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petsc_mhd2d_nonlinear_newton_snes.py
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petsc_mhd2d_nonlinear_newton_snes.py
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'''
Created on Mar 23, 2012
@author: Michael Kraus ([email protected])
'''
import sys, petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
import argparse
import time
import numpy as np
from config import Config
#import PETSc_MHD_NL_Jacobian_Matrix
#from PETSc_MHD_NL_Jacobian_Matrix5d_dofs import PETScJacobian
#from PETSc_MHD_NL_Function import PETScFunction
#from PETSc_MHD_NL_SG_Jacobian_Matrix5d import PETScJacobian
#from PETSc_MHD_NL_SG_Function import PETScFunction
#from PETSc_MHD_NL_FV_Jacobian_Matrix5d import PETScJacobian
#from PETSc_MHD_NL_FV_Function import PETScFunction
#from PETSc_MHD_NL_FVD_Jacobian_Matrix5d import PETScJacobian
#from PETSc_MHD_NL_FVD_Function import PETScFunction
#from PETSc_MHD_NL_FVG_Jacobian_Matrix5d import PETScJacobian # Gawlik Scheme
#from PETSc_MHD_NL_FVG_Function import PETScFunction
from Ideal_MHD_NL_Jacobian_Matrix import PETScJacobian
from Ideal_MHD_NL_Function import PETScFunction
from Ideal_MHD_NL_Matrix import PETScMatrix
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)
# set some PETSc options
OptDB = PETSc.Options()
# OptDB.setValue('snes_lag_preconditioner', 5)
OptDB.setValue('snes_atol', cfg['solver']['petsc_residual'])
OptDB.setValue('snes_rtol', 1E-16)
OptDB.setValue('snes_stol', 1E-18)
OptDB.setValue('snes_max_it', 20)
OptDB.setValue('ksp_rtol', cfg['solver']['petsc_residual'])
OptDB.setValue('ksp_max_it', 100)
OptDB.setValue('snes_monitor', '')
OptDB.setValue('ksp_monitor', '')
# 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
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 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 = 4 for Bx, By, Vx, Vy)
self.da4 = PETSc.DA().create(dim=2, dof=4,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA (dof = 5 for Bx, By, Vx, Vy, P)
self.da5 = PETSc.DA().create(dim=2, dof=5,
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.da4.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.da5.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.da5.createGlobalVec()
self.x = self.da5.createGlobalVec()
self.b = self.da5.createGlobalVec()
# create global RK4 vectors
self.Y = self.da5.createGlobalVec()
self.X0 = self.da5.createGlobalVec()
self.X1 = self.da5.createGlobalVec()
self.X2 = self.da5.createGlobalVec()
self.X3 = self.da5.createGlobalVec()
self.X4 = self.da5.createGlobalVec()
# create local RK4 vectors
self.localX0 = self.da5.createLocalVec()
self.localX1 = self.da5.createLocalVec()
self.localX2 = self.da5.createLocalVec()
self.localX3 = self.da5.createLocalVec()
self.localX4 = self.da5.createLocalVec()
# self.localP = self.da1.createLocalVec()
# create vectors for magnetic and velocity field
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.localBx = self.da1.createLocalVec()
self.localBy = self.da1.createLocalVec()
self.localVx = self.da1.createLocalVec()
self.localVy = self.da1.createLocalVec()
# set variable names
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.da5, nx, ny, self.ht, self.hx, self.hy, mu, nu, eta)
self.petsc_jacobian = PETScJacobian(self.da1, self.da5, nx, ny, self.ht, self.hx, self.hy, mu, nu, eta)
self.petsc_function = PETScFunction(self.da1, self.da5, nx, ny, self.ht, self.hx, self.hy, mu, nu, eta)
# self.petsc_jacobian_4d = PETSc_MHD_NL_Jacobian_Matrix.PETScJacobian(self.da1, self.da5, nx, ny, self.ht, self.hx, self.hy)
# initialise matrix
self.A = self.da5.createMat()
self.A.setOption(self.A.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.A.setUp()
# create jacobian
self.J = self.da5.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().setType('preonly')
# self.snes.getKSP().setType('gmres')
self.snes.getKSP().getPC().setType('lu')
# self.snes.getKSP().getPC().setFactorSolverPackage('superlu_dist')
self.snes.getKSP().getPC().setFactorSolverPackage('mumps')
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
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__("runs." + 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, Lx, Ly)
By_arr[i,j] = init_data.magnetic_y(xc_arr[i,j] + 0.5 * self.hx, yc_arr[i,j], Lx, Ly)
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__("runs." + 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, Lx, Ly)
