def __init__(self, problem):
assert isinstance(
problem, boussinesq_2d_imex), "problem is wrong type of object"
self.Ndof = np.shape(problem.M)[0]
self.order = 2
self.logger = logging()
self.problem = problem
def __init__(self, problem_params, dtype_u, dtype_f):
"""
Initialization routine
Args:
problem_params (dict): custom parameters for the example
dtype_u: particle data type (will be passed parent class)
dtype_f: acceleration data type (will be passed parent class)
"""
# these parameters will be used later, so assert their existence
essential_keys = [
'nvars', 'c_s', 'u_adv', 'Nfreq', 'x_bounds', 'z_bounds',
'order_upw', 'order', 'gmres_maxiter', 'gmres_restart',
'gmres_tol_limit'
]
for key in essential_keys:
if key not in problem_params:
msg = 'need %s to instantiate problem, only got %s' % (
key, str(problem_params.keys()))
raise ParameterError(msg)
# invoke super init, passing number of dofs, dtype_u and dtype_f
super(boussinesq_2d_imex,
self).__init__(problem_params['nvars'], dtype_u, dtype_f,
problem_params)
self.N = [self.params.nvars[1], self.params.nvars[2]]
self.bc_hor = [['periodic', 'periodic'], ['periodic', 'periodic'],
['periodic', 'periodic'], ['periodic', 'periodic']]
self.bc_ver = [['neumann', 'neumann'], ['dirichlet', 'dirichlet'],
['dirichlet', 'dirichlet'], ['neumann', 'neumann']]
self.xx, self.zz, self.h = get2DMesh(self.N, self.params.x_bounds,
self.params.z_bounds,
self.bc_hor[0], self.bc_ver[0])
self.Id, self.M = getBoussinesq2DMatrix(self.N, self.h, self.bc_hor,
self.bc_ver, self.params.c_s,
self.params.Nfreq,
self.params.order)
self.D_upwind = getBoussinesq2DUpwindMatrix(self.N, self.h[0],
self.params.u_adv,
self.params.order_upw)
self.gmres_logger = logging()
def __init__(self, problem, order):
assert isinstance(
problem, boussinesq_2d_imex), "problem is wrong type of object"
self.Ndof = np.shape(problem.M)[0]
self.order = order
self.logger = logging()
self.problem = problem
assert self.order in [2, 22, 3, 4, 5], 'Order must be 2,22,3,4'
if self.order == 2:
self.nstages = 1
self.A = np.zeros((1, 1))
self.A[0, 0] = 0.5
self.tau = [0.5]
self.b = [1.0]
if self.order == 22:
self.nstages = 2
self.A = np.zeros((2, 2))
self.A[0, 0] = 1.0 / 3.0
self.A[1, 0] = 1.0 / 2.0
self.A[1, 1] = 1.0 / 2.0
self.tau = np.zeros(2)
self.tau[0] = 1.0 / 3.0
self.tau[1] = 1.0
self.b = np.zeros(2)
self.b[0] = 3.0 / 4.0
self.b[1] = 1.0 / 4.0
if self.order == 3:
self.nstages = 2
self.A = np.zeros((2, 2))
self.A[0, 0] = 0.5 + 1.0 / (2.0 * math.sqrt(3.0))
self.A[1, 0] = -1.0 / math.sqrt(3.0)
self.A[1, 1] = self.A[0, 0]
self.tau = np.zeros(2)
self.tau[0] = 0.5 + 1.0 / (2.0 * math.sqrt(3.0))
self.tau[1] = 0.5 - 1.0 / (2.0 * math.sqrt(3.0))
self.b = np.zeros(2)
self.b[0] = 0.5
self.b[1] = 0.5
if self.order == 4:
self.nstages = 3
alpha = 2.0 * math.cos(math.pi / 18.0) / math.sqrt(3.0)
self.A = np.zeros((3, 3))
self.A[0, 0] = (1.0 + alpha) / 2.0
self.A[1, 0] = -alpha / 2.0
self.A[1, 1] = self.A[0, 0]
self.A[2, 0] = (1.0 + alpha)
self.A[2, 1] = -(1.0 + 2.0 * alpha)
self.A[2, 2] = self.A[0, 0]
self.tau = np.zeros(3)
self.tau[0] = (1.0 + alpha) / 2.0
self.tau[1] = 1.0 / 2.0
self.tau[2] = (1.0 - alpha) / 2.0
self.b = np.zeros(3)
self.b[0] = 1.0 / (6.0 * alpha * alpha)
self.b[1] = 1.0 - 1.0 / (3.0 * alpha * alpha)
self.b[2] = 1.0 / (6.0 * alpha * alpha)
if self.order == 5:
