Scalar(0,cf) |
| 66 |
for i in range(mydomain.getDim()): |
| 67 |
f_p=Scalar(1,cf) |
| 68 |
for j in range(mydomain.getDim()): |
| 69 |
if i==j: |
| 70 |
f_p*=-2. |
| 71 |
else: |
| 72 |
f_p*=x[j]*(x[j]-l[j]) |
| 73 |
f+=f_p |
| 74 |
|
| 75 |
mypde=Poisson(mydomain) |
| 76 |
mypde.setTolerance(1.e-10) |
| 77 |
mypde.setValue(f=f,q=msk) |
| 78 |
u=mypde.getSolution() |
| 79 |
error=Lsup(u-u_ex)/Lsup(u_ex) |
| 80 |
print("error = ",error) |
| 81 |
return error |
| 82 |
|
| 83 |
def Solve2(mydomain,height): |
| 84 |
print("Partially constraint solution") |
| 85 |
l=[1.,1.,1.] |
| 86 |
l[mydomain.getDim()-1]=height |
| 87 |
print(l) |
| 88 |
cf=ContinuousFunction(mydomain) |
| 89 |
x=cf.getX() |
| 90 |
#construct exact solution: |
| 91 |
u_ex=Scalar(1.,cf) |
| 92 |
for i in range(mydomain.getDim()): |
| 93 |
u_ex*=x[i]*(2*l[i]-x[i]) |
| 94 |
#construct mask: |
| 95 |
msk=Scalar(0.,cf) |
| 96 |
for i in range(mydomain.getDim()): |
| 97 |
msk+=whereZero(x[i]) |
| 98 |
#construct right hand side |
| 99 |
f=Scalar(0,cf) |
| 100 |
for i in range(mydomain.getDim()): |
| 101 |
f_p=Scalar(1,cf) |
| 102 |
for j in range(mydomain.getDim()): |
| 103 |
if i==j: |
| 104 |
f_p*=2. |
| 105 |
else: |
| 106 |
f_p*=x[j]*(2*l[j]-x[j]) |
| 107 |
f+=f_p |
| 108 |
mypde=Poisson(mydomain) |
| 109 |
mypde.setTolerance(1.e-10) |
| 110 |
mypde.setValue(f=f,q=msk) |
| 111 |
u=mypde.getSolution() |
| 112 |
error=Lsup(u-u_ex)/Lsup(u_ex) |
| 113 |
print("error = ",error) |
| 114 |
return error |
| 115 |
|
| 116 |
|
| 117 |
def main() : |
| 118 |
error=0 |
| 119 |
for ne in ne_list: |
| 120 |
for dim in [2,3]: |
| 121 |
# for dim in [2]: |
| 122 |
for height in height_list: |
| 123 |
print("***************************************************************") |
| 124 |
mydomain= getDomain(dim,ne,height) |
| 125 |
print("---------------------------------------------------------------") |
| 126 |
error=max(error,Solve1(mydomain,height)) |
| 127 |
print("---------------------------------------------------------------") |
| 128 |
error=max(error,Solve2(mydomain,height)) |
| 129 |
print("***************************************************************") |
| 130 |
|
| 131 |
print("***************************************************************") |
| 132 |
print("maximum error: ",error) |
| 133 |
print("***************************************************************") |
| 134 |
|
| 135 |
|
| 136 |
|
| 137 |
import profile as Pr, pstats as Ps |
| 138 |
|
| 139 |
|
| 140 |
if __name__ == "__main__": |
| 141 |
pr = Pr.Profile() |
| 142 |
pr.calibrate(10000) |
| 143 |
Pr.run('main()','eos_stats') |
| 144 |
stats = Ps.Stats('eos_stats') |
| 145 |
stats.strip_dirs() |
| 146 |
stats.sort_stats('time') |
| 147 |
stats.print_stats() |
Parent Directory
| 
Revision Log