mrx
0.0

Contents

  • Overview
    • Ways to use mrx
      • Input files
      • JAX and jit-compilation
      • Optimization
    • Mathematical Formulation
    • Finite Element Discretization
    • Geometry and Coordinate Transformations
    • Magnetic Relaxation Method
  • Installation
    • Requirements
    • Installing MRX
    • Optional Packages
    • Post-Installation
  • Generating the Documentation
  • Source code on GitHub
  • Publications

API Reference

  • MRX API Reference
    • Module contents
      • Any
      • Array
        • Array.T
        • Array.addressable_data()
        • Array.addressable_shards
        • Array.all()
        • Array.any()
        • Array.argmax()
        • Array.argmin()
        • Array.argpartition()
        • Array.argsort()
        • Array.astype()
        • Array.at
        • Array.byteswap()
        • Array.choose()
        • Array.clip()
        • Array.committed
        • Array.compress()
        • Array.conj()
        • Array.conjugate()
        • Array.copy()
        • Array.copy_to_host_async()
        • Array.cumprod()
        • Array.cumsum()
        • Array.device
        • Array.diagonal()
        • Array.dot()
        • Array.dtype
        • Array.flat
        • Array.flatten()
        • Array.global_shards
        • Array.imag
        • Array.is_fully_addressable
        • Array.is_fully_replicated
        • Array.item()
        • Array.itemsize
        • Array.mT
        • Array.max()
        • Array.mean()
        • Array.min()
        • Array.nbytes
        • Array.ndim
        • Array.nonzero()
        • Array.prod()
        • Array.ptp()
        • Array.ravel()
        • Array.real
        • Array.repeat()
        • Array.reshape()
        • Array.round()
        • Array.searchsorted()
        • Array.shape
        • Array.sharding
        • Array.size
        • Array.sort()
        • Array.squeeze()
        • Array.std()
        • Array.sum()
        • Array.swapaxes()
        • Array.take()
        • Array.to_device()
        • Array.trace()
        • Array.transpose()
        • Array.var()
        • Array.view()
      • BoundaryConditionPair
        • BoundaryConditionPair.__init__()
        • BoundaryConditionPair.dbc
        • BoundaryConditionPair.free
      • BoundaryIterativeRuntimeTuning
        • BoundaryIterativeRuntimeTuning.__init__()
        • BoundaryIterativeRuntimeTuning.dbc
        • BoundaryIterativeRuntimeTuning.free
      • BoundaryOperator
        • BoundaryOperator.k
        • BoundaryOperator.Lambda_0
        • BoundaryOperator.types
        • BoundaryOperator.nr
        • BoundaryOperator.nt
        • BoundaryOperator.nz
        • BoundaryOperator.dr
        • BoundaryOperator.dt
        • BoundaryOperator.dz
        • BoundaryOperator.n1
        • BoundaryOperator.n2
        • BoundaryOperator.n3
        • BoundaryOperator.n
        • BoundaryOperator.M
        • BoundaryOperator.__init__()
        • BoundaryOperator._element()
        • BoundaryOperator._unravel_index()
        • BoundaryOperator._vector_index()
        • BoundaryOperator.build_extraction()
      • BoundaryProjector
        • BoundaryProjector.__call__()
        • BoundaryProjector._eval_trace_1form()
        • BoundaryProjector._eval_trace_2form()
        • BoundaryProjector._project_1form()
        • BoundaryProjector._project_2form()
        • BoundaryProjector.evaluate_trace()
      • BoundaryShiftedIterativeRuntimeTuning
        • BoundaryShiftedIterativeRuntimeTuning.__init__()
