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Rckirby/moredirks #81

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merged 14 commits into from
Feb 29, 2024
Merged

Rckirby/moredirks #81

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fec359a
Toss in a new dirk from Ketcheson
rckirby Feb 8, 2024
ed1de2e
fix typos
rckirby Feb 8, 2024
6f40a0d
few more typos
rckirby Feb 8, 2024
6a45596
the other two from the paper
rckirby Feb 8, 2024
982f42f
lower-order WSO dirks from earlier ketcheson paper
rckirby Feb 9, 2024
0c9a043
flake, fix -
rckirby Feb 9, 2024
e95807a
typo, add to init
rckirby Feb 16, 2024
116d559
Update doc strings, flake8
rckirby Feb 27, 2024
b38d0b9
Switch StokesTest.py to only use a linear solver
rckirby Feb 27, 2024
4dea863
Tweak solver params
rckirby Feb 27, 2024
853d1e2
Tweak solver params, reprise
rckirby Feb 27, 2024
ed3adb2
Tweak solver params, reprise
rckirby Feb 27, 2024
1807447
Merging -- taking the improved stokes test
rckirby Feb 28, 2024
1671a8f
nullspace
rckirby Feb 28, 2024
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257 changes: 257 additions & 0 deletions irksome/ButcherTableaux.py
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Original file line number Diff line number Diff line change
Expand Up @@ -263,3 +263,260 @@ def __init__(self):

def __str__(self):
return "Alexander()"


class WSODIRK432(ButcherTableau):
""" Third-order, diagonally implicit, 4-stage, L-stable scheme with
weak stage order 2 from Ketcheson et al, Spectral and High Order Methods for
Partial Differential Equations (2020)."""
def __init__(self):
c = numpy.asarray(
[0.01900072890, 0.78870323114, 0.41643499339, 1])
b = numpy.asarray(
[0.02343549374,
-0.41207877888, 0.96661161281, 0.42203167233])
A = numpy.asarray(
[[0.01900072890, 0, 0, 0],
[0.40434605601, 0.38435717512, 0, 0],
[0.06487908412, -0.16389640295, 0.51545231222, 0],
[0.02343549374, -0.41207877888, 0.96661161281, 0.42203167233]])
super(WSODIRK432, self).__init__(A, b, None, c, 3)

def __str__(self):
return "WSODIRK432()"


class WSODIRK433(ButcherTableau):
""" Third-order, diagonally implicit, 4-stage, L-stable scheme with
weak stage order 3 from Ketcheson et al, Spectral and High Order Methods for
Partial Differential Equations (2020)."""
def __init__(self):
c = numpy.array(
[0.13756543551, 0.80179011576, 2.33179673002, 1])
b = numpy.array(
[0.59761291500, -0.43420997584, -0.05305815322, 0.88965521406])
A = numpy.array(
[[0.13756543551, 0, 0, 0],
[0.56695122794, 0.23483888782, 0, 0],
[-1.08354072813, 2.96618223864, 0.44915521951, 0],
[0.59761291500, -0.43420997584, -0.05305815322, 0.88965521406]])
super(WSODIRK433, self).__init__(A, b, None, c, 3)

def __str(self):
return "WSODIRK433()"


class WSODIRK643(ButcherTableau):
""" Fourth-order, diagonally implicit, 6-stage, L-stable scheme with
weak stage order 3 from Ketcheson et al, Spectral and High Order Methods for
Partial Differential Equations (2020)."""
def __init__(self):
c = numpy.array(
[0.079672377876931, 0.464364648310935,
1.348559241946724, 1.312664210308764,
0.989469293495897, 1])
b = numpy.array(
[0.214823667785537, 0.536367363903245,
0.154488125726409, -0.217748592703941,
0.072226422925896, 0.239843012362853])
A = numpy.array(
[[0.079672377876931, 0, 0, 0, 0, 0],
[0.328355391763968, 0.136009256546967, 0, 0, 0, 0],
[-0.650772774016417, 1.742859063495349, 0.256472952467792, 0, 0, 0],
[-0.714580550967259, 1.793745752775934, -0.078254785672497, 0.311753794172585, 0, 0],
[-1.120092779092918, 1.983452339867353, 3.117393885836001, -3.761930177913743, 0.770646024799205, 0],
[0.214823667785537, 0.536367363903245,
0.154488125726409, -0.217748592703941,
0.072226422925896, 0.239843012362853]])
super(WSODIRK643, self).__init__(A, b, None, c, 4)

