def ConvergenceGMRes(params, outkeys, keyinteg):
Inform.Display(params['nodes'], params['itera'], 'ConvergenceGMRes')
bar = progressbar.ProgressBar(widgets=[progressbar.Bar(), ' (', progressbar.ETA(), ') '])
outnames = {key: DataOut( name = outkeys[key], method = 'gm', nd = params['nodes'],
it = params['itera'], pic = params['picit']) for key in outkeys}
type = 'lobatto'
integrate = True
bfield = False
n = Stepsize()
omdt = np.zeros(n.st)
xpos = np.zeros([n.st, 3])
xvel = np.zeros([n.st, 3])
for u in range(n.st):
step = params['tend']/n.step[u]
p = Particle(params['nodes'], n.step[u])
gmres = gmres_sdc(dt = step, nodes = params['nodes'], kiter = params['itera'], pic = params['picit'],
nsteps = int(n.step[u]), type=type, integrate=integrate)
x_gm, v_gm, stats = gmres.run(bfield = bfield, outnames = outnames, params = params)
xpos[u, :] = x_gm[:, int(n.step[u])]
xvel[u, :] = v_gm[:, int(n.step[u])]
omdt[u] = step*p.P.om_c
Inform.storePositions(outnames['positions'].fullname, n.st, xpos, omdt)
Inform.storeConverg(outnames['convergence'].fullname, n.st - 1, xpos, omdt)
def BrefBrs(params, outkeys):
Inform.Display(params['nodes'], params['itera'], 'BrefBrs')
bar = progressbar.ProgressBar(widgets=[progressbar.Bar(), ' (', progressbar.ETA(), ') '])
outnames = {key: DataOut( name = outkeys[key], method = 'brs', nd = params['nodes'],
it = params['itera'], pic = params['picit']) for key in outkeys}
n = Stepsize()
for u in range(n.st):
step = params['tend']/n.step[u]
p = Particle(params['nodes'], n.step[u])
p.S, p.ST, p.SQ, p.Sx, p.QQ, p.Q, p.dt, p.wi = p.GetMatrices(params['nodes'], 0.0, step)
bar = progressbar.ProgressBar()
for i in bar(range(int(n.step[u]))):
p.SweeperNoVelUp(params['nodes'], params['itera'], p.x, p.v, p.x0, p.v0, p.x_, p.v_, 'IntegrateOff')
p.UpdateDat(params['nodes'])
if p.P.Bound(p.xend[params['nodes'] - 1, :]):
lastpnt = i
break
p.GetBrefPoint(i, params['nodes'], step, p.xend, p.vend, p.dt)
p.GetStanDev(step, outnames['deviation'].fullname, params)
p.RHSeval(params, outnames['deviation'].fullname, 'BrefBrs')
def ConvergenceBrs(params, outkeys):
Inform.Display(params['nodes'], params['itera'], 'ConvergenceBrs')
bar = progressbar.ProgressBar(widgets=[progressbar.Bar(), ' (', progressbar.ETA(), ') '])
outnames = {key: DataOut( name = outkeys[key], method = 'brs', nd = params['nodes'],
it = params['itera'], pic = params['picit']) for key in outkeys}
n = Stepsize()
omdt = np.zeros(n.st)
xpos = np.zeros([n.st, 3])
for u in range(n.st):
step = params['tend']/n.step[u]
p = Particle(params['nodes'], n.step[u])
p.S, p.ST, p.SQ, p.Sx, p.QQ, p.Q, p.dt, p.wi = p.GetMatrices(params['nodes'], 0.0, step)
bar = progressbar.ProgressBar()
for i in bar(range(int(n.step[u]))):
p.SweeperNoVelUp(params['nodes'], params['itera'], p.x, p.v, p.x0, p.v0, p.x_, p.v_, 'IntegrateOff')
p.UpdateDat(params['nodes'])
if p.P.Bound(p.xend[params['nodes'] - 1, :]):
lastpnt = i
break