Vy_arr[i,j] = init_data.velocity_y(xc_arr[i,j] + 0.5 * self.hx, yc_arr[i,j], Lx, Ly)
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__("runs." + cfg['initial_data']['pressure_python'], globals(), locals(), ['pressure', ''], 0)
x_arr = self.da5.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]
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)
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, Lx, Ly)
# P_arr[i,j] = init_data.pressure(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1] + 0.5 * self.hy, Lx, Ly) \
# + 0.5 * (0.25 * (Bx_arr[i,j] + Bx_arr[i+1,j])**2 + 0.25 * (By_arr[i,j] + By_arr[i,j+1])**2)
# P_arr[i,j] = init_data.pressure(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1] + 0.5 * self.hy, Lx, Ly) \
# + 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)
# P_arr[i,j] = init_data.pressure(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1] + 0.5 * self.hy, Lx, Ly) \
# + 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) \
# - 1.0 * (0.25 * (Bx_arr[i,j] + Bx_arr[i+1,j])**2 + 0.25 * (By_arr[i,j] + By_arr[i,j+1])**2)
# copy distribution function to solution vector
x_arr = self.da5.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 4] = P_arr [xs:xe, ys:ye]
# update solution history
self.petsc_matrix.update_history(self.x)
self.petsc_jacobian.update_history(self.x)
self.petsc_function.update_history(self.x)
# create HDF5 output file
self.hdf5_viewer = PETSc.ViewerHDF5().create(cfg['io']['hdf5_output'],
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.da4.destroy()
self.da5.destroy()
self.dax.destroy()
self.day.destroy()
def updateJacobian(self, snes, X, J, P):
self.petsc_jacobian.update_previous(X)
self.petsc_jacobian.formMat(J)
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()
# 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_jacobian.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('preonly')
self.ksp.getPC().setType('lu')
# self.ksp.getPC().setFactorSolverPackage('superlu_dist')
self.ksp.getPC().setFactorSolverPackage('mumps')
# 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.da5.globalToLocal(X, self.localX0)
x0 = self.da5.getVecArray(self.localX0)[...]
x1 = self.da5.getVecArray(self.X1)[...]
self.petsc_function.timestep(x0, x1)
self.da5.globalToLocal(self.X1, self.localX1)
x1 = self.da5.getVecArray(self.localX1)[...]
x2 = self.da5.getVecArray(self.X2)[...]
self.petsc_function.timestep(x0 + 0.5 * fac * self.ht * x1, x2)
self.da5.globalToLocal(self.X2, self.localX2)
x2 = self.da5.getVecArray(self.localX2)[...]
x3 = self.da5.getVecArray(self.X3)[...]
self.petsc_function.timestep(x0 + 0.5 * fac * self.ht * x2, x3)
self.da5.globalToLocal(self.X3, self.localX3)
x3 = self.da5.getVecArray(self.localX3)[...]
x4 = self.da5.getVecArray(self.X4)[...]
self.petsc_function.timestep(x0 + 1.0 * fac * self.ht * x3, x4)
y = self.da5.getVecArray(Y)[...]
x0 = self.da5.getVecArray(X)[...]
x1 = self.da5.getVecArray(self.X1)[...]
x2 = self.da5.getVecArray(self.X2)[...]
x3 = self.da5.getVecArray(self.X3)[...]
x4 = self.da5.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.da5.getVecArray(self.x)
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]
P_arr [xs:xe, ys:ye] = x_arr[xs:xe, ys:ye, 4]
# 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.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_jacobian.update_previous(self.x)
# calculate jacobian
self.petsc_jacobian.formMat(self.J)
# create working vectors
Jx = self.da5.createGlobalVec()
dJ = self.da5.createGlobalVec()
ex = self.da5.createGlobalVec()
dx = self.da5.createGlobalVec()
dF = self.da5.createGlobalVec()
Fxm = self.da5.createGlobalVec()
Fxp = self.da5.createGlobalVec()
# sx = -2
# sx = -1
sx = 0
# sx = +1
# sx = +2
# sy = -2
# sy = -1
sy = 0
# sy = +1
# sy = +2
nfield=5
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.da5.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.da5.getVecArray(dJ)
Jx_arr = self.da5.getVecArray(Jx)
Jx_arr[ix, iy, tfield] = dJ_arr[ix, iy, tfield]
# compute F(x - eps ex)
self.x.copy(dx)
dx_arr = self.da5.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.da5.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.da5.getVecArray(Fxm)
Fxp_arr = self.da5.getVecArray(Fxp)
dF_arr = self.da5.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.da5.getVecArray(Jx)[...][:, :, tfield]
dF_arr = self.da5.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()