DRY. so wen can create temporary array for the force vector and the repeating part
"""
tmpRhs = ((1.0-theta) * (A*u[n-1] - F) - theta * F)
rhs = M * u[n-1] + k * M * v[n-1] - k*k * theta * tmpRhs
"""
Create the system matrix
"""
S = M + A * k*k * theta*theta
"""
Apply boundary conditions.
"""
if n==1:
solver.assembleDirichletBC(S,
solver.parseArgToBoundaries([grid.findBoundaryByMarker(1), 1], grid),
rhs)
else:
solver.assembleDirichletBC(S,
solver.parseArgToBoundaries([grid.findBoundaryByMarker(1), 0], grid),
rhs)
solver.assembleDirichletBC(S,
solver.parseArgToBoundaries([grid.findBoundaryByMarker(2), 0], grid),
rhs)
"""
Solve for u
"""
u[n] = solver.linsolve(S, rhs)
DRY. so wen can create temporary array for the force vector and the repeating part
"""
tmpRhs = ((1.0-theta) * (A*u[n-1] - F) - theta * F)
rhs = M * u[n-1] + k * M * v[n-1] - k*k * theta * tmpRhs
"""
Create the system matrix
"""
S = M + A * k*k * theta*theta
"""
Apply boundary conditions.
"""
if n==1:
solver.assembleDirichletBC(S,
solver.parseArgToBoundaries([grid.findBoundaryByMarker(1), 1], grid),
rhs)
else:
solver.assembleDirichletBC(S,
solver.parseArgToBoundaries([grid.findBoundaryByMarker(1), 0], grid),
rhs)
solver.assembleDirichletBC(S,
solver.parseArgToBoundaries([grid.findBoundaryByMarker(2), 0], grid),
rhs)
"""
Solve for u
"""
u[n] = solver.linsolve(S, rhs)
dt = times[1] - times[0]
A = solver.createStiffnessMatrix(grid, np.ones(grid.cellCount()))
M = solver.createMassMatrix(grid, np.ones(grid.cellCount()))
ut = pg.RVector(dof, 0.0)
rhs = pg.RVector(dof, 0.0)
b = pg.RVector(dof, 0.0)
theta = 0
boundUdir = solver.parseArgToBoundaries(dirichletBC, grid)
for n in range(1, len(times)):
b = (M - A * dt) * u[n - 1] + rhs * dt
S = M
solver.assembleDirichletBC(S, boundUdir, rhs=b)
# solver.assembleBoundaryConditions(grid, S,
# rhs=b,
# boundArgs=dirichletBC,
# assembler=solver.assembleDirichletBC)
solve = pg.LinSolver(S)
solve.solve(b, ut)
u[n, :] = ut
# u = solver.solvePoisson(grid, times=times, theta=0.0,
# u0=lambda r: np.sin(np.pi * r[0]),
# uBoundary=dirichletBC)
dt = times[1] - times[0]
A = solver.createStiffnessMatrix(grid, np.ones(grid.cellCount()))
M = solver.createMassMatrix(grid, np.ones(grid.cellCount()))
ut = pg.RVector(dof, 0.0)
rhs = pg.RVector(dof, 0.0)
b = pg.RVector(dof, 0.0)
theta = 0
boundUdir = solver.parseArgToBoundaries(dirichletBC, grid)
for n in range(1, len(times)):
b = (M - A * dt) * u[n - 1] + rhs * dt
S = M
solver.assembleDirichletBC(S, boundUdir, rhs=b)
solve = pg.LinSolver(S)
solve.solve(b, ut)
u[n, :] = ut
plt.plot(times, u[:, probeID], label='Explicit Euler')
theta = 1
for n in range(1, len(times)):
b = (M + A * (dt*(theta - 1.0))) * u[n-1] + \
rhs * (dt*(1.0 - theta)) + \
rhs * dt * theta