xpos[u, :] = p.xend[params['nodes']-1, :]
omdt[u] = step*p.P.om_c
dat = open(outnames['convergence'].fullname, "w")
for u in range(n.st - 1):
ierror = abs(xpos[u, 0] - xpos[u+1, 0])/abs(xpos[u, 0])
dat.write('%e %.16e\n' % (omdt[u], ierror))
dat.close()
def ConvergenceSDC(params, outkeys, keyinteg):
Inform.Display(params['nodes'], params['itera'], 'ConvergenceSDC')
bar = progressbar.ProgressBar(widgets=[progressbar.Bar(), ' (', progressbar.ETA(), ') '])
outnames = {key: DataOut( name = outkeys[key], method = 'sdc', nd = params['nodes'],
it = params['itera'], pic = params['picit']) for key in outkeys}
n = Stepsize()
omdt = np.zeros(n.st)
xpos = np.zeros([n.st, 3])
for u in range(n.st):
step = params['tend']/n.step[u]
p = Particle(params['nodes'], n.step[u])
p.S, p.ST, p.SQ, p.Sx, p.QQ, p.Q, p.dt, p.wi = p.GetMatrices(params['nodes'], 0.0, step)
bar = progressbar.ProgressBar()
for i in bar(range(int(n.step[u]))):
p.Sweeper(params['nodes'], params['itera'], p.x, p.v, p.x0, p.v0, p.x_, p.v_, keyinteg)
p.UpdateDat(params['nodes'])
if p.P.Bound(p.xend[params['nodes'] - 1, :]):
lastpnt = i
break
xpos[u, :] = p.xend[params['nodes']-1, :]
omdt[u] = step*p.P.om_c
Inform.storePositions(outnames['positions'].fullname, n.st, xpos, omdt)
Inform.storeConverg(outnames['convergence'].fullname, n.st - 1, xpos, omdt)
def EnergyBrs(params, outkeys, numsteps):
Inform.Display(params['nodes'], params['itera'], 'EnergyBrs')
lastpnt = 0
bar = progressbar.ProgressBar(widgets=[progressbar.Bar(), ' (', progressbar.ETA(), ') '])
outnames = {key: DataOut( name = outkeys[key], method = 'brs', nd = params['nodes'],
it = params['itera'], pic = params['picit']) for key in outkeys}
step = params['tend']/numsteps
p = Particle(params['nodes'], numsteps)
p.S, p.ST, p.SQ, p.Sx, p.QQ, p.Q, p.dt, p.wi = p.GetMatrices(params['nodes'], 0.0, step)
bar = progressbar.ProgressBar()
for i in bar(range(int(numsteps))):
p.SweeperNoVelUp(params['nodes'], params['itera'], p.x, p.v, p.x0, p.v0, p.x_, p.v_, 'IntegrateOff')
p.UpdateDat(params['nodes'])
p.crd[i, :] = p.xend[params['nodes'] - 1, :]
p.vls[i, :] = p.vend[params['nodes'] - 1, :]
p.nrg[i] = abs(p.Ekin0 - np.dot(p.vls[i,:], p.vls[i,:])/2.0)/p.Ekin0
if p.P.Bound(p.xend[params['nodes'] - 1, :]):
lastpnt = i
break
if lastpnt != 0:
datanum = lastpnt
else:
datanum = numsteps
Inform.storeEnergy(outnames['totalenergy'].fullname, datanum, p.nrg)
def EnergyGMRes(params, outkeys, keyinteg, numsteps):
Inform.Display(params['nodes'], params['itera'], 'EnergyGMRes')
lastpnt = 0
bar = progressbar.ProgressBar(
widgets=[progressbar.Bar(), ' (',
progressbar.ETA(), ') '])
outnames = {
key: DataOut(name=outkeys[key],
method='gm',
nd=params['nodes'],
it=params['itera'],
pic=params['picit'])
for key in outkeys
}
type = 'lobatto'
integrate = True
bfield = False
step = params['tend'] / numsteps
p = Particle(params['nodes'], numsteps)
gmres = gmres_sdc(dt=step,
nodes=params['nodes'],
