kqcircuits.simulations.export.elmer.elmer_solution

class kqcircuits.simulations.export.elmer.elmer_solution.ElmerSolution(*, name: str = '', percent_error: float = 0.005, max_error_scale: float = 2.0, max_outlier_fraction: float = 0.001, maximum_passes: int = 1, minimum_passes: int = 1, is_axisymmetric: bool = False, mesh_levels: int = 1, mesh_size: dict = <factory>, mesh_optimizer: dict | None = None, vtu_output: bool = True, save_elmer_data: bool = False, linear_system_method: str = 'GCR', convergence_tolerance: float = 1e-09, max_iterations: int = 500, linear_system_preconditioning: str = 'ILU0', abort_not_converged: bool = False, use_multigrid_solver: bool = True, mg_smoother: str = 'SGS', mg_smoothing_iterations: int | None = None, mg_relaxation_factor: float = 0.28, mg_lowest_method: str = 'CG')

Bases: Solution

A Base class for Elmer Solution parameters

Parameters:

• percent_error – Stopping criterion in adaptive meshing.

• max_error_scale – Maximum element error, relative to percent_error, allowed in individual elements.

• max_outlier_fraction – Maximum fraction of outliers from the total number of elements

• maximum_passes – Maximum number of adaptive meshing iterations.

• minimum_passes – Minimum number of adaptive meshing iterations.

• is_axisymmetric – Simulate with Axi Symmetric coordinates along \(y\Big|_{x=0}\) (Default: False)

• mesh_levels – If set larger than 1 Elmer will make the mesh finer by dividing each element into 2^(dim) elements mesh_levels times. Default 1.

• mesh_size – Dictionary to determine the mesh refinement. The keys (string) denote the entities where to apply the refinement and values (double) denote the maximal length of the mesh elements. Optionally, the values can be set as a lists of doubles. Then, value[0] is the maximal mesh element length inside at the entity and its expansion, value[1] is expansion distance in which the maximal mesh element length is constant (default=value[0]), and value[2] is the slope of the increase in the maximal mesh element length outside the entity. The key can be a single layer name, or it can consist of multiple layer names separated with the & symbol, meaning the entity will be an intersection of listed layers. Optionally, one can use a pattern for layer names with the * symbol representing any string in a layer name. The ! symbol before the layer name or pattern means that the complement of layer(s) is used instead. The key ‘global_max’ is reserved for setting global maximal element length. For example, if the dictionary is {‘substrate*’: 10, ‘substrate*&vacuum’: [2, 5], ‘global_max’: 100}, then the maximal mesh element length is 10 inside the substrates and 2 on region which is less than 5 units away from any substrate-vacuum interface. Outside these regions, the mesh element size can increase up to 100.

• mesh_optimizer – Dictionary to determine mesh optimization, or None (default) to ignore optimization. The dictionary can contain keywords ‘method’, ‘force’, ‘niter’ and ‘dimTags’. See Gmsh manual (gmsh.model.mesh.optimize) for details. The default value for ‘method’ is ‘Netgen’.

• vtu_output – Output vtu files to view fields in Paraview. Turning this off will make the simulations slightly faster

• save_elmer_data – Save the full Elmer model after simulation. This can be used to restart the simulation or extract result field values as a post-processing step.

• linear_system_method – Method for solving the FEM linear system of equations in Elmer. For iterative methods use “GCR”, “bicgstab” or any other iterative solver mentioned in ElmerSolver manual section 4.3.1. For direct methods “umfpack”, “mumps”, “pardiso” or “superlu” can be used, but note that other methods than “umfpack” require Elmer to be explicitly compiled with the corresponding solver software. If a direct method is used the parameters “convergence_tolerance”, “max_iterations”, “linear_system_preconditioning”, “abort_not_converged” and all multigrid options (“mg_*”) are redundant.

• convergence_tolerance – Convergence tolerance of the iterative solver.

• max_iterations – Maximum number of iterations for the iterative solver.

• linear_system_preconditioning – Choice of preconditioner before using an iterative linear system solver. If using multigrid, the preconditioning is applied on the lowest iteration level.

• abort_not_converged – Stop Elmer execution immediately if an iterative linear system solver fails to reach convergence. If False, a warning is printed after the simulation finishes.

• use_multigrid_solver – Use hierarchical iterative multigrid solver.

• mg_smoother – Choice of smoother in multigrid solver. Tested options for electrostatic simulations are “SGS”, “CG” and “wjacobi”. VectorHelmholtzSolution support “cjacobi”.

• mg_smoothing_iterations – Number of smoothing iterations.

• mg_relaxation_factor – Parameter for tuning the smoothers “wjacobi” and “cjacobi”.

