dedalus.core.solvers

Solver classes.

Module Contents

logger
class SolverBase(problem, ncc_cutoff=1e-06, max_ncc_terms=None, entry_cutoff=1e-12, matrix_coupling=None, matsolver=None, bc_top=None, tau_left=None, interleave_components=None, store_expanded_matrices=None)

Base class for PDE solvers.

Parameters

  • problem (Problem object) – Dedalus problem.

  • ncc_cutoff (float, optional) – Mode amplitude cutoff for LHS NCC expansions (default: 1e-6)

  • max_ncc_terms (int, optional) – Maximum terms to include in LHS NCC expansions (default: None (no limit))

  • entry_cutoff (float, optional) – Matrix entry cutoff to avoid fill-in from cancellation errors (default: 1e-12)

  • matrix_coupling (tuple of bool, optional) – Matrix coupling override.

  • matsolver (str or Matsolver class, optional) – Matrix solver. Default taken from config.

  • bc_top (bool, optional) – Whether to place boundary conditions at top of matrices. Default taken from config.

  • tau_left (bool, optional) – Whether to place tau columns at left of matrices. Default taken from config.

  • interleave_components (bool, optional) – Whether to interleave components before variables. Default taken from config.

  • store_expanded_matrices (bool, optional) – Whether to store right-preconditioned matrices. Default taken from config.

build_matrices(subproblems=None, matrices=None)

Build matrices for selected subproblems.

class EigenvalueSolver(problem, **kw)

Linear eigenvalue problem solver.

Parameters

  • problem (Problem object) – Dedalus eigenvalue problem.

  • **kw – Other options passed to ProblemBase.

Variables

  • state (list of Field objects) – Problem variables containing solution (after set_state method is called).

  • eigenvalues (ndarray) – Vector of eigenvalues.

  • eigenvectors (ndarray) – Array of eigenvectors. The eigenvector corresponding to the i-th eigenvalues is eigenvectors[:, i].

  • eigenvalue_subproblem (Subproblem object) – The subproblem for which the EVP has een solved.

matsolver_default = 'MATRIX_FACTORIZER'
matrices = ['M', 'L']
print_subproblem_ranks(subproblems=None, target=0)

Print rank of each subproblem LHS.

solve_dense(subproblem, rebuild_matrices=False, left=False, normalize_left=True, **kw)

Perform dense eigenvector search for selected subproblem. This routine finds all eigenvectors but is computationally expensive.

Parameters

  • subproblem (Subproblem object) – Subproblem for which to solve the EVP.

  • rebuild_matrices (bool, optional) – Rebuild LHS matrices if coefficients have changed (default: False).

  • left (bool, optional) – Solve for the left eigenvectors of the system in addition to the right eigenvectors. The left eigenvectors are the right eigenvectors of the conjugate-transposed problem. Follows same definition described in scipy.linalg.eig documentation (default: False).

  • normalize_left (bool, optional) – Normalize the left eigenvectors such that the modified left eigenvectors form a biorthonormal (not just biorthogonal) set with respect to the right eigenvectors (default: True).

  • **kw – Other keyword options passed to scipy.linalg.eig.

solve_sparse(subproblem, N, target, rebuild_matrices=False, left=False, normalize_left=True, raise_on_mismatch=True, **kw)

Perform targeted sparse eigenvector search for selected subproblem. This routine finds a subset of eigenvectors near the specified target.

Parameters

  • subproblem (Subproblem object) – Subproblem for which to solve the EVP.

  • N (int) – Number of eigenvectors to solve for. Note: the dense method may be more efficient for finding large numbers of eigenvectors.

  • target (complex) – Target eigenvalue for search.

  • rebuild_matrices (bool, optional) – Rebuild LHS matrices if coefficients have changed (default: False).

  • left (bool, optional) – Solve for the left eigenvectors of the system in addition to the right eigenvectors. The left eigenvectors are the right eigenvectors of the conjugate-transposed problem. Follows same definition described in scipy.linalg.eig documentation (default: False).

  • normalize_left (bool, optional) – Normalize the left eigenvectors such that the modified left eigenvectors form a biorthonormal (not just biorthogonal) set with respect to the right eigenvectors (default: True).

