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inertial_mhd2d_nonlinear_newton_snes_gmres.py
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inertial_mhd2d_nonlinear_newton_snes_gmres.py
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'''
Created on Mar 23, 2012
@author: Michael Kraus (michael.kraus@ipp.mpg.de)
'''
import sys, petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
import argparse
import time
import numpy as np
import h5py
from config import Config
from imhd.integrators.Inertial_MHD_Nonlinear import PETScFunction
from imhd.integrators.Inertial_MHD_Linear import PETScMatrix
from imhd.integrators.MHD_Derivatives import MHD_Derivatives
class petscMHD2D(object):
'''
PETSc/Python Vlasov Poisson Solver in 1D.
'''
def __init__(self, cfgfile):
'''
Constructor
'''
# stencil = 1
stencil = 2
# load run config file
cfg = Config(cfgfile)
self.cfg = cfg
cfg.set_petsc_options()
# timestep setup
self.ht = cfg['grid']['ht'] # timestep size
self.nt = cfg['grid']['nt'] # number of timesteps
self.nsave = cfg['io']['nsave'] # save only every nsave'th timestep
# grid setup
nx = cfg['grid']['nx'] # number of points in x
ny = cfg['grid']['ny'] # number of points in y
Lx = cfg['grid']['Lx'] # spatial domain in x
x1 = cfg['grid']['x1'] #
x2 = cfg['grid']['x2'] #
Ly = cfg['grid']['Ly'] # spatial domain in y
y1 = cfg['grid']['y1'] #
y2 = cfg['grid']['y2'] #
self.nx = nx
self.ny = ny
if x1 != x2:
Lx = x2-x1
else:
x1 = 0.0
x2 = Lx
if y1 != y2:
Ly = y2-y1
else:
y1 = 0.0
y2 = Ly
self.hx = Lx / nx # gridstep size in x
self.hy = Ly / ny # gridstep size in y
# friction, viscosity and resistivity
mu = cfg['initial_data']['mu'] # friction
nu = cfg['initial_data']['nu'] # viscosity
eta = cfg['initial_data']['eta'] # resistivity
de = cfg['initial_data']['de'] # electron skin depth
# self.update_jacobian = True
if PETSc.COMM_WORLD.getRank() == 0:
print()
print("nt = %i" % (self.nt))
print("nx = %i" % (self.nx))
print("ny = %i" % (self.ny))
print()
print("ht = %e" % (self.ht))
print("hx = %e" % (self.hx))
print("hy = %e" % (self.hy))
print()
print("Lx = %e" % (Lx))
print("Ly = %e" % (Ly))
print()
print("mu = %e" % (mu))
print("nu = %e" % (nu))
print("eta = %e" % (eta))
print()
self.time = PETSc.Vec().createMPI(1, PETSc.DECIDE, comm=PETSc.COMM_WORLD)
self.time.setName('t')
if PETSc.COMM_WORLD.getRank() == 0:
self.time.setValue(0, 0.0)
# create derivatives object
self.derivatives = MHD_Derivatives(nx, ny, self.ht, self.hx, self.hy)
# create DA with single dof
self.da1 = PETSc.DA().create(dim=2, dof=1,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA (dof = 7 for Vx, Vy, Bx, By, Bix, Biy, P)
self.da7 = PETSc.DA().create(dim=2, dof=7,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA for x grid
self.dax = PETSc.DA().create(dim=1, dof=1,
sizes=[nx],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# create DA for y grid
self.day = PETSc.DA().create(dim=1, dof=1,
sizes=[ny],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# initialise grid
self.da1.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.da7.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.dax.setUniformCoordinates(xmin=x1, xmax=x2)
self.day.setUniformCoordinates(xmin=y1, xmax=y2)
# create solution and RHS vector
self.f = self.da7.createGlobalVec()
self.x = self.da7.createGlobalVec()
self.b = self.da7.createGlobalVec()
# create global RK4 vectors
self.Y = self.da7.createGlobalVec()
self.X0 = self.da7.createGlobalVec()
self.X1 = self.da7.createGlobalVec()
