[docs]
class Magnetosonic(Propagator):
r"""FEEC discretization of the following equations:
find :math:`\tilde{\rho} \in L^2, \tilde{\mathbf U} \in \{H(\textnormal{curl}), H(\textnormal{div}), (H^1)^3\}, \tilde p \in L^2` such that
.. math::
\frac{\partial \tilde{\rho}}{\partial t} + \nabla\cdot(\rho_0 \tilde{\mathbf{U}}) &= 0
\\[2mm]
\int_{\Omega} \rho_0\frac{\partial \tilde{\mathbf{U}}}{\partial t} \cdot \mathbf V\,\textrm{d}\mathbf x - \int_{\Omega} \tilde p\,\nabla\cdot\mathbf V\,\textrm{d}\mathbf x &= \int_{\Omega} (\nabla\times\mathbf{B}_0)\times\tilde{\mathbf{B}}\cdot\mathbf V\,\textrm{d}\mathbf x \qquad \forall\,\mathbf V \in \{H(\textnormal{curl}), H(\textnormal{div}), (H^1)^3\}
\\[2mm]
\frac{\partial \tilde p}{\partial t} + \nabla\cdot(p_0 \tilde{\mathbf{U}}) + \frac{2}{3}\,p_0\nabla\cdot\tilde{\mathbf{U}} &= 0
Time discretization: Crank-Nicolson (implicit mid-point).
System size reduction via :class:`~struphy.linear_algebra.schur_solver.SchurSolver`:
"""
[docs]
class Variables:
"""Container for variables advanced by :class:`Magnetosonic`.
Attributes
----------
n : FEECVariable
Density perturbation variable in ``"L2"`` space.
u : FEECVariable
Velocity perturbation variable in one of ``"Hcurl"``, ``"Hdiv"``,
or ``"H1vec"``.
p : FEECVariable
Pressure perturbation variable in ``"L2"`` space.
"""
def __init__(self):
self._n: FEECVariable = None
self._u: FEECVariable = None
self._p: FEECVariable = None
@property
def n(self) -> FEECVariable:
return self._n
@n.setter
def n(self, new):
assert isinstance(new, FEECVariable)
assert new.space == "L2"
self._n = new
@property
def u(self) -> FEECVariable:
return self._u
@u.setter
def u(self, new):
assert isinstance(new, FEECVariable)
assert new.space in ("Hcurl", "Hdiv", "H1vec")
self._u = new
@property
def p(self) -> FEECVariable:
return self._p
@p.setter
def p(self, new):
assert isinstance(new, FEECVariable)
assert new.space == "L2"
self._p = new
def __init__(self, b_field: FEECVariable = None):
"""
Parameters
----------
b_field : FEECVariable, default=None
Magnetic 2-form (``"Hdiv"`` space) providing the equilibrium magnetic field.
If ``None``, an empty ``FEECVariable(space="Hdiv")`` is created internally.
"""
self.variables = self.Variables()
self.b_field = b_field if b_field is not None else FEECVariable(space="Hdiv")
[docs]
@dataclass(repr=False)
class Options(OptionsBase):
"""Configuration options for :class:`Magnetosonic`.
Parameters
----------
u_space : LiteralOptions.OptsVecSpace, default="Hdiv"
FEEC space used for the velocity variable ``u``.
solver : LiteralOptions.OptsGenSolver, default="pbicgstab"
Iterative solver used by :class:`SchurSolver`.
precond : LiteralOptions.OptsMassPrecond, default="MassMatrixPreconditioner"
Preconditioner applied to the mass matrix block associated with
``u_space``.
solver_params : SolverParameters, default=None
Iterative-solver controls. If ``None``, defaults to
``SolverParameters()``.
