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.

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().

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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