self.X2 = self.da7.createGlobalVec()
self.X3 = self.da7.createGlobalVec()
self.X4 = self.da7.createGlobalVec()
# create local RK4 vectors
self.localX0 = self.da7.createLocalVec()
self.localX1 = self.da7.createLocalVec()
self.localX2 = self.da7.createLocalVec()
self.localX3 = self.da7.createLocalVec()
self.localX4 = self.da7.createLocalVec()
# self.localP = self.da1.createLocalVec()
# create vectors for magnetic and velocity field
self.Bix = self.da1.createGlobalVec()
self.Biy = self.da1.createGlobalVec()
self.Bx = self.da1.createGlobalVec()
self.By = self.da1.createGlobalVec()
self.Vx = self.da1.createGlobalVec()
self.Vy = self.da1.createGlobalVec()
self.P = self.da1.createGlobalVec()
self.xcoords = self.da1.createGlobalVec()
self.ycoords = self.da1.createGlobalVec()
# create local vectors for initialisation of pressure
self.localBix = self.da1.createLocalVec()
self.localBiy = self.da1.createLocalVec()
self.localBx = self.da1.createLocalVec()
self.localBy = self.da1.createLocalVec()
self.localVx = self.da1.createLocalVec()
self.localVy = self.da1.createLocalVec()
# set variable names
self.Bix.setName('Bix')
self.Biy.setName('Biy')
self.Bx.setName('Bx')
self.By.setName('By')
self.Vx.setName('Vx')
self.Vy.setName('Vy')
self.P.setName('P')
# create Matrix object
self.petsc_matrix = PETScMatrix (self.da1, self.da7, nx, ny, self.ht, self.hx, self.hy, mu, nu, eta, de)
self.petsc_function = PETScFunction(self.da1, self.da7, nx, ny, self.ht, self.hx, self.hy, mu, nu, eta, de)
# initialise matrix
self.A = self.da7.createMat()
self.A.setOption(self.A.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.A.setUp()
# create jacobian
self.J = self.da7.createMat()
self.J.setOption(self.J.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.J.setUp()
# create nonlinear solver
self.snes = PETSc.SNES().create()
self.snes.setFunction(self.petsc_function.snes_mult, self.f)
self.snes.setJacobian(self.updateJacobian, self.J)
self.snes.setFromOptions()
# self.snes.getKSP().setInitialGuessNonzero(True)
# self.snes.getKSP().getPC().setReusePreconditioner(True)
self.ksp = None
# set initial data
(xs, xe), (ys, ye) = self.da1.getRanges()
# coords = self.da1.getCoordinatesLocal()
xc_arr = self.da1.getVecArray(self.xcoords)
yc_arr = self.da1.getVecArray(self.ycoords)
for i in range(xs, xe):
for j in range(ys, ye):
xc_arr[i,j] = x1 + i*self.hx
yc_arr[i,j] = y1 + j*self.hy
if cfg['io']['hdf5_input'] != None:
hdf5_filename = self.cfg["io"]["hdf5_input"]
if PETSc.COMM_WORLD.getRank() == 0:
print(" Input: %s" % hdf5_filename)
hdf5in = h5py.File(hdf5_filename, "r", driver="mpio", comm=PETSc.COMM_WORLD.tompi4py())
# assert self.nx == hdf5in.attrs["grid.nx"]
# assert self.ny == hdf5in.attrs["grid.ny"]
# assert self.hx == hdf5in.attrs["grid.hx"]
# assert self.hy == hdf5in.attrs["grid.hy"]
# assert self.Lx == hdf5in.attrs["grid.Lx"]
# assert self.Ly == hdf5in.attrs["grid.Ly"]
#
# assert self.de == hdf5in.attrs["initial_data.skin_depth"]
timestep = len(hdf5in["t"][...].flatten()) - 1
hdf5in.close()
hdf5_viewer = PETSc.ViewerHDF5().create(cfg['io']['hdf5_input'],
mode=PETSc.Viewer.Mode.READ,
comm=PETSc.COMM_WORLD)
hdf5_viewer.setTimestep(timestep)
self.Bix.load(hdf5_viewer)
self.Biy.load(hdf5_viewer)
self.Bx.load(hdf5_viewer)
self.By.load(hdf5_viewer)
self.Vx.load(hdf5_viewer)
self.Vy.load(hdf5_viewer)
self.P.load(hdf5_viewer)
hdf5_viewer.destroy()
# copy modified magnetic induction to solution vector
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