        • BoundaryShiftedIterativeRuntimeTuning.dbc
        • BoundaryShiftedIterativeRuntimeTuning.free
      • DeRhamSequence
        • DeRhamSequence.ns
        • DeRhamSequence.ps
        • DeRhamSequence.quad
        • DeRhamSequence.geometry
        • DeRhamSequence.basis_r_jk
        • DeRhamSequence.basis_t_jk
        • DeRhamSequence.basis_z_jk
        • DeRhamSequence.d_basis_r_jk
        • DeRhamSequence.d_basis_t_jk
        • DeRhamSequence.d_basis_z_jk
        • DeRhamSequence.__init__()
        • DeRhamSequence._add_boundary_dual()
        • DeRhamSequence._apply_reference_mass_matrix()
        • DeRhamSequence._apply_reference_mass_matrix_preconditioner()
        • DeRhamSequence._compute_nullspaces()
        • DeRhamSequence._find_nullspace_vectors()
        • DeRhamSequence._form_comp_info()
        • DeRhamSequence._get_nullspace()
        • DeRhamSequence._get_saddle_point_nullspaces()
        • DeRhamSequence._grad_1d()
        • DeRhamSequence._require_geometry()
        • DeRhamSequence._require_operators()
        • DeRhamSequence._require_reference_mass_matrix()
        • DeRhamSequence._resolve_operators()
        • DeRhamSequence._sync_operators()
        • DeRhamSequence.apply_bc_mass_correction()
        • DeRhamSequence.apply_derivative_matrix()
        • DeRhamSequence.apply_hodge_laplacian()
        • DeRhamSequence.apply_hodge_laplacian_approx()
        • DeRhamSequence.apply_hodge_laplacian_preconditioner()
        • DeRhamSequence.apply_incidence_matrix()
        • DeRhamSequence.apply_inverse_hodge_laplacian()
        • DeRhamSequence.apply_inverse_laplacian()
        • DeRhamSequence.apply_inverse_mass_matrix()
        • DeRhamSequence.apply_inverse_mass_plus_eps_laplace_matrix()
        • DeRhamSequence.apply_inverse_reference_mass_matrix()
        • DeRhamSequence.apply_inverse_shifted_hodge_laplacian()
        • DeRhamSequence.apply_inverse_shifted_laplacian()
        • DeRhamSequence.apply_laplacian()
        • DeRhamSequence.apply_laplacian_approx()
        • DeRhamSequence.apply_laplacian_preconditioner()
        • DeRhamSequence.apply_leray_projection()
        • DeRhamSequence.apply_mass_matrix()
        • DeRhamSequence.apply_mass_matrix_preconditioner()
        • DeRhamSequence.apply_mass_plus_eps_laplace_matrix()
        • DeRhamSequence.apply_projection_matrix()
        • DeRhamSequence.apply_stiffness()
        • DeRhamSequence.apply_strong_curl()
        • DeRhamSequence.apply_strong_div()
        • DeRhamSequence.apply_strong_grad()
        • DeRhamSequence.apply_weak_curl()
        • DeRhamSequence.apply_weak_div()
        • DeRhamSequence.apply_weak_grad()
        • DeRhamSequence.assemble_all_dense()
        • DeRhamSequence.assemble_all_sparse()
        • DeRhamSequence.assemble_derivative_matrix()
        • DeRhamSequence.assemble_hodge_laplacian()
        • DeRhamSequence.assemble_incidence_matrix()
        • DeRhamSequence.assemble_laplacian()
        • DeRhamSequence.assemble_leray_projection()
        • DeRhamSequence.assemble_mass_matrix()
        • DeRhamSequence.assemble_projection_matrix()
        • DeRhamSequence.assemble_reference_mass_matrix()
        • DeRhamSequence.basis_0
        • DeRhamSequence.basis_1
        • DeRhamSequence.basis_2
        • DeRhamSequence.basis_3
        • DeRhamSequence.basis_r_jk
        • DeRhamSequence.basis_t_jk
        • DeRhamSequence.basis_z_jk
        • DeRhamSequence.bc_lift()
        • DeRhamSequence.build_spline_map()
        • DeRhamSequence.compute_nullspaces()
