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https://github.com/wassname/simpeg.git
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Lars Ruthotto
114 lines
3.4 KiB
Python
114 lines
3.4 KiB
Python
import sys
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sys.path.append('../../')
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from SimPEG import TensorMesh
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import numpy as np
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import unittest
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class OrderTest(unittest.TestCase):
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"""
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OrderTest is a base class for testing convergence orders with respect to mesh
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sizes of integral/differential operators.
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Mathematical Problem:
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Given are an operator A and its discretization A[h]. For a given test function f
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and h --> 0 we compare:
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error(h) = \| A[h](f) - A(f) \|_{\infty}
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Note that you can provide any norm.
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Test is passed when estimated rate order of convergence is at least 90% of the
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estimated rate supplied by the user.
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Minimal example for a curl operator:
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class TestCURL(OrderTest):
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name = "Curl"
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def getError(self):
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# For given Mesh, generate A[h], f and A(f) and return norm of error.
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fun = lambda x: np.cos(x) # i (cos(y)) + j (cos(z)) + k (cos(x))
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sol = lambda x: np.sin(x) # i (sin(z)) + j (sin(x)) + k (sin(y))
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Ex = fun(self.M.gridEx[:, 1])
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Ey = fun(self.M.gridEy[:, 2])
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Ez = fun(self.M.gridEz[:, 0])
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f = np.concatenate((Ex, Ey, Ez))
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Fx = sol(self.M.gridFx[:, 2])
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Fy = sol(self.M.gridFy[:, 0])
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Fz = sol(self.M.gridFz[:, 1])
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Af = np.concatenate((Fx, Fy, Fz))
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# Generate DIV matrix
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Ah = self.M.edgeCurl
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curlE = Ah*E
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err = np.linalg.norm((Ah*f -Af), np.inf)
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return err
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def test_order(self):
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# runs the test
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self.orderTest()
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See also: test_operatorOrder.py
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"""
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name = "Order Test"
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expectedOrder = 2
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meshSizes = [4, 8, 16, 32]
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def setupMesh(self, nc):
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"""
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For a given number of cells nc, generate a TensorMesh with uniform cells with edge length h=1/nc.
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"""
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h1 = np.ones(nc)/nc
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h2 = np.ones(nc)/nc
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h3 = np.ones(nc)/nc
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h = [h1, h2, h3]
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self.M = TensorMesh(h)
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def getError(self):
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"""For given h, generate A[h], f and A(f) and return norm of error."""
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return 1.
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def orderTest(self):
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"""
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For number of cells specified in meshSizes setup mesh, call getError
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and prints mesh size, error, ratio between current and previous error,
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and estimated order of convergence.
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"""
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order = []
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err_old = 0.
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nc_old = 0.
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for ii, nc in enumerate(self.meshSizes):
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self.setupMesh(nc)
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err = self.getError()
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if ii == 0:
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print ''
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print 'Testing order of: ' + self.name
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print '_____________________________________________'
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print ' h | error | e(i-1)/e(i) | order'
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print '~~~~~~|~~~~~~~~~~~~~|~~~~~~~~~~~~~|~~~~~~~~~~'
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print '%4i | %8.2e |' % (nc, err)
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else:
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order.append(np.log(err/err_old)/np.log(float(nc_old)/float(nc)))
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print '%4i | %8.2e | %6.4f | %6.4f' % (nc, err, err_old/err, order[-1])
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err_old = err
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nc_old = nc
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print '---------------------------------------------'
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self.assertTrue(len(np.where(np.array(order) > 0.9*self.expectedOrder)[0]) > np.floor(0.75*len(order)))
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if __name__ == '__main__':
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unittest.main()
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