fedoo.problem.Linear

class Linear(assembly: Assembly, time_step: float | None = None, integrator: GeneralizedAlpha | None = None, name: str = 'MainProblem')

Class that defines linear problems.

This simple class allows a linear problem to be built from an assembly object. The discretized problem is written as A * X = B + D, where A is the matrix built by the assembly, X is the solution vector, B contains the Neumann boundary conditions, and D is the vector built by the assembly.

Parameters:

• assembly (Assembly-like object or str) – Assembly used to construct the matrix A and vector D, or the name of a registered assembly.

• time_step (float, optional) – Constant time increment used when a second-order integrator is attached. Omit it for the original static behavior.

• integrator (fedoo.time.Newmark or fedoo.time.GeneralizedAlpha, optional) – Implicit second-order time integrator. The stiffness and consistent mass matrices are assembled once by initialize() and reused at every constant-size increment. Only the right-hand side is rebuilt.

• name (str, default="MainProblem") – Name of the problem.

__init__(assembly: Assembly, time_step: float | None = None, integrator: GeneralizedAlpha | None = None, name: str = 'MainProblem')

Methods

Linear.GetElasticEnergy()	returns : sum (0.5 * U.transposed * K * U)
Linear.GetNodalElasticEnergy()	returns : 0.5 * K * U .
Linear.add_global_dof(variable_names[, ...])	Add global degrees of freedom to the problem.
Linear.add_output(filename, assembly[, ...])	Register an output for automatic saving managed by solve methods.
Linear.apply_boundary_conditions([t_fact, ...])
Linear.change_assembly(assembling[, update])	Modify the assembly associated to the problem and update the problem (see Assembly.update for more information)
Linear.check_boundary_conditions()	Look for boundary conditions applied twice on the same dof.
Linear.clear_outputs()	Stop automatic output by removing all registered requests.
Linear.get_A()
Linear.get_B()
Linear.get_D()
Linear.get_X()
Linear.get_acceleration([name])	Return the current transient acceleration.
Linear.get_active()	Return the active Problem.
Linear.get_all()	Return the list of all problems.
Linear.get_disp([name])	Return the displacement components.
Linear.get_dof_solution([name])
Linear.get_elastic_energy()	returns : sum (0.5 * U.transposed * K * U)
Linear.get_ext_forces([name, include_mpc])	Return the nodal Forces in global coordinates system.
Linear.get_kinetic_energy()	Return 0.5 * velocity.T * M * velocity.
Linear.get_nodal_elastic_energy()	returns : 0.5 * K * U .
Linear.get_results(*args, **kargs)	Extract some results from the current problem.
Linear.get_rot([name])	Return the rotation components.
Linear.get_velocity([name])	Return the current transient velocity.
Linear.init_bc_start_value()
Linear.initialize()	Initialize and cache the optional linear transient operators.
Linear.invalidate_factorization()	Invalidate any cached factorization.
Linear.make_active()	Define the problem instance as the active Problem.
Linear.reset()
Linear.save_results([iterOutput])	Write the current state to every registered output.
Linear.set_A(A)
Linear.set_B(B)
Linear.set_D(D)
Linear.set_X(value)
Linear.set_active(name)	Define the active Problem from its name.
Linear.set_dof(name, value)	Set a static solution field or the current dynamic displacement.
Linear.set_initial_acceleration(name, value)	Set a transient initial acceleration component.
Linear.set_initial_displacement(name, value)	Set a transient initial displacement component.
Linear.set_initial_velocity(name, value)	Set a transient initial velocity component.
Linear.set_reuse_factorization([reuse])	Enable or disable factorization reuse for repeated solves.
Linear.set_solver([solver, symmetric])	Define the solver for the linear system resolution.
Linear.set_time_integrator(evolution, integrator)	Attach a linear implicit second-order time integrator.
Linear.solve(**kargs)	Solve the linear problem and optionally update assembly fields.
Linear.solve_history(tmax[, dt, ...])	Solve a complete cached linear transient history.
Linear.solve_time_increment([...])	Solve and advance one complete linear transient increment.
Linear.update([dtime, compute, update_weakform])	Assemble the matrix including the following modification:
Linear.update_boundary_conditions()

Linear.active
Linear.assembly
Linear.global_dof
Linear.is_dynamic	Whether this linear problem has a time integrator attached.
Linear.n_dof
Linear.n_global_dof
Linear.n_node_dof
Linear.name	Return the name of the Problem.
Linear.results
Linear.solver	Return the current solver used for the problem.
Linear.space	Return the ModelingSpace associated to the Problem if defined.
Linear.time_integrator	Return the attached second-order integrator, or None.
Linear.bc	Boundary conditions defined on the problem.