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test_pattern.py
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# -*- coding:utf-8 -*-
import math
import sys
import petsc4py
petsc4py.init(sys.argv)
from petsc4py import PETSc
from mpi4py import MPI
class Pattern():
def __init__(self, da):
self.da = da
self.local_vec_Y = da.createLocalVec()
self.L = 2.5
self.Du = 8.0e-5
self.Dv = 4.0e-5
self.phi = 0.024
self.kappa = 0.06
self.IFcn_called = False
self.IJac_called = False
self.RHSFcn_called = False
self.RHSJac_called = False
# in system form F(t,Y,dot Y) = G(t,Y), compute G():
# G^u(t,u,v) = - u v^2 + phi (1 - u)
# G^v(t,u,v) = + u v^2 - (phi + kappa) v
def FormRHSFunctionLocal(self, ts, t, vec_Y, vec_G):
self.RHSFcn_called = True
self.da.globalToLocal(vec_Y, self.local_vec_Y)
aY = da.getVecArray(self.local_vec_Y)
aG = da.getVecArray(vec_G)
(xs, xe), (ys, ye) = da.getRanges()
uv2 = aY[xs:xe, ys:ye, 0] * aY[xs:xe, ys:ye, 1] * aY[xs:xe, ys:ye, 1]
aG[xs:xe, ys:ye, 0] = -uv2 + self.phi*(1.0 - aY[xs:xe, ys:ye,0])
aG[xs:xe, ys:ye, 1] = uv2 - (self.phi+self.kappa)*aY[xs:xe, ys:ye, 1]
# for j in range(ys, ye):
# for i in range(xs, xe):
# uv2 = aY[i,j,0]*aY[i,j,1]*aY[i,j,1]
# aG[i,j,0] = -uv2 + self.phi*(1.0 - aY[i,j,0])
# aG[i,j,1] = +uv2 - (self.phi+self.kappa)*aY[i,j,1]
return True
def FormRHSJacobianLocal(self, ts, t, vec_Y, Mat_J, Mat_P):
self.RHSJac_called = True
aY = da.getVecArray(vec_Y)
row = PETSc.Mat.Stencil()
col = [PETSc.Mat.Stencil(), PETSc.Mat.Stencil()]
v = [0, 0]
(xs, xe), (ys, ye) = da.getRanges()
for j in range(ys, ye):
row.j = j; col[0].j = j; col[1].j = j
for i in range(xs, xe):
row.i = i; col[0].i = i; col[1].i = i
uv = aY[i, j, 0] * aY[i, j, 1]
v2 = aY[i, j, 1] * aY[i, j, 1]
# u equation
row.c = 0; col[0].c = 0; col[1].c = 1
v[0] = - v2 - self.phi
v[1] = - 2.0 * uv
Mat_P.setValueStencil(row, col[0], v[0], PETSc.InsertMode.INSERT_VALUES)
Mat_P.setValueStencil(row, col[1], v[1], PETSc.InsertMode.INSERT_VALUES)
# v equation
row.c = 1; col[0].c = 0; col[1].c = 1
v[0] = v2
v[1] = 2.0 * uv - (self.phi + self.kappa)
Mat_P.setValueStencil(row, col[0], v[0], PETSc.InsertMode.INSERT_VALUES)
Mat_P.setValueStencil(row, col[1], v[1], PETSc.InsertMode.INSERT_VALUES)
Mat_P.assemble()
if Mat_J != Mat_P:
Mat_J.assemble()
return True
# Callable[[TS, float, Vec, Vec, Vec], None]
def FormIFunctionLocal(self, ts, t, vec_Y, vec_Ydot, vec_F):
self.da.globalToLocal(vec_Y, self.local_vec_Y)
aY = self.da.getVecArray(self.local_vec_Y)
aYdot = self.da.getVecArray(vec_Ydot)
aF = self.da.getVecArray(vec_F)
mx, my = self.da.getSizes()
h = self.L / mx
Cu = self.Du / (6.0*h*h)
Cv = self.Dv / (6.0*h*h)
self.IFcn_called = True
(xs, xe), (ys, ye) = da.getRanges()
u = aY[xs:xe, ys:ye, 0]