  • raise_on_mismatch (bool, optional) – Raise a RuntimeError if the left and right eigenvalues do not match (default: True).

  • **kw – Other keyword options passed to scipy.sparse.linalg.eig.

set_state(index, subsystem)

Set state vector to the specified eigenmode.

Parameters

  • index (int) – Index of desired eigenmode.

  • subsystem (Subsystem object or int) – Subsystem that will be set to the corresponding eigenmode. If an integer, the corresponding subsystem of the last specified eigenvalue_subproblem will be used.

class LinearBoundaryValueSolver(problem, **kw)

Linear boundary value problem solver.

Parameters

  • problem (Problem object) – Dedalus problem.

  • **kw – Other options passed to ProblemBase.

Variables

state (list of Field objects) – Problem variables containing solution (after solve method is called).

matsolver_default = 'MATRIX_FACTORIZER'
matrices = ['L']
print_subproblem_ranks(subproblems=None)

Print rank of each subproblem LHS.

solve(subproblems=None, rebuild_matrices=False)

Solve BVP over selected subproblems.

Parameters

  • subproblems (Subproblem object or list of Subproblem objects, optional) – Subproblems for which to solve the BVP (default: None (all)).

  • rebuild_matrices (bool, optional) – Rebuild LHS matrices if coefficients have changed (default: False).

evaluate_handlers(handlers=None)

Evaluate specified list of handlers (all by default).

class NonlinearBoundaryValueSolver(problem, **kw)

Nonlinear boundary value problem solver.

Parameters

  • problem (Problem object) – Dedalus problem.

  • **kw – Other options passed to ProblemBase.

Variables

  • state (list of Field objects) – Problem variables containing solution.

  • perturbations (list of Field objects) – Perturbations to problem variables from each Newton iteration.

  • iteration (int) – Current iteration.

matsolver_default = 'MATRIX_SOLVER'
matrices = ['dH']
newton_iteration(damping=1)

Update solution with a Newton iteration.

evaluate_handlers(handlers=None)

Evaluate specified list of handlers (all by default).

class InitialValueSolver(problem, timestepper, enforce_real_cadence=100, warmup_iterations=10, **kw)

Initial value problem solver.

Parameters

  • problem (Problem object) – Dedalus problem.

  • timestepper (Timestepper class or str) – Timestepper to use in evolving initial conditions.

  • enforce_real_cadence (int, optional) – Iteration cadence for enforcing Hermitian symmetry on real variables (default: 100).

  • warmup_iterations (int, optional) – Number of warmup iterations to disregard when computing runtime statistics (default: 10).

  • **kw – Other options passed to ProblemBase.

Variables

  • state (list of Field objects) – Problem variables containing solution.

  • stop_sim_time (float) – Simulation stop time, in simulation units.

  • stop_wall_time (float) – Wall stop time, in seconds from instantiation.

  • stop_iteration (int) – Stop iteration.

  • sim_time (float) – Current simulation time.

  • iteration (int) – Current iteration.

  • dt (float) – Last timestep.

property sim_time
property world_time
property wall_time

Seconds ellapsed since instantiation.

property proceed

Check that current time and iteration pass stop conditions.

matsolver_default = 'MATRIX_FACTORIZER'
matrices = ['M', 'L']
load_state(path, index=- 1, allow_missing=False)

Load state from HDF5 file. Currently can only load grid space data.

Parameters

  • path (str or pathlib.Path) – Path to Dedalus HDF5 savefile

  • index (int, optional) – Local write index (within file) to load (default: -1)

  • allow_missing (bool, optional) – Do not raise an error if state variables are missing from the savefile (default: False).

Returns

  • write (int) – Global write number of loaded write

  • dt (float) – Timestep at loaded write

enforce_hermitian_symmetry(fields)

Transform fields to grid and back.

step(dt)

Advance system by one iteration/timestep.

evolve(timestep_function, log_cadence=100)

Advance system until stopping criterion is reached.

print_subproblem_ranks(subproblems=None, dt=1)

Print rank of each subproblem LHS.

evaluate_handlers_now(dt, handlers=None)
evaluate_handlers(handlers=None, dt=0)

Evaluate specified list of handlers (all by default).

log_stats(format='.4g')

Log timing statistics with specified string formatting (optional).