def __str(self):
return "WSODIRK643()"


class WSODIRK744(ButcherTableau):
""" Fourth-order, diagonally implicit, 7-stage, L-stable scheme with
weak stage order 4 from Biswas, et al, Communications in Applied
Mathematics and Computational Science 18(1), 2023."""
def __init__(self):
c = numpy.asarray(
[1.290066345260422e-01, 4.492833135308985e-01,
9.919659086525534e-03, 1.230475897454758e+00,
2.978701803613543e+00, 1.247908693583052e+00,
1.000000000000000e+00])
b = numpy.asarray(
[2.387938238483883e-01, 4.762495400483653e-01,
1.233935151213300e-02, 6.011995982693821e-02,
6.553618225489034e-05, -1.270730910442124e-01,
3.395048796261326e-01])
A = numpy.array(
[[1.290066345260422e-01, 0, 0, 0, 0, 0, 0],
[3.315354455306989e-01, 1.177478680001996e-01,
0, 0, 0, 0, 0],
[-8.009819642882672e-02, -2.408450965101765e-03, 9.242630648045402e-02, 0, 0, 0, 0],
[-1.730636616639455e+00, 1.513225984674677e+00, 1.221258626309848e+00, 2.266279031096887e-01, 0, 0, 0],
[1.475353790517696e-01, 3.618481772236499e-01, -5.603544220240282e-01, 2.455453653222619e+00, 5.742190161395324e-01, 0, 0],
[2.099717815888321e-01, 7.120237463672882e-01, -2.012023940726332e-02, -1.913828539529156e-02, -5.556044541810300e-03, 3.707277349712966e-01, 0],
[2.387938238483883e-01, 4.762495400483653e-01, 1.233935151213300e-02, 6.011995982693821e-02, 6.553618225489034e-05, -1.270730910442124e-01, 3.395048796261326e-01]])
super(WSODIRK744, self).__init__(A, b, None, c, 4)

def __str__(self):
return "WSODIRK744()"


class WSODIRK1254():
""" Fifth-order, diagonally implicit, 12-stage, L-stable scheme with
weak stage order 4 from Biswas, et al, Communications in Applied
Mathematics and Computational Science 18(1), 2023."""
def __init__(self):
c = numpy.array(
[2.345371908646273e-01, 7.425871511958302e-01,
3.296674204078279e-02, 7.379564717201322e-01,
2.376643917109970e-01, 1.750238160341377e+00,
2.990308150015702e+00, 2.882138003112822e+00,
2.914399924907188e+00, 2.573507348677332e+00,
3.567266961364713e+00, 1.000000000000000e+00])
b = numpy.array(
[-7.433675378768276e-01, 1.490594423766965e-01,
-2.042884056742363e-02, 8.565329438087443e-04,
1.357261590983184e+00, 2.067512027776675e-03,
9.836884265759428e-02, -1.357936974507222e-02,
-5.428992174996300e-02, -3.803299038293005e-02,
-9.150525836295019e-03, 2.712352651694511e-01])
A = numpy.array(
[[2.345371908646273e-01,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[6.874344413888787e-01, 5.515270980695153e-02,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1.183552669539587e-01, 5.463563002913454e-03,
1.458584459918280e-01,
0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1.832235204042292e-01, 5.269029412008775e-02,
8.203685085133529e-01, 4.812118949092085e-02,
0, 0, 0, 0, 0, 0, 0, 0],
[9.941572060659400e-02, 4.977904930055774e-03,
5.414758174284321e-02, -1.666571741820749e-03,
8.078975617332473e-02,
0, 0, 0, 0, 0, 0, 0],
[-9.896614721582678e-01, 2.860682690577833e+00,
-1.236119341063179e+00, 2.130219523351530e+00,
-1.260655031676537e+00, 2.457717913099987e-01,
0, 0, 0, 0, 0, 0],
[-5.656238413439102e-02, 1.661985685769353e-01,
6.464600922362508e-01, 6.608854962269927e-01,
3.736054198873429e-01, 6.294456964407685e-01,
5.702752607818027e-01,
0, 0, 0, 0, 0],
[8.048962104724392e-01, -6.232034990249100e-02,
5.737234603323347e-01, -9.613723511489970e-02,
5.524106361737929e-01, 5.961002486833255e-01,
1.978411600659203e-01, 3.156238724024008e-01,
0, 0, 0, 0],
[-1.606381759216300e-01, 6.833397073337708e-01,
4.734578665308685e-01, 8.037708984872738e-01,
-1.094498069459834e-02, 6.151263362711297e-01,
3.908946848682723e-01, 8.966103265353116e-02,
2.973255537857041e-02,
0, 0, 0],
[7.074283235644631e-01, 4.392037300952482e-01,
-3.623592480237268e-02, 7.189990308645932e-04,
5.820968279166545e-01, 3.302003177175218e-01,
-2.394564021215881e-01, -7.540283547997615e-03,
1.702137469523672e-01, 6.268780138721711e-01,
0, 0],
[1.361197981133694e-01, -7.486549901902831e-01,
1.893908350024949e+00, 3.940485196730028e-01,
6.240233526545023e-02, 7.511983862200027e-01,
-5.283465265730526e-01, -1.661625677872943e+00,
9.998723833190827e-01, 1.377776742457387e+00,
8.905676409277480e-01, 0],
[-7.433675378768276e-01, 1.490594423766965e-01,
-2.042884056742363e-02, 8.565329438087443e-04,
1.357261590983184e+00, 2.067512027776675e-03,
9.836884265759428e-02, -1.357936974507222e-02,
-5.428992174996300e-02, -3.803299038293005e-02,
-9.150525836295019e-03, 2.712352651694511e-01]])