Bix_arr = self.da1.getVecArray(self.Bix)
Biy_arr = self.da1.getVecArray(self.Biy)
P_arr = self.da1.getVecArray(self.P)
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 0] = Vx_arr [xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 1] = Vy_arr [xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 2] = Bx_arr [xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 3] = By_arr [xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 4] = Bix_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 5] = Biy_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 6] = P_arr [xs:xe, ys:ye]
else:
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
xc_arr = self.da1.getVecArray(self.xcoords)
yc_arr = self.da1.getVecArray(self.ycoords)
if cfg['initial_data']['magnetic_python'] != None:
init_data = __import__("examples." + cfg['initial_data']['magnetic_python'], globals(), locals(), ['magnetic_x', 'magnetic_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Bx_arr[i,j] = init_data.magnetic_x(xc_arr[i,j], yc_arr[i,j] + 0.5 * self.hy, self.hx, self.hy)
By_arr[i,j] = init_data.magnetic_y(xc_arr[i,j] + 0.5 * self.hx, yc_arr[i,j], self.hx, self.hy)
else:
Bx_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
By_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
if cfg['initial_data']['velocity_python'] != None:
init_data = __import__("examples." + cfg['initial_data']['velocity_python'], globals(), locals(), ['velocity_x', 'velocity_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Vx_arr[i,j] = init_data.velocity_x(xc_arr[i,j], yc_arr[i,j] + 0.5 * self.hy, self.hx, self.hy)
Vy_arr[i,j] = init_data.velocity_y(xc_arr[i,j] + 0.5 * self.hx, yc_arr[i,j], self.hx, self.hy)
else:
Vx_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
Vy_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
if cfg['initial_data']['pressure_python'] != None:
init_data = __import__("examples." + cfg['initial_data']['pressure_python'], globals(), locals(), ['pressure', ''], 0)
# Fourier Filtering
from scipy.fftpack import rfft, irfft
nfourier_x = cfg['initial_data']['nfourier_Bx']
nfourier_y = cfg['initial_data']['nfourier_By']
if nfourier_x >= 0 or nfourier_y >= 0:
print("Fourier Filtering B")
# obtain whole Bx vector everywhere
scatter, Xglobal = PETSc.Scatter.toAll(self.Bx)
scatter.begin(self.Bx, Xglobal, PETSc.InsertMode.INSERT, PETSc.ScatterMode.FORWARD)
scatter.end (self.Bx, Xglobal, PETSc.InsertMode.INSERT, PETSc.ScatterMode.FORWARD)
petsc_indices = self.da1.getAO().app2petsc(np.arange(self.nx*self.ny, dtype=np.int32))
BxTmp = Xglobal.getValues(petsc_indices).copy().reshape((self.ny, self.nx)).T
scatter.destroy()
Xglobal.destroy()
# obtain whole By vector everywhere
scatter, Xglobal = PETSc.Scatter.toAll(self.By)
scatter.begin(self.By, Xglobal, PETSc.InsertMode.INSERT, PETSc.ScatterMode.FORWARD)
scatter.end (self.By, Xglobal, PETSc.InsertMode.INSERT, PETSc.ScatterMode.FORWARD)
petsc_indices = self.da1.getAO().app2petsc(np.arange(self.nx*self.ny, dtype=np.int32))
ByTmp = Xglobal.getValues(petsc_indices).copy().reshape((self.ny, self.nx)).T
scatter.destroy()
Xglobal.destroy()
if nfourier_x >= 0:
# compute FFT, cut, compute inverse FFT
BxFft = rfft(BxTmp, axis=1)
ByFft = rfft(ByTmp, axis=1)
BxFft[:,nfourier_x+1:] = 0.
ByFft[:,nfourier_x+1:] = 0.
BxTmp = irfft(BxFft, axis=1)
ByTmp = irfft(ByFft, axis=1)
if nfourier_y >= 0:
BxFft = rfft(BxTmp, axis=0)
ByFft = rfft(ByTmp, axis=0)
BxFft[nfourier_y+1:,:] = 0.
ByFft[nfourier_y+1:,:] = 0.
