medypt.model

Base class for phase-field models.

Classes

ModelBase

Base class for phase-field models.

Module Contents

class medypt.model.ModelBase

Base class for phase-field models.

opts: dict[str, Any]

A dictionary of numerical options. Initialized with default values and can be modified in subclasses. Contents include:

'has_thermal_noise' (bool): Whether to include thermal noise. Default is False.
'rand_seed' (int): Random seed for thermal noise generation. Default is 8347142.
'quadr_deg' (int): Quadrature degree for numerical integration. Default is 6.
'petsc' (dict): A dictionary of PETSc solver options (see this for example). Default to use Newton nonlinear solver with MUMPS direct linear solver.
't_step_rtol' (float): Relative tolerance for time discretization error. Default is 0.01.
'dt_min_rescalar' (float): Minimum factor to reduce time step upon failure. Default is 0.2.
'dt_max_rescalar' (float): Maximum factor to increase time step upon success. Default is 4.0.
'dt_reducer' (float): Factor to reduce time step rescalar. Default is 0.9.
'max_successive_fail' (int): Maximum number of successive failures before stopping. Default is 100.
'min_dt' (float): Minimum time step size. Default is 1e-9.
'max_dt' (float): Maximum time step size. Default is 10.0.
'save_period' (int): Time step period for saving solution. Default is 1.
'log_file_name' (str): File name for logging evolution. Default is evolution.txt.
'sol_file_name' (str): File name for saving solution. Default is solution.xdmf. If the suffix is not .xdmf or if no suffix, save solutions using dolfinx.io.VTXWriter into a folder with the given name.
'verbose' (bool): Whether to print verbose output. Default is False.

params: dict[str, Any]: A dictionary of physical parameters. Initialized to empty dictionary and should be set in subclasses.

mesh_data: dolfinx.io.gmsh.MeshData: dolfinx.io.gmsh.MeshData object containing mesh and boundary tags. Initialized to None and should be set in subclasses.

fields: dict[str, dolfinx.fem.Function]: A dictionary mapping field names to their dolfinx.fem.Function objects. Initialized to empty dictionary and should be set in subclasses.

load_mesh(comm: mpi4py.MPI.Comm, mesh: gmsh.model | str, **kwargs: Any)

Load the mesh data.

Parameters:

comm (MPI.Comm) – MPI communicator.
mesh (gmsh.model | str) – Gmsh model or a file name with the .msh or .xdmf format.
kwargs (dict[str, Any]) –
Additional keyword arguments passed to create_mesh():
- mesh_dim (int): Geometric dimension of the mesh. Required when mesh is a gmsh model or a .msh file.
- rank (int): Rank of the MPI process used for generating from gmsh model or reading from .msh files. Required when mesh is a gmsh model or a .msh file.
- mesh_name (str): Name (identifier) of the mesh to read from the .xdmf file. Required when mesh is a .xdmf file.

Returns:

None

set_bcs(bcs: list[tuple[str, int | collections.abc.Callable[[Any], Any], dolfinx.fem.Constant | dolfinx.fem.Function | numpy.ndarray | collections.abc.Callable[[Any], Any]]])

Set essential and natural boundary conditions.

Parameters:

bcs (list[tuple[str, int | Callable[[Any], Any], fem.Constant | fem.Function | np.ndarray | Callable[[Any], Any]]]) –

A list of tuples specifying boundary conditions. Each tuple is (name, b, bc), where:

name (str): The name of the field to which the boundary condition applies.
b (int | Callable[[Any], Any]): The tag of or a callable defining the boundary. The tag is only for boundaries with codimension 1. The callable is only for Dirichlet boundary conditions and will have a calling signature b(x), where x is the spatial coordinate treated as a 2D numpy array with shape (geom_dim, num_points). It should return a boolean array of shape (num_points,) indicating whether each point is on the boundary.
bc (Constant | Function | ndarray | Callable[[Any], Any]): A variable or callable defining the boundary condition. A variable is for Dirichlet boundary conditions, while a callable is for natural boundary conditions. The callable will have a calling signature bc(fields), where fields is treated as a tuple containing the splitted fields. It covers boundary conditions of the Neumann, Robin, and other general types implemented using the Nistche’s trick [1] [2]. The default is the zero-flux boundary condition.

Tip

One can make an evolving boundary condition by defining a global dolfinx.fem.Constant or dolfinx.fem.Function object and using it in the boundary-condition expression. One will then need to define an update function to update the value of the global object for a given time and pass that function to solve().

create_problem(): Create the finite element problem that is ready to be solved.

solve(tspan: float, dt: float | None = None, ics: dict[str, collections.abc.Callable[[Any], Any] | dolfinx.fem.Function] | None = None, update: collections.abc.Callable[[float], None] = lambda t: ...) → bool

Solve the time-dependent finite-element problem.

It uses adapative backward Euler time stepping algorithm for time integration. The time step is automatically controlled by the time discretization error specified in opts. The advantage of backward Euler algorithm is its stability.

Parameters:

tspan (float) – Time span to solve over.
dt (float | None) – Initial time step. Defaults to None to use the current time step.
ics (dict[str, Callable[[Any], Any] | fem.Function] | None) – Initial conditions, defined as a dictionary mapping field names to callables that return the initial value for that field. The callables have a calling signature ic(x), where x is the spatial coordinate treated as a 2D numpy array with shape (geom_dim, num_points). Defaults to None to use the current values of the fields.
update (Callable[[float], None]) – A callable to update any time-dependent parameters (must be defined a priori as global dolfinx.fem.Constant or dolfinx.fem.Function) at each time step. It takes the current time as the only argument. Defaults to a no-op function.

Returns:

True if the solve completed successfully, False otherwise.

Return type:

bool