super(WSODIRK1254, self).__init__(A, b, None, c, 5)

def __str__(self):
return "WSODIRK1254()"


class WSODIRK1255(ButcherTableau):
""" Fifth-order, diagonally implicit, 12-stage, L-stable scheme with
weak stage order 5 from Biswas, et al, Communications in Applied
Mathematics and Computational Science 18(1), 2023."""
def __init__(self):
c = numpy.array(
[4.113473525867655e-02, 2.269850660400232e-01,
6.222969192243949e-01, 1.377989449231234e+00,
1.259841986970257e+00, 1.228350442796143e+00,
1.269855051265635e+00, 2.496200652601413e+00,
2.783820705331141e+00, 3.337101417632813e+00,
4.173423133876636e+00, 1.000000000000000e+00])
b = numpy.array(
[1.207394392845339e-02, 5.187080074649261e-01,
1.121304244847239e-01, -4.959806334780896e-03,
-1.345031364651444e+00, 3.398828703760807e-01,
8.159251531671077e-01, -2.640104266439604e-03,
1.439060901763520e-02, -6.556567796749947e-03,
6.548135446843367e-04, 5.454220210658036e-01])
A = numpy.array(
[[4.113473525867655e-02,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1.603459327727949e-01, 6.663913326722831e-02,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-3.424389044264752e-01, 8.658006324816373e-01,
9.893519116923277e-02,
0, 0, 0, 0, 0, 0, 0, 0, 0],
[9.437182028870806e+00, -1.088783359642350e+01,
2.644025436733866e+00, 1.846155800500574e-01,
0, 0, 0, 0, 0, 0, 0, 0],
[-3.425409029430815e-01, 5.172239272544332e-01,
9.163589909678043e-01, 5.225142808845742e-02,
1.165485436026433e-01,
0, 0, 0, 0, 0, 0, 0],
[-2.094441177460360e+00, 2.577655753533404e+00,
5.704405293326313e-01, 1.213637180023516e-01,
-4.752289775376601e-01, 5.285605969257756e-01,
0, 0, 0, 0, 0, 0],
[3.391631788320480e-01, -2.797427027028997e-01,
1.039483063369094e+00, 5.978770926212172e-02,
-2.132900327070380e-01, 8.344318363436753e-02,
2.410106515779412e-01,
0, 0, 0, 0, 0],
[5.904282488642163e+00, 3.171195765985073e+00,
-1.236822836316587e+01, -4.989519066913001e-01,
2.160529620826442e+00, 1.916104322021480e+00,
1.988059486291180e+00, 2.232092386922440e-01,
0, 0, 0, 0],
[4.616443509508975e-01, -1.933433560549238e-01,
-1.212541486279519e-01, 6.662362039716674e-02,
4.254912950625259e-01, 7.856131647013712e-01,
8.369551389357689e-01, 1.604780447895926e-01,
3.616125951766939e-01,
0, 0, 0],
[-7.087669749878204e-01, 6.466527094491541e-01,
4.758821526542215e-01, -2.570518451375722e-01,
1.123185062554392e+00, 5.546921612875290e-01,
3.192424333237050e-01, 3.612077612576969e-01,
5.866779836068974e-01, 2.353799736246102e-01,
0, 0],
[4.264162484855930e-01, 1.322816663477840e+00,
4.245673729758231e-01, -2.530402764527700e+00,
-7.822016897497742e-02, 1.054463080605071e+00,
4.645590541391895e-01, 1.145097379521439e+00,
4.301337846893282e-01, 1.499513057076809e+00,
1.447942640822165e-02, 0],
[1.207394392845339e-02, 5.187080074649261e-01,
1.121304244847239e-01, -4.959806334780896e-03,
-1.345031364651444e+00, 3.398828703760807e-01,
8.159251531671077e-01, -2.640104266439604e-03,
1.439060901763520e-02, -6.556567796749947e-03,
6.548135446843367e-04, 5.454220210658036e-01]])