BxTmp = irfft(BxFft, axis=0)
ByTmp = irfft(ByFft, axis=0)
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Bx_arr[:,:] = BxTmp[xs:xe, ys:ye]
By_arr[:,:] = ByTmp[xs:xe, ys:ye]
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 0] = Vx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 1] = Vy_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 2] = Bx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 3] = By_arr[xs:xe, ys:ye]
# compure generalised magnetic induction
self.da1.globalToLocal(self.Bx, self.localBx)
self.da1.globalToLocal(self.By, self.localBy)
self.da1.globalToLocal(self.Vx, self.localVx)
self.da1.globalToLocal(self.Vy, self.localVy)
Bx_arr = self.da1.getVecArray(self.localBx)
By_arr = self.da1.getVecArray(self.localBy)
Vx_arr = self.da1.getVecArray(self.localVx)
Vy_arr = self.da1.getVecArray(self.localVy)
Bix_arr = self.da1.getVecArray(self.Bix)
Biy_arr = self.da1.getVecArray(self.Biy)
for i in range(xs, xe):
for j in range(ys, ye):
Bix_arr[i,j] = self.derivatives.Bix(Bx_arr[...], By_arr[...], i-xs+2, j-ys+2, de)
Biy_arr[i,j] = self.derivatives.Biy(Bx_arr[...], By_arr[...], i-xs+2, j-ys+2, de)
# copy modified magnetic induction to solution vector
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 4] = Bix_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 5] = Biy_arr[xs:xe, ys:ye]
# compute pressure
self.da1.globalToLocal(self.Bix, self.localBix)
self.da1.globalToLocal(self.Biy, self.localBiy)
Bix_arr = self.da1.getVecArray(self.localBix)
Biy_arr = self.da1.getVecArray(self.localBiy)
P_arr = self.da1.getVecArray(self.P)
for i in range(xs, xe):
for j in range(ys, ye):
P_arr[i,j] = init_data.pressure(xc_arr[i,j] + 0.5 * self.hx, yc_arr[i,j] + 0.5 * self.hy, self.hx, self.hy) \
- 0.5 * 0.25 * (Bix_arr[i,j] + Bix_arr[i+1,j]) * (Bx_arr[i,j] + Bx_arr[i+1,j]) \
- 0.5 * 0.25 * (Biy_arr[i,j] + Biy_arr[i,j+1]) * (By_arr[i,j] + By_arr[i,j+1]) \
# - 0.5 * (0.25 * (Vx_arr[i,j] + Vx_arr[i+1,j])**2 + 0.25 * (Vy_arr[i,j] + Vy_arr[i,j+1])**2)
# copy pressure to solution vector
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 6] = P_arr [xs:xe, ys:ye]
# update solution history
self.petsc_matrix.update_history(self.x)
self.petsc_function.update_history(self.x)
hdf5_filename = cfg['io']['hdf5_output']
if PETSc.COMM_WORLD.getRank() == 0:
print(" Output: %s" % hdf5_filename)
hdf5out = h5py.File(hdf5_filename, "w", driver="mpio", comm=PETSc.COMM_WORLD.tompi4py())
for cfg_group in self.cfg:
for cfg_item in self.cfg[cfg_group]:
if self.cfg[cfg_group][cfg_item] != None:
value = self.cfg[cfg_group][cfg_item]
else:
value = ""
hdf5out.attrs[cfg_group + "." + cfg_item] = value
# if self.cfg["initial_data"]["python"] != None and self.cfg["initial_data"]["python"] != "":
# python_input = open("runs/" + self.cfg['initial_data']['python'] + ".py", 'r')
# python_file = python_input.read()
# python_input.close()
# else:
# python_file = ""
# hdf5out.attrs["initial_data.python_file"] = python_file
hdf5out.close()
# create HDF5 output file
self.hdf5_viewer = PETSc.ViewerHDF5().create(hdf5_filename,
mode=PETSc.Viewer.Mode.WRITE,
comm=PETSc.COMM_WORLD)
self.hdf5_viewer.pushGroup("/")