kiter=params['itera'],
pic=params['picit'],
nsteps=numsteps,
type=type,
integrate=integrate)
x_gm, v_gm, stats = gmres.run(bfield=bfield,
outnames=outnames,
params=params)
Inform.storeEnergy(outnames['totalenergy'].fullname, numsteps,
stats['energy_errors'])
def Trajectory(params, outkeys, keyinteg, numsteps):
Inform.Display(params['nodes'], params['itera'], 'Trajectory')
lastpnt = 0
bar = progressbar.ProgressBar(
widgets=[progressbar.Bar(), ' (',
progressbar.ETA(), ') '])
outnames = {
key: DataOut(name=outkeys[key],
method='sdc',
nd=params['nodes'],
it=params['itera'],
pic=params['picit'])
for key in outkeys
}
step = params['tend'] / numsteps
p = Particle(params['nodes'], numsteps)
p.S, p.ST, p.SQ, p.Sx, p.QQ, p.Q, p.dt, p.wi = p.GetMatrices(
params['nodes'], 0.0, step)
bar = progressbar.ProgressBar()
for i in bar(range(int(numsteps))):
p.Sweeper(params['nodes'], params['itera'], p.x, p.v, p.x0, p.v0,
p.x_, p.v_, keyinteg)
p.UpdateDat(params['nodes'])
p.crd[i, :] = p.xend[params['nodes'] - 1, :]
p.vls[i, :] = p.vend[params['nodes'] - 1, :]
p.mu[i] = (p.vmod**2 - (p.vmod * p.phi)**2) / p.P.Bmod(
p.xend[params['nodes'] - 1, :])
if p.P.Bound(p.xend[params['nodes'] - 1, :]):
lastpnt = i
break
if lastpnt != 0:
datanum = lastpnt
else:
datanum = numsteps
dat = open(outnames['trajectory'].fullname, "w")
for u in range(datanum):
if ((u + 1) % 100) == 0:
dat.write('%e %e %e\n' %
(p.crd[u, 0], p.crd[u, 1], p.crd[u, 2]))
dat.close()
def __init__(self, dt, nodes, kiter, nsteps, type, integrate=True):
self.dt = dt
self.kiter = kiter
self.nsteps = nsteps
self.nodes = nodes
g = Particle(nodes, nsteps)
self.S, dum1, dum2, dum3, dum4, dum5, self.delta_tau, self.q = g.GetMatrices(
nodes, 0.0, dt)
self.integrate = integrate
if type == 'legendre':
if not self.integrate:
print(
"Overiding integrate=False... for Legendre nodes, integrate needs to be set to True"
)
self.integrate = True
if (self.kiter == 0) and (self.integrate):
print(
"Setting kiter=0 but integrate=True will NOT reproduce the standard Boris integrator"
)
# Define the problem
self.P = problem()
self.stats = {}
self.stats['residuals'] = np.zeros((kiter + 1, nsteps))
self.stats['increments'] = np.zeros((kiter, nsteps))
self.stats['energy_errors'] = np.zeros(nsteps)
# Buffers to store approximations at time steps
self.positions = np.zeros((3, nsteps + 1))
self.velocities = np.zeros((3, nsteps + 1))
self.positions[:, 0] = self.P.pos0
self.velocities[:, 0] = self.P.vel0
self.stats['exact_energy'] = self.P.Energy(self.positions[:, 0],
self.velocities[:, 0])
self.stats['errors'] = np.zeros((2, nsteps + 1))
self.stats['errors'][0, 0] = 0.0
self.stats['errors'][1, 0] = 0.0
def BrefGMRes(params, outkeys, keyinteg):
Inform.Display(params['nodes'], params['itera'], 'BrefGMRes')
bar = progressbar.ProgressBar(widgets=[progressbar.Bar(), ' (', progressbar.ETA(), ') '])
outnames = {key: DataOut( name = outkeys[key], method = 'gm', nd = params['nodes'],