self.nstages = 5
# From Kennedy, Carpenter "Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations.
# A Review"
self.A = np.zeros((5, 5))
self.A[0, 0] = 4024571134387. / 14474071345096.
self.A[1, 0] = 9365021263232. / 12572342979331.
self.A[1, 1] = self.A[0, 0]
self.A[2, 0] = 2144716224527. / 9320917548702.
self.A[2, 1] = -397905335951. / 4008788611757.
self.A[2, 2] = self.A[0, 0]
self.A[3, 0] = -291541413000. / 6267936762551.
self.A[3, 1] = 226761949132. / 4473940808273.
self.A[3, 2] = -1282248297070. / 9697416712681.
self.A[3, 3] = self.A[0, 0]
self.A[4, 0] = -2481679516057. / 4626464057815.
self.A[4, 1] = -197112422687. / 6604378783090.
self.A[4, 2] = 3952887910906. / 9713059315593.
self.A[4, 3] = 4906835613583. / 8134926921134.
self.A[4, 4] = self.A[0, 0]
self.b = np.zeros(5)
self.b[0] = -2522702558582. / 12162329469185.
self.b[1] = 1018267903655. / 12907234417901.
self.b[2] = 4542392826351. / 13702606430957.
self.b[3] = 5001116467727. / 12224457745473.
self.b[4] = 1509636094297. / 3891594770934.
self.stages = np.zeros((self.nstages, self.Ndof))
def __init__(self, problem, method, pparams):
assert isinstance(
problem, boussinesq_2d_imex), "problem is wrong type of object"
self.Ndof = np.shape(problem.M)[0]
self.method = method
self.logger = logging()
self.problem = problem
self.pparams = pparams
self.NdofTher = 2 * problem.N[0] * problem.N[1]
self.NdofMom = 2 * problem.N[0] * problem.N[1]
self.ns = None
# print("dx ",problem.h[0])
# print("dz ",problem.h[1])
assert self.method in ["MIS4_4", "RK3"], 'Method must be MIS4_4'
if self.method == 'RK3':
self.nstages = 3
self.aRunge = np.zeros((4, 4))
self.aRunge[0, 0] = 1. / 3.
self.aRunge[1, 1] = 1. / 2.
self.aRunge[2, 2] = 1.