• mg_lowest_method – Linear system method used for solving the smallest/lowest order linear system in multigrid. See linear_system_method for options.

tool: ClassVar[str] = ''

percent_error: float = 0.005

max_error_scale: float = 2.0

max_outlier_fraction: float = 0.001

maximum_passes: int = 1

minimum_passes: int = 1

is_axisymmetric: bool = False

mesh_levels: int = 1

mesh_size: dict

mesh_optimizer: dict | None = None

vtu_output: bool = True

save_elmer_data: bool = False

linear_system_method: str = 'GCR'

convergence_tolerance: float = 1e-09

max_iterations: int = 500

linear_system_preconditioning: str = 'ILU0'

abort_not_converged: bool = False

use_multigrid_solver: bool = True

mg_smoother: str = 'SGS'

mg_smoothing_iterations: int | None = None

mg_relaxation_factor: float = 0.28

mg_lowest_method: str = 'CG'

get_solution_data()

Return the solution data in dictionary form.

class kqcircuits.simulations.export.elmer.elmer_solution.ElmerVectorHelmholtzSolution(*, name: str = '', percent_error: float = 0.005, max_error_scale: float = 2.0, max_outlier_fraction: float = 0.001, maximum_passes: int = 1, minimum_passes: int = 1, is_axisymmetric: bool = False, mesh_levels: int = 1, mesh_size: dict = <factory>, mesh_optimizer: dict | None = None, vtu_output: bool = True, save_elmer_data: bool = False, linear_system_method: str = 'GCR', convergence_tolerance: float = 1e-06, max_iterations: int = 200, linear_system_preconditioning: str = 'none', abort_not_converged: bool = False, use_multigrid_solver: bool = True, mg_smoother: str = 'cjacobi', mg_smoothing_iterations: int | None = None, mg_relaxation_factor: float = 0.28, mg_lowest_method: str = 'zmumps', frequency: float | list[float] = 5, frequency_batch: int = 3, sweep_type: str = 'explicit', max_delta_s: float = 0.01, london_penetration_depth: float = 0, quadratic_approximation: bool = True, second_kind_basis: bool = False, use_av: bool = False, conductivity: float = 0, nested_iteration: bool = False)

Bases: ElmerSolution

Class for Elmer wave-equation solution parameters

Parameters:

• frequency – Units are in GHz. Give a list of frequencies if using interpolating sweep.

• frequency_batch – Number of frequencies calculated between each round of fitting in interpolating sweep

• sweep_type – Type of frequency sweep. Options “explicit” and “interpolating”.

• max_delta_s – Convergence tolerance in interpolating sweep

• london_penetration_depth – Allows supercurrent to flow on the metal boundaries within a layer of thickness london_penetration_depth

• quadratic_approximation – Use edge finite elements of second order. Otherwise use first order. If False, a direct solver such as linear_system_method=zmumps should be used.

• second_kind_basis – Use Nedelec finite elements of second kind.

• use_av – Use a formulation of VectorHelmHoltz equation based on potentials A-V instead of electric field E. For details see https://www.nic.funet.fi/pub/sci/physics/elmer/doc/ElmerModelsManual.pdf WARNING: This option is experimental and might lead to poor convergence.

• conductivity – Adds a specified film conductivity on metal boundaries. Applies only when use_av=True

• nested_iteration – Enables alternative nested iterative solver to be used. Applies only when use_av=True

tool: ClassVar[str] = 'wave_equation'

frequency: float | list[float] = 5

frequency_batch: int = 3

sweep_type: str = 'explicit'

max_delta_s: float = 0.01

london_penetration_depth: float = 0

quadratic_approximation: bool = True

second_kind_basis: bool = False

use_av: bool = False

conductivity: float = 0

nested_iteration: bool = False

mg_smoother: str = 'cjacobi'

convergence_tolerance: float = 1e-06

max_iterations: int = 200

linear_system_preconditioning: str = 'none'

mg_lowest_method: str = 'zmumps'

class kqcircuits.simulations.export.elmer.elmer_solution.ElmerCapacitanceSolution(*, name: str = '', percent_error: float = 0.005, max_error_scale: float = 2.0, max_outlier_fraction: float = 0.001, maximum_passes: int = 1, minimum_passes: int = 1, is_axisymmetric: bool = False, mesh_levels: int = 1, mesh_size: dict = <factory>, mesh_optimizer: dict | None = None, vtu_output: bool = True, save_elmer_data: bool = False, linear_system_method: str = 'GCR', convergence_tolerance: float = 1e-09, max_iterations: int = 500, linear_system_preconditioning: str = 'ILU0', abort_not_converged: bool = False, use_multigrid_solver: bool = True, mg_smoother: str = 'SGS', mg_smoothing_iterations: int | None = None, mg_relaxation_factor: float = 0.28, mg_lowest_method: str = 'CG', p_element_order: int = 3, integrate_energies: bool = False, electric_infinity_bc: bool = False)