"""
u_space: LiteralOptions.OptsVecSpace = "Hdiv"
solver: LiteralOptions.OptsGenSolver = "pbicgstab"
precond: LiteralOptions.OptsMassPrecond = "MassMatrixPreconditioner"
solver_params: SolverParameters = None
def __post_init__(self):
# checks
check_option(self.u_space, LiteralOptions.OptsVecSpace)
check_option(self.solver, LiteralOptions.OptsGenSolver)
check_option(self.precond, LiteralOptions.OptsMassPrecond)
# defaults
if self.solver_params is None:
self.solver_params = SolverParameters()
@property
def options(self) -> Options:
if not hasattr(self, "_options"):
self._options = self.Options()
return self._options
@options.setter
def options(self, new):
assert isinstance(new, self.Options)
self._options = new
logger.info(f"\nNew options for propagator '{self.__class__.__name__}':\n{self._options}")
@profile
def allocate(self):
u_space = self.options.u_space
self._info = self.options.solver_params.info
self._bc = self.derham.dirichlet_bc
# define block matrix [[A B], [C I]] (without time step size dt in the diagonals)
id_Mn = "M" + self.derham.space_to_form[u_space] + "n"
id_MJ = "M" + self.derham.space_to_form[u_space] + "J"
if u_space == "Hcurl":
id_S, id_U, id_K, id_Q = "S1", "U1", "K3", "Q1"
elif u_space == "Hdiv":
id_S, id_U, id_K, id_Q = "S2", None, "K3", "Q2"
elif u_space == "H1vec":
id_S, id_U, id_K, id_Q = "Sv", "Uv", "K3", "Qv"
_A = getattr(self.mass_ops, id_Mn)
_S = getattr(self.basis_ops, id_S)
_K = getattr(self.basis_ops, id_K)
if id_U is None:
_U = IdentityOperator(self.variables.u.spline.vector.space)
_UT = IdentityOperator(self.variables.u.spline.vector.space)
else:
_U = getattr(self.basis_ops, id_U)
_UT = _U.T
self._B = -1 / 2.0 * _UT @ self.derham.div.T @ self.mass_ops.M3
self._C = 1 / 2.0 * self.derham.div @ _S + 2 / 3 * _K @ self.derham.div @ _U
self._MJ = getattr(self.mass_ops, id_MJ)
self._DQ = self.derham.div @ getattr(self.basis_ops, id_Q)
self.b_field.allocate(self.derham, self.domain)
self._b = self.b_field.spline.vector
# preconditioner
if self.options.precond is None:
pc = None
else:
pc_class = getattr(preconditioner, self.options.precond)
pc = pc_class(getattr(self.mass_ops, id_Mn))
# instantiate Schur solver (constant in this case)
_BC = self._B @ self._C
self._schur_solver = SchurSolver(
_A,
_BC,
self.options.solver,
precond=pc,
solver_params=self.options.solver_params,
)
# allocate dummy vectors to avoid temporary array allocations
self._u_tmp1 = self.variables.u.spline.vector.space.zeros()
self._u_tmp2 = self.variables.u.spline.vector.space.zeros()
self._p_tmp1 = self.variables.p.spline.vector.space.zeros()
self._n_tmp1 = self.variables.n.spline.vector.space.zeros()
self._b_tmp1 = self._b.space.zeros()
self._byn1 = self._B.codomain.zeros()
self._byn2 = self._B.codomain.zeros()
@profile
def __call__(self, dt):
# current FE coeffs
nn = self.variables.n.spline.vector
un = self.variables.u.spline.vector
pn = self.variables.p.spline.vector
# solve for new u coeffs (no tmps created here)
byn1 = self._B.dot(pn, out=self._byn1)
byn2 = self._MJ.dot(self._b, out=self._byn2)
byn2 *= 1 / 2
byn1 -= byn2
un1, info = self._schur_solver(un, byn1, dt, out=self._u_tmp1)
# new p, n, b coeffs (no tmps created here)
_u = un.copy(out=self._u_tmp2)
_u += un1
pn1 = self._C.dot(_u, out=self._p_tmp1)
pn1 *= -dt
pn1 += pn
nn1 = self._DQ.dot(_u, out=self._n_tmp1)
nn1 *= -dt / 2
nn1 += nn
diffs = self.update_feec_variables(n=nn1, u=un1, p=pn1)
if self._info and MPI.COMM_WORLD.Get_rank() == 0:
logger.info(f"Status for Magnetosonic: {info['success']}")
logger.info(f"Iterations for Magnetosonic: {info['niter']}")
logger.info(f"Maxdiff n3 for Magnetosonic: {diffs['n']}")
logger.info(f"Maxdiff up for Magnetosonic: {diffs['u']}")
logger.info(f"Maxdiff p3 for Magnetosonic: {diffs['p']}")
logger.info("")