self.dRunge = np.zeros((4, 4))
self.gRunge = np.zeros((4, 4))
if self.method == 'MIS4_4':
self.nstages = 4
self.aRunge = np.zeros((4, 4))
self.aRunge[0, 0] = 0.38758444641450318
self.aRunge[1, 0] = -2.5318448354142823e-002
self.aRunge[1, 1] = 0.38668943087310403
self.aRunge[2, 0] = 0.20899983523553325
self.aRunge[2, 1] = -0.45856648476371231
self.aRunge[2, 2] = 0.43423187573425748
self.aRunge[3, 0] = -0.10048822195663100
self.aRunge[3, 1] = -0.46186171956333327
self.aRunge[3, 2] = 0.83045062122462809
self.aRunge[3, 3] = 0.27014914900250392
self.dRunge = np.zeros((4, 4))
self.dRunge[1, 1] = 0.52349249922385610
self.dRunge[2, 1] = 1.1683374366893629
self.dRunge[2, 2] = -0.75762080241712637
self.dRunge[3, 1] = -3.6477233846797109e-002
self.dRunge[3, 2] = 0.56936148730740477
self.dRunge[3, 3] = 0.47746263002599681
self.gRunge = np.zeros((4, 4))
self.gRunge[1, 1] = 0.13145089796226542
self.gRunge[2, 1] = -0.36855857648747881
self.gRunge[2, 2] = 0.33159232636600550
self.gRunge[3, 1] = -6.5767130537473045E-002
self.gRunge[3, 2] = 4.0591093109036858E-002
self.gRunge[3, 3] = 6.4902111640806712E-002
self.dtRunge = np.zeros(self.nstages)
for i in range(0, self.nstages):
self.dtRunge[i] = 0
temp = 1.
for j in range(0, i + 1):
self.dtRunge[i] = self.dtRunge[i] + self.aRunge[i, j]
temp = temp - self.dRunge[i, j]
self.dRunge[i, 0] = temp
for j in range(0, i + 1):
self.aRunge[i, j] = self.aRunge[i, j] / self.dtRunge[i]
self.gRunge[i, j] = self.gRunge[i, j] / self.dtRunge[i]
self.U = np.zeros((self.Ndof, self.nstages + 1))
self.F = np.zeros((self.Ndof, self.nstages))
self.FSlow = np.zeros(self.Ndof)
self.nsMin = 8
self.logger.nsmall = 0
def __init__(self, problem, order):
assert order in [1, 2, 3, 4, 5], "Order must be between 1 and 5"
self.order = order
if self.order == 1:
self.A = np.array([[0, 0], [0, 1]])
self.A_hat = np.array([[0, 0], [1, 0]])
self.b = np.array([0, 1])
self.b_hat = np.array([1, 0])
self.nstages = 2
elif self.order == 2:
self.A = np.array([[0, 0], [0, 0.5]])
self.A_hat = np.array([[0, 0], [0.5, 0]])
self.b = np.array([0, 1])
self.b_hat = np.array([0, 1])
self.nstages = 2
elif self.order == 3:
# parameter from Pareschi and Russo, J. Sci. Comp. 2005
alpha = 0.24169426078821
beta = 0.06042356519705
eta = 0.12915286960590
self.A_hat = np.array([[0, 0, 0, 0], [0, 0, 0, 0], [0, 1.0, 0, 0],
[0, 1.0 / 4.0, 1.0 / 4.0, 0]])
self.A = np.array([[alpha, 0, 0, 0], [-alpha, alpha, 0, 0],
[0, 1.0 - alpha, alpha, 0],
[beta, eta, 0.5 - beta - eta - alpha, alpha]])
self.b_hat = np.array([0, 1.0 / 6.0, 1.0 / 6.0, 2.0 / 3.0])
self.b = self.b_hat
self.nstages = 4
elif self.order == 4:
self.A_hat = np.array(
[[0, 0, 0, 0, 0, 0], [1. / 2, 0, 0, 0, 0, 0],
[13861. / 62500., 6889. / 62500., 0, 0, 0, 0],
[
-116923316275. / 2393684061468.,
-2731218467317. / 15368042101831.,
9408046702089. / 11113171139209., 0, 0, 0
],
[
-451086348788. / 2902428689909.,
-2682348792572. / 7519795681897.,
12662868775082. / 11960479115383.,
3355817975965. / 11060851509271., 0, 0
],
[
647845179188. / 3216320057751.,
73281519250. / 8382639484533.,
552539513391. / 3454668386233.,
3354512671639. / 8306763924573., 4040. / 17871., 0
]])
self.A = np.array(
[[0, 0, 0, 0, 0, 0], [1. / 4, 1. / 4, 0, 0, 0, 0],
[8611. / 62500., -1743. / 31250., 1. / 4, 0, 0, 0],
[
5012029. / 34652500., -654441. / 2922500.,
174375. / 388108., 1. / 4, 0, 0
],
[
15267082809. / 155376265600., -71443401. / 120774400.,
730878875. / 902184768., 2285395. / 8070912., 1. / 4, 0
],
[
82889. / 524892., 0, 15625. / 83664., 69875. / 102672.,
-2260. / 8211, 1. / 4
]])
self.b = np.array([
82889. / 524892., 0, 15625. / 83664., 69875. / 102672.,
-2260. / 8211, 1. / 4
])
self.b_hat = np.array([
4586570599. / 29645900160., 0, 178811875. / 945068544.,
814220225. / 1159782912., -3700637. / 11593932.,
61727. / 225920.
