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# ex11.py: 2-D Laplacian eigenproblem solved with contour integral
# ================================================================
#
# This example is similar to ``ex2.py``, but employs a contour integral
# solver. It illustrates how to define a region of the complex plane
# using an `RG` object.
#
# The full source code for this demo can be `downloaded here
# <../_static/ex11.py>`__.
# Initialization is similar to previous examples.
try: range = xrange
except: pass
import sys, slepc4py
slepc4py.init(sys.argv)
from petsc4py import PETSc
from slepc4py import SLEPc
Print = PETSc.Sys.Print
# Build the finite-difference 2-D Laplacian matrix.
def construct_operator(m, n):
# Create matrix for 2D Laplacian operator
A = PETSc.Mat().create()
A.setSizes([m*n, m*n])
A.setFromOptions()
# Fill matrix
hx = 1.0/(m-1) # x grid spacing
hy = 1.0/(n-1) # y grid spacing
diagv = 2.0*hy/hx + 2.0*hx/hy
offdx = -1.0*hy/hx
offdy = -1.0*hx/hy
Istart, Iend = A.getOwnershipRange()
for I in range(Istart, Iend) :
A[I,I] = diagv
i = I//n # map row number to
j = I - i*n # grid coordinates
if i> 0 : J = I-n; A[I,J] = offdx
if i< m-1: J = I+n; A[I,J] = offdx
if j> 0 : J = I-1; A[I,J] = offdy
if j< n-1: J = I+1; A[I,J] = offdy
A.assemble()
return A
# In the main function, first two command-line options are processed to
# set the grid dimensions. Then the matrix is built and passed to the
# solver object. In this case, the solver is configured to use the contour
# integral method. Next, the region of interest is defined, in this case
# an ellipse centered at the origin, with radius 0.2 and vertical scaling
# of 0.1. Finally, the solver is run. In this example, we illustrate how to
# print the solution using the solver method `errorView() <EPS.errorView()>`.
def main():
opts = PETSc.Options()
n = opts.getInt('n', 32)
m = opts.getInt('m', 32)
Print("2-D Laplacian Eigenproblem solved with contour integral, "
"N=%d (%dx%d grid)\n" % (m*n, m, n))
A = construct_operator(m,n)
E = SLEPc.EPS().create()
E.setOperators(A)
E.setProblemType(SLEPc.EPS.ProblemType.HEP)
E.setType(SLEPc.EPS.Type.CISS)
R = E.getRG()
R.setType(SLEPc.RG.Type.ELLIPSE)
R.setEllipseParameters(0.0,0.2,0.1)
E.setFromOptions()
E.solve()
vw = PETSc.Viewer.STDOUT()
vw.pushFormat(PETSc.Viewer.Format.ASCII_INFO_DETAIL)
E.errorView(viewer=vw)
vw.popFormat()
if __name__ == '__main__':
main()
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