Bases: ElmerSolution

Class for Elmer capacitance solution parameters

Parameters:

• p_element_order – polynomial order of p-elements

• integrate_energies – Calculate energy integrals over each object. Used in EPR simulations

• electric_infinity_bc – effectively extend the model domain to infinity using spherical boundary conditions

tool: ClassVar[str] = 'capacitance'

p_element_order: int = 3

integrate_energies: bool = False

electric_infinity_bc: bool = False

class kqcircuits.simulations.export.elmer.elmer_solution.ElmerCrossSectionSolution(*, name: str = '', percent_error: float = 0.005, max_error_scale: float = 2.0, max_outlier_fraction: float = 0.001, maximum_passes: int = 1, minimum_passes: int = 1, is_axisymmetric: bool = False, mesh_levels: int = 1, mesh_size: dict = <factory>, mesh_optimizer: dict | None = None, vtu_output: bool = True, save_elmer_data: bool = False, linear_system_method: str = 'GCR', convergence_tolerance: float = 1e-09, max_iterations: int = 500, linear_system_preconditioning: str = 'ILU0', abort_not_converged: bool = False, use_multigrid_solver: bool = True, mg_smoother: str = 'SGS', mg_smoothing_iterations: int | None = None, mg_relaxation_factor: float = 0.28, mg_lowest_method: str = 'CG', p_element_order: int = 3, integrate_energies: bool = False, boundary_conditions: dict = <factory>, run_inductance_sim: bool = True, voltage_excitations: list[float] | None = None, electric_infinity_bc: bool = False)

Bases: ElmerSolution

Class for Elmer cross-section solution parameters. By default both 2D Capacitance and 2D Inductance simulation will be run when using this Solution type. The linear system solver parameters are hardcoded for the inductance simulation and the solver related parameters in ElmerSolution only have effect on the Capacitance simulation.

Parameters:

• p_element_order – polynomial order of p-elements

• integrate_energies – Calculate energy integrals over each object. Used in EPR simulations

• boundary_conditions – Parameters to determine boundary conditions for potential on the edges of simulation box. Supported keys are xmin , xmax ,`ymin` and ymax Example: boundary_conditions = {“xmin”: {“potential”: 0}}

• run_inductance_sim – Can be used to skip running the inductance simulation and just do 2D capacitance. No impendance can then be calculated but useful for making EPR simulations faster

• voltage_excitations – Can be used to excite signals with arbitrary voltages, instead of 1V. If this parameter is used, no capacitances will be computed.

• electric_infinity_bc – effectively extend the model domain to infinity using spherical boundary conditions

tool: ClassVar[str] = 'cross-section'

p_element_order: int = 3

integrate_energies: bool = False

boundary_conditions: dict

run_inductance_sim: bool = True

voltage_excitations: list[float] | None = None

electric_infinity_bc: bool = False

class kqcircuits.simulations.export.elmer.elmer_solution.ElmerEPR3DSolution(*, name: str = '', percent_error: float = 0.005, max_error_scale: float = 2.0, max_outlier_fraction: float = 0.001, maximum_passes: int = 1, minimum_passes: int = 1, is_axisymmetric: bool = False, mesh_levels: int = 1, mesh_size: dict = <factory>, mesh_optimizer: dict | None = None, vtu_output: bool = True, save_elmer_data: bool = False, linear_system_method: str = 'GCR', convergence_tolerance: float = 1e-09, max_iterations: int = 500, linear_system_preconditioning: str = 'ILU0', abort_not_converged: bool = False, use_multigrid_solver: bool = True, mg_smoother: str = 'SGS', mg_smoothing_iterations: int | None = None, mg_relaxation_factor: float = 0.28, mg_lowest_method: str = 'CG', p_element_order: int = 3, voltage_excitations: list[float] | None = None, electric_infinity_bc: bool = False)

Bases: ElmerSolution

Class for Elmer 3D EPR simulations. Similar to electrostatics simulations done with ElmerCapacitanceSolution, but supports separating energies by PartitionRegions. Always reports energies for each layer.

Parameters:

• p_element_order – polynomial order of p-elements

• voltage_excitations – Can be used to excite signals with arbitrary voltages, instead of 1V. If this parameter is used, no capacitances will be computed.

• electric_infinity_bc – effectively extend the model domain to infinity using spherical boundary conditions

tool: ClassVar[str] = 'epr_3d'

p_element_order: int = 3

voltage_excitations: list[float] | None = None

electric_infinity_bc: bool = False

kqcircuits.simulations.export.elmer.elmer_solution.get_elmer_solution(tool='capacitance', **solution_params)

Returns an instance of ElmerSolution subclass.

Parameters:

• tool – Determines the subclass of ElmerSolution.

• solution_params – Arguments passed for ElmerSolution subclass.