        • DeRhamSequence.cross_product_load()
        • DeRhamSequence.d_basis_r_jk
        • DeRhamSequence.d_basis_t_jk
        • DeRhamSequence.d_basis_z_jk
        • DeRhamSequence.e0
        • DeRhamSequence.e0_T
        • DeRhamSequence.e0_bc
        • DeRhamSequence.e0_bc_T
        • DeRhamSequence.e0_dbc
        • DeRhamSequence.e0_dbc_T
        • DeRhamSequence.e1
        • DeRhamSequence.e1_T
        • DeRhamSequence.e1_bc
        • DeRhamSequence.e1_bc_T
        • DeRhamSequence.e1_dbc
        • DeRhamSequence.e1_dbc_T
        • DeRhamSequence.e2
        • DeRhamSequence.e2_T
        • DeRhamSequence.e2_bc
        • DeRhamSequence.e2_bc_T
        • DeRhamSequence.e2_dbc
        • DeRhamSequence.e2_dbc_T
        • DeRhamSequence.e3
        • DeRhamSequence.e3_T
        • DeRhamSequence.e3_bc
        • DeRhamSequence.e3_bc_T
        • DeRhamSequence.e3_dbc
        • DeRhamSequence.e3_dbc_T
        • DeRhamSequence.eval_basis_0_ijk()
        • DeRhamSequence.eval_basis_1_ijk()
        • DeRhamSequence.eval_basis_2_ijk()
        • DeRhamSequence.eval_basis_3_ijk()
        • DeRhamSequence.eval_d_basis_0_ijk()
        • DeRhamSequence.eval_d_basis_1_ijk()
        • DeRhamSequence.eval_d_basis_2_ijk()
        • DeRhamSequence.evaluate_1d()
        • DeRhamSequence.geometry
        • DeRhamSequence.geometry_from_spline_map()
        • DeRhamSequence.get_operators()
        • DeRhamSequence.init_nullspaces()
        • DeRhamSequence.interpolate()
        • DeRhamSequence.jacobian_j
        • DeRhamSequence.l2_norm()
        • DeRhamSequence.l2_norm_sq()
        • DeRhamSequence.load()
        • DeRhamSequence.map
        • DeRhamSequence.metric_inv_jkl
        • DeRhamSequence.metric_jkl
        • DeRhamSequence.ns
        • DeRhamSequence.null_0
        • DeRhamSequence.null_0_dbc
        • DeRhamSequence.null_1
        • DeRhamSequence.null_1_dbc
        • DeRhamSequence.null_2
        • DeRhamSequence.null_2_dbc
        • DeRhamSequence.null_3
        • DeRhamSequence.null_3_dbc
        • DeRhamSequence.pressure_load()
        • DeRhamSequence.ps
        • DeRhamSequence.quad
        • DeRhamSequence.set_geometry()
        • DeRhamSequence.set_geometry_terms()
        • DeRhamSequence.set_map()
        • DeRhamSequence.set_operators()
        • DeRhamSequence.set_spline_map()
        • DeRhamSequence.update_diffusion_runtime_tuning()
        • DeRhamSequence.update_mass_runtime_tuning()
        • DeRhamSequence.update_scalar_hodge_runtime_tuning()
        • DeRhamSequence.update_scalar_laplacian_runtime_tuning()
        • DeRhamSequence.update_schur_runtime_tuning()
      • DegreeIterativeRuntimeTuning
        • DegreeIterativeRuntimeTuning.__init__()
        • DegreeIterativeRuntimeTuning.k0
        • DegreeIterativeRuntimeTuning.k1
        • DegreeIterativeRuntimeTuning.k2
        • DegreeIterativeRuntimeTuning.k3
      • DegreeShiftedIterativeRuntimeTuning
        • DegreeShiftedIterativeRuntimeTuning.__init__()
        • DegreeShiftedIterativeRuntimeTuning.k0
        • DegreeShiftedIterativeRuntimeTuning.k1
        • DegreeShiftedIterativeRuntimeTuning.k2
        • DegreeShiftedIterativeRuntimeTuning.k3
      • DenseSequenceOperators
        • DenseSequenceOperators.__init__()
        • DenseSequenceOperators.d0
        • DenseSequenceOperators.d1
        • DenseSequenceOperators.d2
        • DenseSequenceOperators.l0
        • DenseSequenceOperators.l1
        • DenseSequenceOperators.l2
        • DenseSequenceOperators.l3
        • DenseSequenceOperators.m0