])
self.nstages = 6
elif self.order == 5:
# from Kennedy and Carpenter
# copied from http://www.mcs.anl.gov/petsc/petsc-3.2/src/ts/impls/arkimex/arkimex.c
self.A_hat = np.zeros((8, 8))
getcontext().prec = 56
self.A_hat[1, 0] = Decimal(41.0) / Decimal(100.0)
self.A_hat[2, 0] = Decimal(367902744464.) / Decimal(2072280473677.)
self.A_hat[2, 1] = Decimal(677623207551.) / Decimal(8224143866563.)
self.A_hat[3,
0] = Decimal(1268023523408.) / Decimal(10340822734521.)
self.A_hat[3, 1] = 0.0
self.A_hat[3,
2] = Decimal(1029933939417.) / Decimal(13636558850479.)
self.A_hat[4,
0] = Decimal(14463281900351.) / Decimal(6315353703477.)
self.A_hat[4, 1] = 0.0
self.A_hat[4,
2] = Decimal(66114435211212.) / Decimal(5879490589093.)
self.A_hat[4,
3] = Decimal(-54053170152839.) / Decimal(4284798021562.)
self.A_hat[5,
0] = Decimal(14090043504691.) / Decimal(34967701212078.)
self.A_hat[5, 1] = 0.0
self.A_hat[5,
2] = Decimal(15191511035443.) / Decimal(11219624916014.)
self.A_hat[
5, 3] = Decimal(-18461159152457.) / Decimal(12425892160975.)
self.A_hat[5,
4] = Decimal(-281667163811.) / Decimal(9011619295870.)
self.A_hat[6,
0] = Decimal(19230459214898.) / Decimal(13134317526959.)
self.A_hat[6, 1] = 0.0
self.A_hat[6,
2] = Decimal(21275331358303.) / Decimal(2942455364971.)
self.A_hat[6,
3] = Decimal(-38145345988419.) / Decimal(4862620318723.)
self.A_hat[6, 4] = Decimal(-1.0) / Decimal(8.0)
self.A_hat[6, 5] = Decimal(-1.0) / Decimal(8.0)
self.A_hat[
7, 0] = Decimal(-19977161125411.) / Decimal(11928030595625.)
self.A_hat[7, 1] = 0.0
self.A_hat[7,
2] = Decimal(-40795976796054.) / Decimal(6384907823539.)
self.A_hat[
7, 3] = Decimal(177454434618887.) / Decimal(12078138498510.)
self.A_hat[7, 4] = Decimal(782672205425.) / Decimal(8267701900261.)
self.A_hat[7,
5] = Decimal(-69563011059811.) / Decimal(9646580694205.)
self.A_hat[7,
6] = Decimal(7356628210526.) / Decimal(4942186776405.)
self.b_hat = np.zeros(8)
self.b_hat[0] = Decimal(-872700587467.) / Decimal(9133579230613.)
self.b_hat[1] = 0.0
self.b_hat[2] = 0.0
self.b_hat[3] = Decimal(22348218063261.) / Decimal(9555858737531.)