super(WSODIRK1255, self).__init__(A, b, None, c, 5)

def __str__(self):
return "WSODIRK1255()"
38 changes: 22 additions & 16 deletions irksome/__init__.py
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,16 +1,22 @@
from .ButcherTableaux import Alexander # noqa: F401
from .ButcherTableaux import GaussLegendre # noqa: F401
from .ButcherTableaux import LobattoIIIA # noqa: F401
from .ButcherTableaux import LobattoIIIC # noqa: F401
from .ButcherTableaux import BackwardEuler # noqa: F401
from .ButcherTableaux import RadauIIA # noqa: F401
from .ButcherTableaux import PareschiRusso # noqa: F401
from .ButcherTableaux import QinZhang # noqa: F401
from .deriv import Dt # noqa: F401
from .dirk_stepper import DIRKTimeStepper # noqa: F401
from .getForm import getForm # noqa: F401
from .imex import RadauIIAIMEXMethod # noqa: F401
from .pc import RanaBase, RanaDU, RanaLD # noqa: F401
from .stage import StageValueTimeStepper # noqa: F401
from .stepper import TimeStepper # noqa: F401
from .tools import MeshConstant # noqa: F401
from .ButcherTableaux import Alexander # noqa: F401
from .ButcherTableaux import BackwardEuler # noqa: F401
from .ButcherTableaux import GaussLegendre # noqa: F401
from .ButcherTableaux import LobattoIIIA # noqa: F401
from .ButcherTableaux import LobattoIIIC # noqa: F401
from .ButcherTableaux import PareschiRusso # noqa: F401
from .ButcherTableaux import QinZhang # noqa: F401
from .ButcherTableaux import RadauIIA # noqa: F401
from .ButcherTableaux import WSODIRK432 # noqa: F401
from .ButcherTableaux import WSODIRK433 # noqa: F401
from .ButcherTableaux import WSODIRK643 # noqa: F401
from .ButcherTableaux import WSODIRK744 # noqa: F401
from .ButcherTableaux import WSODIRK1254 # noqa: F401
from .ButcherTableaux import WSODIRK1255 # noqa: F401
from .deriv import Dt # noqa: F401
from .dirk_stepper import DIRKTimeStepper # noqa: F401
from .getForm import getForm # noqa: F401
from .imex import RadauIIAIMEXMethod # noqa: F401
from .pc import RanaBase, RanaDU, RanaLD # noqa: F401
from .stage import StageValueTimeStepper # noqa: F401
from .stepper import TimeStepper # noqa: F401
from .tools import MeshConstant # noqa: F401
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