        • DenseSequenceOperators.m1
        • DenseSequenceOperators.m2
        • DenseSequenceOperators.m3
        • DenseSequenceOperators.p03
        • DenseSequenceOperators.p12
        • DenseSequenceOperators.p21
        • DenseSequenceOperators.p30
        • DenseSequenceOperators.s0
        • DenseSequenceOperators.s1
        • DenseSequenceOperators.s2
        • DenseSequenceOperators.s3
      • DerivativeSpline
        • DerivativeSpline.n
        • DerivativeSpline.p
        • DerivativeSpline.type
        • DerivativeSpline.T
        • DerivativeSpline.s
        • DerivativeSpline.__call__()
        • DerivativeSpline.__getitem__()
        • DerivativeSpline.__init__()
        • DerivativeSpline.evaluate()
        • DerivativeSpline.greville_spans()
        • DerivativeSpline.histopolation_matrix()
      • DifferentialForm
        • DifferentialForm.__call__()
        • DifferentialForm.__getitem__()
        • DifferentialForm.__init__()
        • DifferentialForm._ravel_index()
        • DifferentialForm._unravel_index()
        • DifferentialForm._vector_index()
        • DifferentialForm.d
        • DifferentialForm.evaluate()
        • DifferentialForm.k
        • DifferentialForm.n
        • DifferentialForm.nr
        • DifferentialForm.ns
        • DifferentialForm.nt
        • DifferentialForm.nz
        • DifferentialForm.pr
        • DifferentialForm.pt
        • DifferentialForm.pz
      • DiscreteFunction
        • DiscreteFunction.__call__()
        • DiscreteFunction.__init__()
      • IterativeRuntimeTuning
        • IterativeRuntimeTuning.__init__()
        • IterativeRuntimeTuning.lambda_max
        • IterativeRuntimeTuning.lambda_min
      • K0TensorHodgePreconditionerFactors
        • K0TensorHodgePreconditionerFactors.__init__()
        • K0TensorHodgePreconditionerFactors.bulk_V_r
        • K0TensorHodgePreconditionerFactors.bulk_V_t
        • K0TensorHodgePreconditionerFactors.bulk_V_z
        • K0TensorHodgePreconditionerFactors.bulk_alpha
        • K0TensorHodgePreconditionerFactors.bulk_lam_r
        • K0TensorHodgePreconditionerFactors.bulk_lam_t
        • K0TensorHodgePreconditionerFactors.bulk_lam_z
        • K0TensorHodgePreconditionerFactors.bulk_mass_r
        • K0TensorHodgePreconditionerFactors.bulk_mass_t
        • K0TensorHodgePreconditionerFactors.bulk_mass_z
        • K0TensorHodgePreconditionerFactors.bulk_modal_basis_r
        • K0TensorHodgePreconditionerFactors.bulk_modal_basis_t
        • K0TensorHodgePreconditionerFactors.bulk_modal_basis_z
        • K0TensorHodgePreconditionerFactors.bulk_modal_denom
        • K0TensorHodgePreconditionerFactors.bulk_modal_inv_denom
        • K0TensorHodgePreconditionerFactors.bulk_modal_mass_r
        • K0TensorHodgePreconditionerFactors.bulk_modal_mass_t
        • K0TensorHodgePreconditionerFactors.bulk_modal_mass_z
        • K0TensorHodgePreconditionerFactors.bulk_modal_op_r
        • K0TensorHodgePreconditionerFactors.bulk_modal_op_t
        • K0TensorHodgePreconditionerFactors.bulk_modal_op_z
        • K0TensorHodgePreconditionerFactors.bulk_modal_stiff_r
        • K0TensorHodgePreconditionerFactors.bulk_modal_stiff_t
        • K0TensorHodgePreconditionerFactors.bulk_modal_stiff_z
        • K0TensorHodgePreconditionerFactors.bulk_radial_block_inv
        • K0TensorHodgePreconditionerFactors.bulk_shape
        • K0TensorHodgePreconditionerFactors.bulk_stiff_r
        • K0TensorHodgePreconditionerFactors.bulk_stiff_t
        • K0TensorHodgePreconditionerFactors.bulk_stiff_z