# write grid data to hdf5 file
coords_x = self.dax.getCoordinates()
coords_y = self.day.getCoordinates()
coords_x.setName('x')
coords_y.setName('y')
self.hdf5_viewer(coords_x)
self.hdf5_viewer(coords_y)
# write initial data to hdf5 file
self.hdf5_viewer.setTimestep(0)
self.save_hdf5_vectors()
def __del__(self):
self.hdf5_viewer.destroy()
self.snes.destroy()
self.A.destroy()
self.J.destroy()
self.da1.destroy()
self.da7.destroy()
self.dax.destroy()
self.day.destroy()
def updateJacobian(self, snes, X, J, P):
self.petsc_function.update_previous(X)
self.petsc_function.formMat(J)
# if self.update_jacobian:
# self.petsc_jacobian.update_previous(X)
# self.petsc_jacobian.formMat(J)
# self.update_jacobian = False
# else:
# return PETSc.Mat().Structure.SAME_PRECONDITIONER
def run(self):
for itime in range(1, self.nt+1):
if PETSc.COMM_WORLD.getRank() == 0:
localtime = time.asctime( time.localtime(time.time()) )
print("\nit = %4d, t = %10.4f, %s" % (itime, self.ht*itime, localtime) )
print()
self.time.setValue(0, self.ht*itime)
# calculate initial guess
# self.calculate_initial_guess()
# update Jacobian
self.update_jacobian = True
# solve
self.snes.solve(None, self.x)
# output some solver info
fnorm = self.snes.getFunction()[0].norm()
if PETSc.COMM_WORLD.getRank() == 0:
print(" Linear Solver: %5i iterations" % (self.snes.getLinearSolveIterations()) )
print(" Nonlinear Solver: %5i iterations, funcnorm = %24.16E" % (self.snes.getIterationNumber(), fnorm) )
# update history
self.petsc_matrix.update_history(self.x)
self.petsc_function.update_history(self.x)
# save to hdf5 file
if itime % self.nsave == 0 or itime == self.nt + 1:
self.save_to_hdf5()
def calculate_initial_guess(self):
self.ksp = PETSc.KSP().create()
self.ksp.setFromOptions()
self.ksp.setOperators(self.A)
self.ksp.setType('gmres')
self.ksp.getPC().setType('none')
# self.ksp.setType('preonly')
# self.ksp.getPC().setType('lu')
# build matrix
self.petsc_matrix.formMat(self.A)
# build RHS
self.petsc_matrix.formRHS(self.b)
# solve
self.ksp.solve(self.b, self.x)
# destroy
self.ksp.destroy()
def rk4(self, X, Y, fac=1.0):
self.da7.globalToLocal(X, self.localX0)
x0 = self.da7.getVecArray(self.localX0)[...]
x1 = self.da7.getVecArray(self.X1)[...]
self.petsc_function.timestep(x0, x1)
self.da7.globalToLocal(self.X1, self.localX1)
x1 = self.da7.getVecArray(self.localX1)[...]
x2 = self.da7.getVecArray(self.X2)[...]
self.petsc_function.timestep(x0 + 0.5 * fac * self.ht * x1, x2)
self.da7.globalToLocal(self.X2, self.localX2)
x2 = self.da7.getVecArray(self.localX2)[...]
x3 = self.da7.getVecArray(self.X3)[...]
self.petsc_function.timestep(x0 + 0.5 * fac * self.ht * x2, x3)
self.da7.globalToLocal(self.X3, self.localX3)
x3 = self.da7.getVecArray(self.localX3)[...]
x4 = self.da7.getVecArray(self.X4)[...]
self.petsc_function.timestep(x0 + 1.0 * fac * self.ht * x3, x4)
y = self.da7.getVecArray(Y)[...]
x0 = self.da7.getVecArray(X)[...]
x1 = self.da7.getVecArray(self.X1)[...]
x2 = self.da7.getVecArray(self.X2)[...]
x3 = self.da7.getVecArray(self.X3)[...]
x4 = self.da7.getVecArray(self.X4)[...]
y[:,:,:] = x0 + fac * self.ht * (x1 + 2.*x2 + 2.*x3 + x4) / 6.