it = params['itera'], pic = params['picit']) for key in outkeys}
type = 'lobatto'
integrate = True
bfield = True
n = Stepsize()
for u in range(n.st):
step = params['tend']/n.step[u]
p = Particle(params['nodes'], n.step[u])
gmres = gmres_sdc(dt = step, nodes = params['nodes'], kiter = params['itera'], pic = params['picit'],
nsteps = int(n.step[u]), type=type, integrate=integrate)
x_gm, v_gm, stats = gmres.run(bfield = bfield, outnames = outnames, params = params)
p.RHSeval(params, outnames['deviation'].fullname, 'BrefGMRes')
def run(self, bfield, outnames, params):
# Buffers for k+1 and k solution at integer step
x_old = np.zeros((3, self.nodes))
v_old = np.zeros((3, self.nodes))
x_new = np.zeros((3, self.nodes))
v_new = np.zeros((3, self.nodes))
# Store values for Bref subroutine:
xu = np.zeros([self.nodes, 3])
vu = np.zeros([self.nodes, 3])
p = Particle(self.nodes, self.nsteps)
bar = progressbar.ProgressBar()
for nn in bar(range(self.nsteps)):
'''
Predictor: solve (Id - Q_delta *F) u^1 = u0 + 0.5*Fu0 + v00 (see notes for definitions)
'''
x0 = np.kron(
np.ones(self.nodes).transpose(), self.positions[:, nn])
v0 = np.kron(
np.ones(self.nodes).transpose(), self.velocities[:, nn])
u0 = self.pack(x0, v0)
Fu0 = self.F(self.positions[:, nn], self.velocities[:, nn])
Fu0 = np.kron(np.ones(self.nodes).transpose(), Fu0)
Fu0 = self.pack(self.delta_tau[0]**2 * Fu0,
self.delta_tau[0] * Fu0)
v00 = self.pack(
self.delta_tau[0] * np.kron(
np.ones(self.nodes).transpose(), self.velocities[:, nn]),
np.zeros(self.dim / 2))
u_old = self.sweep(u0 + 0.5 * Fu0 + v00)
x_old, v_old = self.unpack(u_old)
'''
SDC iteration
'''
if self.kpic > 0:
precond = lambda b: self.sweep_linear(b, x_old)
quadrature = lambda u: u - self.quad(u, x_old)
else:
precond = lambda b: self.sweep(b)
quadrature = lambda u: u - self.quad(u)
u_new, self.stats['residuals'][0:self.kiter, nn] = mygmres(
quadrature, u0, u_old, self.kiter, precond)
'''
Picard iteration to adjust for nonlinearity
'''
for kk in range(self.kpic):
u_new = u0 + self.quad(u_new)
x_old, v_old = self.unpack(u_new)
for i in range(self.nodes):
xu[i, :] = x_old[:, i]
vu[i, :] = v_old[:, i]
'''
Prepare next time step
'''
# Compute residual after final iteration
self.stats['residuals'][self.kiter, nn] = self.getResiduals(
self.positions[:, nn], self.velocities[:, nn], x_old, v_old)
self.positions[:,
nn + 1], self.velocities[:, nn +
1] = self.finalUpdateStep(
x_old, v_old,
self.positions[:, nn],
self.velocities[:, nn])
self.stats['energy_errors'][nn] = self.getEnergyError(
self.positions[:, nn + 1], self.velocities[:, nn + 1])
xu[self.nodes - 1, :] = self.positions[:, nn + 1]
vu[self.nodes - 1, :] = self.velocities[:, nn + 1]
if p.P.Bound(xu[self.nodes - 1, :]):
break
if bfield:
p.GetBrefPoint(nn, self.nodes, self.dt, xu, vu, self.delta_tau)
p.GetStanDev(self.dt, outnames['deviation'].fullname, params)
return self.positions, self.velocities, self.stats