        • K0TensorHodgePreconditionerFactors.bulk_term_mass_r
        • K0TensorHodgePreconditionerFactors.bulk_term_mass_t
        • K0TensorHodgePreconditionerFactors.bulk_term_mass_z
        • K0TensorHodgePreconditionerFactors.bulk_term_op_r
        • K0TensorHodgePreconditionerFactors.bulk_term_op_t
        • K0TensorHodgePreconditionerFactors.bulk_term_op_z
        • K0TensorHodgePreconditionerFactors.bulk_term_stiff_r
        • K0TensorHodgePreconditionerFactors.bulk_term_stiff_t
        • K0TensorHodgePreconditionerFactors.bulk_term_stiff_z
        • K0TensorHodgePreconditionerFactors.core_coupling
        • K0TensorHodgePreconditionerFactors.core_size
        • K0TensorHodgePreconditionerFactors.cp_final_delta
        • K0TensorHodgePreconditionerFactors.cp_relative_error
        • K0TensorHodgePreconditionerFactors.precompute_coupling
        • K0TensorHodgePreconditionerFactors.schur_inv
        • K0TensorHodgePreconditionerFactors.schur_projector
      • K1MassSurgeryPreconditionerFactors
        • K1MassSurgeryPreconditionerFactors.__init__()
        • K1MassSurgeryPreconditionerFactors.apply_data
        • K1MassSurgeryPreconditionerFactors.ass
        • K1MassSurgeryPreconditionerFactors.bulk_indices
        • K1MassSurgeryPreconditionerFactors.bulk_rt_size
        • K1MassSurgeryPreconditionerFactors.bulk_to_surgery_data
        • K1MassSurgeryPreconditionerFactors.bulk_zeta_size
        • K1MassSurgeryPreconditionerFactors.coupling_sb
        • K1MassSurgeryPreconditionerFactors.r_indices
        • K1MassSurgeryPreconditionerFactors.rt_art_data
        • K1MassSurgeryPreconditionerFactors.rt_atr_data
        • K1MassSurgeryPreconditionerFactors.rt_indices
        • K1MassSurgeryPreconditionerFactors.rt_r_size
        • K1MassSurgeryPreconditionerFactors.rt_theta_size
        • K1MassSurgeryPreconditionerFactors.rt_to_zeta_data
        • K1MassSurgeryPreconditionerFactors.surgery_diaginv
        • K1MassSurgeryPreconditionerFactors.surgery_indices
        • K1MassSurgeryPreconditionerFactors.surgery_size
        • K1MassSurgeryPreconditionerFactors.surgery_to_bulk_data
        • K1MassSurgeryPreconditionerFactors.theta_bulk_indices
        • K1MassSurgeryPreconditionerFactors.zeta_bulk_indices
        • K1MassSurgeryPreconditionerFactors.zeta_to_rt_data
      • K1TensorCurlCurlForwardModel
        • K1TensorCurlCurlForwardModel.__init__()
        • K1TensorCurlCurlForwardModel.cp_final_delta
        • K1TensorCurlCurlForwardModel.cp_relative_error
        • K1TensorCurlCurlForwardModel.curl_r_shape
        • K1TensorCurlCurlForwardModel.curl_theta_shape
        • K1TensorCurlCurlForwardModel.curl_zeta_shape
        • K1TensorCurlCurlForwardModel.g_r
        • K1TensorCurlCurlForwardModel.g_t
        • K1TensorCurlCurlForwardModel.g_z
        • K1TensorCurlCurlForwardModel.r_shape
        • K1TensorCurlCurlForwardModel.rank
        • K1TensorCurlCurlForwardModel.rr_mass_r_terms
        • K1TensorCurlCurlForwardModel.rr_mass_t_terms
        • K1TensorCurlCurlForwardModel.rr_mass_z_terms
        • K1TensorCurlCurlForwardModel.theta_shape
        • K1TensorCurlCurlForwardModel.tt_mass_r_terms
        • K1TensorCurlCurlForwardModel.tt_mass_t_terms
        • K1TensorCurlCurlForwardModel.tt_mass_z_terms
        • K1TensorCurlCurlForwardModel.zeta_shape
        • K1TensorCurlCurlForwardModel.zz_mass_r_terms
        • K1TensorCurlCurlForwardModel.zz_mass_t_terms
        • K1TensorCurlCurlForwardModel.zz_mass_z_terms
      • K1TensorMassPreconditionerFactors
