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Implemented framework for spectral methods and Rayleigh Benard Convection with ultraspherical method #476

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merged 13 commits into from
Sep 20, 2024
Merged

Implemented framework for spectral methods and Rayleigh Benard Convection with ultraspherical method #476

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217d776
Implemented framework for spectral methods and Rayleigh Benard
brownbaerchen Sep 6, 2024
5355e91
Forgot to remove some BS
brownbaerchen Sep 6, 2024
821829d
Addressing review by @tlunet
brownbaerchen Sep 6, 2024
6fbfa72
Added some problem documentation and renamed the guy
brownbaerchen Sep 6, 2024
477ad93
Implemented caching of LU matrix decompositions in generic spectral
brownbaerchen Sep 8, 2024
fc74383
Put BCs in rhs with fewer transforms
brownbaerchen Sep 9, 2024
042c28c
Implemented option to stay in spectral space after solving etc.
brownbaerchen Sep 9, 2024
cc4297b
Eliminating Nyquist mode for even resolution in RBC
brownbaerchen Sep 10, 2024
d94ad53
Accelerated transposes by reusing transfer objects
brownbaerchen Sep 12, 2024
d31b5fc
Small bugfix
brownbaerchen Sep 12, 2024
016a784
Merge remote-tracking branch 'upstream/master' into spectral_methods
brownbaerchen Sep 13, 2024
f33a7e9
Updated some things for GPUs
brownbaerchen Sep 13, 2024
0e8e997
Implemented changes requested by @tlunet
brownbaerchen Sep 15, 2024
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13 changes: 9 additions & 4 deletions pySDC/implementations/problem_classes/Burgers.py
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Expand Up @@ -5,6 +5,11 @@


class Burgers1D(GenericSpectralLinear):
"""
See https://en.wikipedia.org/wiki/Burgers'_equation
Discretization is done with a Chebychov method, which requires a first order derivative formulation.
Feel free to do a more efficient implementation using an ultraspherical method to avoid the first order business.
"""
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dtype_u = mesh
dtype_f = imex_mesh
Expand Down Expand Up @@ -125,9 +130,12 @@ def plot(self, u, t=None, fig=None, comp='u'): # pragma: no cover


class Burgers2D(GenericSpectralLinear):
"""
See documentation of `Burgers1D`.
"""

dtype_u = mesh
dtype_f = imex_mesh
xp = np

def __init__(self, nx=64, nz=64, epsilon=0.1, fux=2, fuz=1, mode='T2U', **kwargs):
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self._makeAttributeAndRegister(*locals().keys(), localVars=locals(), readOnly=True)
Expand Down Expand Up @@ -187,9 +195,6 @@ def u_exact(self, t=0, *args, noise_level=0, **kwargs):
me[iu] = self.xp.cos(self.X * self.fux) * self.xp.sin(self.Z * np.pi * self.fuz) + self.BCtopu
me[iux] = -self.xp.sin(self.X * self.fux) * self.fux * self.xp.sin(self.Z * np.pi * self.fuz)
me[iuz] = self.xp.cos(self.X * self.fux) * self.xp.cos(self.Z * np.pi * self.fuz) * np.pi * self.fuz
# me[iu] = self.xp.cos(self.X * self.fux) * (self.Z+1)*(self.Z-1) + self.BCtopu
# me[iux] = -self.xp.sin(self.X * self.fux) * self.fux * (self.Z+1)*(self.Z-1)
# me[iuz] = self.xp.cos(self.X * self.fux) * 2 * self.Z

me[iv] = (self.BCtop + self.BCbottom) / 2 + (self.BCtop - self.BCbottom) / 2 * self.Z
me[ivz][:] = (self.BCtop - self.BCbottom) / 2
Expand Down