v = aY[xs:xe, ys:ye, 1]
lapu = aY[(xs-1):(xe-1),(ys+1):(ye+1),0] \
+ 4.0*aY[xs:xe,(ys+1):(ye+1),0] + aY[(xs+1):(xe+1),(ys+1):(ye+1),0] \
+ 4.0*aY[(xs-1):(xe-1),ys:ye,0] - 20.0*u + 4.0*aY[(xs+1):(xe+1), ys:ye, 0] \
+ aY[(xs-1):(xe-1),(ys-1):(ye-1),0] + 4.0*aY[xs:xe,(ys-1):(ye-1),0] \
+ aY[(xs+1):(xe+1),(ys-1):(ye-1),0]
lapv = aY[(xs-1):(xe-1),(ys+1):(ye+1),1] \
+ 4.0*aY[xs:xe,(ys+1):(ye+1),1] + aY[(xs+1):(xe+1),(ys+1):(ye+1),1] \
+ 4.0*aY[(xs-1):(xe-1),ys:ye,1] - 20.0*v + 4.0*aY[(xs+1):(xe+1), ys:ye, 1] \
+ aY[(xs-1):(xe-1),(ys-1):(ye-1),1] + 4.0*aY[xs:xe,(ys-1):(ye-1),1] \
+ aY[(xs+1):(xe+1),(ys-1):(ye-1),1]
aF[xs:xe, ys:ye, 0] = aYdot[xs:xe, ys:ye, 0] - Cu*lapu
aF[xs:xe, ys:ye, 1] = aYdot[xs:xe, ys:ye, 1] - Cv*lapv
# for j in range(ys, ye):
# for i in range(xs, xe):
# u = aY[i, j, 0]
# v = aY[i, j, 1]
# lapu = aY[i-1,j+1,0] + 4.0*aY[i,j+1,0] + aY[i+1,j+1,0] + 4.0*aY[i-1,j,0] - 20.0*u + 4.0*aY[i+1, j, 0] + aY[i-1,j-1,0] + 4.0*aY[i,j-1,0] + aY[i+1,j-1,0]
# lapv = aY[i-1,j+1,1] + 4.0*aY[i,j+1,1] + aY[i+1,j+1,1] + 4.0*aY[i-1,j,1] - 20.0*v + 4.0*aY[i+1, j, 1] + aY[i-1,j-1,1] + 4.0*aY[i,j-1,1] + aY[i+1,j-1,1]
# aF[i,j,0] = aYdot[i,j,0] - Cu*lapu
# aF[i,j,1] = aYdot[i,j,1] - Cv*lapv
return True
# in system form F(t,Y,dot Y) = G(t,Y), compute combined/shifted
# Jacobian of F():
# J = (shift) dF/d(dot Y) + dF/dY
# Callable[[TS, float, Vec, Vec, float, Mat, Mat], None]
def FormIJacobianLocal(self, ts, t, vec_Y, vec_Ydot, shift, Mat_J, Mat_P):
row = PETSc.Mat.Stencil()
col = [PETSc.Mat.Stencil() for i in range(9)]
val = [0]*9
mx, my = self.da.getSizes()
h = self.L / mx
Cu = self.Du / (6.0*h*h)
Cv = self.Dv / (6.0*h*h)
Mat_P.zeroEntries() # workaround to address PETSc issue #734
self.IJac_called = True
(xs, xe), (ys, ye) = da.getRanges()
for j in range(ys, ye):
row.j = j
for i in range(xs, xe):
row.i = i
for c in [0, 1]:
row.c = c
CC = Cu if c == 0 else Cv
for s in range(9):
col[s].c = c
col[0].i = i; col[0].j = j
val[0] = shift + 20.0 * CC
col[1].i = i-1; col[1].j = j; val[1] = - 4.0 * CC
col[2].i = i+1; col[2].j = j; val[2] = - 4.0 * CC
col[3].i = i; col[3].j = j-1; val[3] = - 4.0 * CC
col[4].i = i; col[4].j = j+1; val[4] = - 4.0 * CC
col[5].i = i-1; col[5].j = j-1; val[5] = - CC
col[6].i = i-1; col[6].j = j+1; val[6] = - CC
col[7].i = i+1; col[7].j = j-1; val[7] = - CC
col[8].i = i+1; col[8].j = j+1; val[8] = - CC
for s in range(9):
Mat_P.setValueStencil(row, col[s], val[s], PETSc.InsertMode.INSERT_VALUES)
Mat_P.assemble()
if Mat_J != Mat_P:
Mat_J.assemble()
return True
def InitialState(da, Y, noiselevel, pattern_obj:Pattern):
ledge = (pattern_obj.L - 0.5) / 2.0
redge = pattern_obj.L - ledge
Y.set(0.0)
if noiselevel > 0.0:
Y.setRandom()
Y.scale(noiselevel)
(xs, xe), (ys, ye) = da.getRanges()