self.b_hat[4] = Decimal(-1143369518992.) / Decimal(8141816002931.)
self.b_hat[5] = Decimal(-39379526789629.) / Decimal(
19018526304540.)
self.b_hat[6] = Decimal(32727382324388.) / Decimal(42900044865799.)
self.b_hat[7] = Decimal(41.0) / Decimal(200.0)
self.A = np.zeros((8, 8))
self.A[1, 0] = Decimal(41.) / Decimal(200.)
self.A[1, 1] = Decimal(41.) / Decimal(200.)
self.A[2, 0] = Decimal(41.) / Decimal(400.)
self.A[2, 1] = Decimal(-567603406766.) / Decimal(11931857230679.)
self.A[2, 2] = Decimal(41.) / Decimal(200.)
self.A[3, 0] = Decimal(683785636431.) / Decimal(9252920307686.)
self.A[3, 1] = 0.0
self.A[3, 2] = Decimal(-110385047103.) / Decimal(1367015193373.)
self.A[3, 3] = Decimal(41.) / Decimal(200.)
self.A[4, 0] = Decimal(3016520224154.) / Decimal(10081342136671.)
self.A[4, 1] = 0.0
self.A[4, 2] = Decimal(30586259806659.) / Decimal(12414158314087.)
self.A[4, 3] = Decimal(-22760509404356.) / Decimal(11113319521817.)
self.A[4, 4] = Decimal(41.) / Decimal(200.)
self.A[5, 0] = Decimal(218866479029.) / Decimal(1489978393911.)
self.A[5, 1] = 0.0
self.A[5, 2] = Decimal(638256894668.) / Decimal(5436446318841.)
self.A[5, 3] = Decimal(-1179710474555.) / Decimal(5321154724896.)
self.A[5, 4] = Decimal(-60928119172.) / Decimal(8023461067671.)
self.A[5, 5] = Decimal(41.) / Decimal(200.)
self.A[6, 0] = Decimal(1020004230633.) / Decimal(5715676835656.)
self.A[6, 1] = 0.0
self.A[6, 2] = Decimal(25762820946817.) / Decimal(25263940353407.)
self.A[6, 3] = Decimal(-2161375909145.) / Decimal(9755907335909.)
self.A[6, 4] = Decimal(-211217309593.) / Decimal(5846859502534.)
self.A[6, 5] = Decimal(-4269925059573.) / Decimal(7827059040749.)
self.A[6, 6] = Decimal(41.) / Decimal(200.)
self.A[7, 0] = Decimal(-872700587467.) / Decimal(9133579230613.)
self.A[7, 1] = 0.0
self.A[7, 2] = 0.0
self.A[7, 3] = Decimal(22348218063261.) / Decimal(9555858737531.)
self.A[7, 4] = Decimal(-1143369518992.) / Decimal(8141816002931.)
self.A[7, 5] = Decimal(-39379526789629.) / Decimal(19018526304540.)
self.A[7, 6] = Decimal(32727382324388.) / Decimal(42900044865799.)
self.A[7, 7] = Decimal(41.) / Decimal(200.)
self.b = np.zeros(8)
self.b[0] = Decimal(-975461918565.) / Decimal(9796059967033.)
self.b[1] = 0.0
self.b[2] = 0.0
self.b[3] = Decimal(78070527104295.) / Decimal(32432590147079.)
self.b[4] = Decimal(-548382580838.) / Decimal(3424219808633.)
self.b[5] = Decimal(-33438840321285.) / Decimal(15594753105479.)
self.b[6] = Decimal(3629800801594.) / Decimal(4656183773603.)
self.b[7] = Decimal(4035322873751.) / Decimal(18575991585200.)
self.nstages = 8
self.problem = problem
self.ndof = np.shape(problem.M)[0]
self.logger = logging()
self.stages = np.zeros((self.nstages, self.ndof))