def save_to_hdf5(self):
(xs, xe), (ys, ye) = self.da1.getRanges()
# copy solution to B and V vectors
x_arr = self.da7.getVecArray(self.x)
Bix_arr = self.da1.getVecArray(self.Bix)
Biy_arr = self.da1.getVecArray(self.Biy)
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
P_arr = self.da1.getVecArray(self.P)
Vx_arr [xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 0]
Vy_arr [xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 1]
Bx_arr [xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 2]
By_arr [xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 3]
Bix_arr[xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 4]
Biy_arr[xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 5]
P_arr [xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 6]
# save timestep
self.hdf5_viewer.setTimestep(self.hdf5_viewer.getTimestep() + 1)
# save data
self.save_hdf5_vectors()
def save_hdf5_vectors(self):
self.hdf5_viewer(self.time)
self.hdf5_viewer(self.Bix)
self.hdf5_viewer(self.Biy)
self.hdf5_viewer(self.Bx)
self.hdf5_viewer(self.By)
self.hdf5_viewer(self.Vx)
self.hdf5_viewer(self.Vy)
self.hdf5_viewer(self.P)
def check_jacobian(self):
(xs, xe), (ys, ye) = self.da1.getRanges()
eps = 1.E-7
# calculate initial guess
# self.calculate_initial_guess()
# update previous iteration
self.petsc_function.update_previous(self.x)
# calculate jacobian
self.petsc_function.formMat(self.J)
# create working vectors
Jx = self.da7.createGlobalVec()
dJ = self.da7.createGlobalVec()
ex = self.da7.createGlobalVec()
dx = self.da7.createGlobalVec()
dF = self.da7.createGlobalVec()
Fxm = self.da7.createGlobalVec()
Fxp = self.da7.createGlobalVec()
# sx = -2
# sx = -1
sx = 0
# sx = +1
# sx = +2
# sy = -2
# sy = -1
sy = 0
# sy = +1
# sy = +2
nfield=7
for ifield in range(0, nfield):
for ix in range(xs, xe):
for iy in range(ys, ye):
for tfield in range(0, nfield):
# compute ex
ex_arr = self.da7.getVecArray(ex)
ex_arr[:] = 0.
ex_arr[(ix+sx) % self.nx, (iy+sy) % self.ny, ifield] = 1.
# compute J.e
self.J.mult(ex, dJ)
dJ_arr = self.da7.getVecArray(dJ)
Jx_arr = self.da7.getVecArray(Jx)
Jx_arr[ix, iy, tfield] = dJ_arr[ix, iy, tfield]
# compute F(x - eps ex)
self.x.copy(dx)
dx_arr = self.da7.getVecArray(dx)
dx_arr[(ix+sx) % self.nx, (iy+sy) % self.ny, ifield] -= eps
self.petsc_function.matrix_mult(dx, Fxm)
# compute F(x + eps ex)
self.x.copy(dx)
dx_arr = self.da7.getVecArray(dx)
dx_arr[(ix+sx) % self.nx, (iy+sy) % self.ny, ifield] += eps
self.petsc_function.matrix_mult(dx, Fxp)
# compute dF = [F(x + eps ex) - F(x - eps ex)] / (2 eps)
Fxm_arr = self.da7.getVecArray(Fxm)
Fxp_arr = self.da7.getVecArray(Fxp)
dF_arr = self.da7.getVecArray(dF)
dF_arr[ix, iy, tfield] = ( Fxp_arr[ix, iy, tfield] - Fxm_arr[ix, iy, tfield] ) / (2. * eps)
diff = np.zeros(nfield)
for tfield in range(0,nfield):
# print()
# print("Fields: (%5i, %5i)" % (ifield, tfield))
# print()
Jx_arr = self.da7.getVecArray(Jx)[...][:, :, tfield]
dF_arr = self.da7.getVecArray(dF)[...][:, :, tfield]
# print("Jacobian:")
# print(Jx_arr)
# print()
#
# print("[F(x+dx) - F(x-dx)] / [2 eps]:")
# print(dF_arr)
# print()
#
# print("Difference:")
# print(Jx_arr - dF_arr)
# print()
# if ifield == 3 and tfield == 2:
# print("Jacobian:")
# print(Jx_arr)
# print()
#
# print("[F(x+dx) - F(x-dx)] / [2 eps]:")
# print(dF_arr)
# print()
diff[tfield] = (Jx_arr - dF_arr).max()
print()
for tfield in range(0,nfield):
print("max(difference)[fields=%i,%i] = %16.8E" % ( ifield, tfield, diff[tfield] ))
print()
if __name__ == '__main__':
parser = argparse.ArgumentParser(description='PETSc MHD Solver in 2D')
parser.add_argument('runfile', metavar='runconfig', type=str,
help='Run Configuration File')
args = parser.parse_args()
petscvp = petscMHD2D(args.runfile)
petscvp.run()
# petscvp.check_jacobian()