Exemple #1
0
def evolve(nx, C, tmax, xmax=None):

    xmin = 0.0
    if xmax == None:
        xmax = 1.0

    # create a dummy patch to store some info in the same way the MG
    # solver will
    myGrid = patch1d.grid1d(nx, ng=1, xmin=xmin, xmax=xmax)

    # initialize the data
    phi = myGrid.scratchArray()

    # initial solution -- this fills the GC too
    phi[:] = phi_a(myGrid, 0.0)

    # time info
    dt = C * 0.5 * myGrid.dx**2 / k
    t = 0.0

    # evolve
    while (t < tmax):

        if (t + dt > tmax):
            dt = tmax - t

        # create the multigrid object
        a = multigrid.ccMG1d(nx,
                             xmin=xmin,
                             xmax=xmax,
                             alpha=1.0,
                             beta=0.5 * dt * k,
                             xlBCtype="neumann",
                             xrBCtype="neumann",
                             verbose=0)

        # initialize the RHS
        a.initRHS(phi + 0.5 * dt * k * lap(a.solnGrid, phi))

        # initialize the solution to 0
        a.initZeros()

        # solve to a relative tolerance of 1.e-11
        a.solve(rtol=1.e-11)

        # get the solution
        v = a.getSolution()

        # store the new solution
        phi[:] = v[:]

        t += dt

    return a.solnGrid, phi
def evolve(nx, C, tmax, xmax=None):

    xmin = 0.0
    if xmax == None: xmax = 1.0

    # create a dummy patch to store some info in the same way the MG
    # solver will
    myGrid = patch1d.grid1d(nx, ng=1,
                            xmin=xmin, xmax=xmax)


    
    # initialize the data
    phi = myGrid.scratchArray()

    # initial solution -- this fills the GC too
    phi[:] = phi_a(myGrid, 0.0)
    
    # time info
    dt = C*0.5*myGrid.dx**2/k            
    t = 0.0

    # evolve
    while (t < tmax):

        if (t + dt > tmax):
            dt = tmax - t


        # create the multigrid object
        a = multigrid.ccMG1d(nx, xmin=xmin, xmax=xmax, 
                             alpha = 1.0, beta = 0.5*dt*k,
                             xlBCtype="neumann", xrBCtype="neumann",
                             verbose=0)
        
        # initialize the RHS
        a.initRHS(phi + 0.5*dt*k*lap(a.solnGrid, phi))
    
        # initialize the solution to 0
        a.initZeros()

        # solve to a relative tolerance of 1.e-11
        a.solve(rtol=1.e-11)

        # get the solution 
        v = a.getSolution()

        # store the new solution
        phi[:] = v[:]

        t += dt

    return a.solnGrid, phi
Exemple #3
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def mgsolve(nx):
                
    # create the multigrid object
    a = multigrid.ccMG1d(nx, xlBCtype="dirichlet", xrBCtype="dirichlet",
                         verbose=0)

    # initialize the solution to 0
    a.initSolution(a.solnGrid.scratchArray())

    # initialize the RHS using the function f
    a.initRHS(f(a.x))

    # solve to a relative tolerance of 1.e-11
    a.solve(rtol=1.e-11)

    # get the solution 
    v = a.getSolution()

    # compute the error from the analytic solution
    return error(a.solnGrid, v - true(a.x))
Exemple #4
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def smoothRun(nx):

    # create the multigrid object
    a = multigrid.ccMG1d(nx,
                         xlBCtype="dirichlet",
                         xrBCtype="dirichlet",
                         verbose=0)

    # initialize the solution to 0
    a.initSolution(a.solnGrid.scratchArray())

    # initialize the RHS using the function f
    a.initRHS(f(a.x))

    # smooth
    n = numpy.arange(20000) + 1
    e = []
    r = []

    for i in n:

        # do 1 smoothing at the finest level
        a.smooth(a.nlevels - 1, 1)

        # compute the true error (wrt the analytic solution)
        v = a.getSolution()
        e.append(error(a.solnGrid, v - true(a.x)))

        # compute the residual
        a.computeResidual(a.nlevels - 1)
        r.append(error(a.solnGrid, a.grids[a.nlevels - 1].getVarPtr("r")))

    r = numpy.array(r)
    e = numpy.array(e)

    return n, r, e
    # normalize
    return numpy.sqrt(myg.dx * numpy.sum((r[myg.ilo:myg.ihi + 1]**2)))


# the righthand side
def f(x):
    return numpy.sin(x)


# test the multigrid solver
nx = 64


# create the multigrid object
a = multigrid.ccMG1d(nx,
                     xlBCtype="dirichlet", xrBCtype="dirichlet",
                     verbose=1)

# initialize the solution to 0
init = a.solnGrid.scratchArray()

a.initSolution(init)

# initialize the RHS using the function f
rhs = f(a.x)
a.initRHS(rhs)

# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)

# alternately, we can just use smoothing by uncommenting the following
Exemple #6
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    # L2 norm of elements in r, multiplied by dx to
    # normalize
    return numpy.sqrt(myg.dx * numpy.sum((r[myg.ilo:myg.ihi + 1]**2)))


# the righthand side
def f(x):
    return numpy.sin(x)


# test the multigrid solver
nx = 64

# create the multigrid object
a = multigrid.ccMG1d(nx, xlBCtype="dirichlet", xrBCtype="dirichlet", verbose=1)

# initialize the solution to 0
init = a.solnGrid.scratchArray()

a.initSolution(init)

# initialize the RHS using the function f
rhs = f(a.x)
a.initRHS(rhs)

# solve to a relative tolerance of 1.e-11
a.solve(rtol=1.e-11)

# alternately, we can just use smoothing by uncommenting the following
# a.smooth(a.nlevels-1,50000)