# getCoordinates returns a Vec which contains the (x,y)
# coordinates of all the grid points on the mesh
# It is one dimensional object and hard to use.
# So we convert it to an array which has the same dimension
# as the mesh ...
aC = da.getVecArray(da.getCoordinates())
aY = da.getVecArray(Y)
for j in range(ys, ye):
for i in range(xs, xe):
x = aC[i, j, 0]
y = aC[i, j, 1]
if (x >= ledge and x <= redge and y >= ledge and y <= redge):
sx = math.sin(4.0 * math.pi * x)
sy = math.sin(4.0 * math.pi * y)
aY[i, j, 1] += 0.5*sx*sx*sy*sy # "u" 0, "v" 1
aY[i, j, 0] += 1.0 - 2.0*aY[i, j, 1]
return True
OptDB = PETSc.Options("ptn_")
call_back_report = OptDB.getBool("-call_back_report", False)
no_ijacobian = OptDB.getBool("-no_ijacobian", False)
no_rhsjacobian = OptDB.getBool("-no_rhsjacobian", False)
noiselevel = OptDB.getReal("noisy_init", -1.0)
Du = OptDB.getReal("Du", 8.0e-5)
Dv = OptDB.getReal("Dv", 4.0e-5)
kappa = OptDB.getReal("kappa", 0.06)
L = OptDB.getReal("L", 2.5)
phi = OptDB.getReal("phi", 0.024)
da = PETSc.DMDA()
da.create(comm = PETSc.COMM_WORLD,
dim=2,
sizes=(3, 3),
proc_sizes=None,
boundary_type=(PETSc.DM.BoundaryType.PERIODIC, PETSc.DM.BoundaryType.PERIODIC),
stencil_type=PETSc.DMDA.StencilType.BOX,
stencil_width=1,
dof=2,
setup=False)
da.setFromOptions()
da.setUp()
#da.setFieldName(0, "u")
#da.setFieldName(1, "v")
(mx, my) = da.getSizes()
if mx != my:
raise RuntimeError("mx must equals to my")
da.setUniformCoordinates(0.0, L, 0.0, L)
PETSc.Sys.Print("running on %d x %d grid with square cells of side h = %.6f ..."%(mx, my, L/mx))
pattern = Pattern(da)
pattern.Du = Du
pattern.Dv = Dv
pattern.kappa = kappa
pattern.L = L
pattern.phi = phi
ts = PETSc.TS().create(comm=PETSc.COMM_WORLD)
ts.setProblemType(PETSc.TS.ProblemType.NONLINEAR)
ts.setDM(da)
ts.setRHSFunction(pattern.FormRHSFunctionLocal)
if not no_rhsjacobian:
ts.setRHSJacobian(pattern.FormRHSJacobianLocal)
ts.setIFunction(pattern.FormIFunctionLocal)
if not no_ijacobian:
ts.setIJacobian(pattern.FormIJacobianLocal)
ts.setType(PETSc.TS.Type.ARKIMEX)
ts.setTime(0.0)
ts.setMaxTime(200.0)
ts.setTimeStep(5.0)
ts.setExactFinalTime(PETSc.TS.ExactFinalTime.MATCHSTEP)
ts.setFromOptions()
x = da.createGlobalVec()
InitialState(da, x, noiselevel, pattern)
ts.solve(x)
if call_back_report:
ts_type = ts.getType()
PETSc.Sys.Print("CALL-BACK REPORT\n solver type: %s"%(ts_type))
PETSc.Sys.Print(" IFunction: %d | IJacobian: %d"%(int(pattern.IFcn_called), int(pattern.IJac_called)))
PETSc.Sys.Print(" RHSFunction: %d | RHSJacobian: %d"%(int(pattern.RHSFcn_called), int(pattern.RHSJac_called)))
x.destroy()
ts.destroy()
da.destroy()