        • K1TensorMassPreconditionerFactors.__init__()
        • K1TensorMassPreconditionerFactors.arr
        • K1TensorMassPreconditionerFactors.r_indices
        • K1TensorMassPreconditionerFactors.rt_r_size
        • K1TensorMassPreconditionerFactors.rt_theta_size
        • K1TensorMassPreconditionerFactors.schur_inv
        • K1TensorMassPreconditionerFactors.theta
        • K1TensorMassPreconditionerFactors.theta_bulk_indices
        • K1TensorMassPreconditionerFactors.use_inner_schur
        • K1TensorMassPreconditionerFactors.zeta
        • K1TensorMassPreconditionerFactors.zeta_bulk_indices
      • K1TensorStiffnessPreconditioner
        • K1TensorStiffnessPreconditioner.__init__()
        • K1TensorStiffnessPreconditioner.factors
        • K1TensorStiffnessPreconditioner.surgery
      • K2MassSurgeryPreconditionerFactors
        • K2MassSurgeryPreconditionerFactors.__init__()
        • K2MassSurgeryPreconditionerFactors.apply_data
        • K2MassSurgeryPreconditionerFactors.ass
        • K2MassSurgeryPreconditionerFactors.bulk_indices
        • K2MassSurgeryPreconditionerFactors.bulk_to_surgery_data
        • K2MassSurgeryPreconditionerFactors.coupling_sb
        • K2MassSurgeryPreconditionerFactors.r_bulk_indices
        • K2MassSurgeryPreconditionerFactors.r_bulk_size
        • K2MassSurgeryPreconditionerFactors.r_to_theta_data
        • K2MassSurgeryPreconditionerFactors.rt_to_zeta_data
        • K2MassSurgeryPreconditionerFactors.surgery_diaginv
        • K2MassSurgeryPreconditionerFactors.surgery_indices
        • K2MassSurgeryPreconditionerFactors.surgery_size
        • K2MassSurgeryPreconditionerFactors.surgery_to_bulk_data
        • K2MassSurgeryPreconditionerFactors.theta_indices
        • K2MassSurgeryPreconditionerFactors.theta_size
        • K2MassSurgeryPreconditionerFactors.theta_to_r_data
        • K2MassSurgeryPreconditionerFactors.zeta_indices
        • K2MassSurgeryPreconditionerFactors.zeta_size
        • K2MassSurgeryPreconditionerFactors.zeta_to_rt_data
      • K2TensorDivDivForwardModel
        • K2TensorDivDivForwardModel.__init__()
        • K2TensorDivDivForwardModel.component_mass_r_terms
        • K2TensorDivDivForwardModel.component_mass_t_terms
        • K2TensorDivDivForwardModel.component_mass_z_terms
        • K2TensorDivDivForwardModel.cp_final_delta
        • K2TensorDivDivForwardModel.cp_relative_error
        • K2TensorDivDivForwardModel.g_r
        • K2TensorDivDivForwardModel.g_t
        • K2TensorDivDivForwardModel.g_z
        • K2TensorDivDivForwardModel.mass_r_terms
        • K2TensorDivDivForwardModel.mass_t_terms
        • K2TensorDivDivForwardModel.mass_z_terms
        • K2TensorDivDivForwardModel.r_shape
        • K2TensorDivDivForwardModel.rank
        • K2TensorDivDivForwardModel.scalar_shape
        • K2TensorDivDivForwardModel.theta_shape
        • K2TensorDivDivForwardModel.zeta_shape
      • K2TensorMassPreconditionerFactors
        • K2TensorMassPreconditionerFactors.__init__()
        • K2TensorMassPreconditionerFactors.r_bulk
        • K2TensorMassPreconditionerFactors.r_bulk_indices
        • K2TensorMassPreconditionerFactors.r_bulk_size
        • K2TensorMassPreconditionerFactors.schur_inv
        • K2TensorMassPreconditionerFactors.theta
        • K2TensorMassPreconditionerFactors.theta_indices
        • K2TensorMassPreconditionerFactors.theta_size
        • K2TensorMassPreconditionerFactors.use_inner_schur
        • K2TensorMassPreconditionerFactors.zeta
        • K2TensorMassPreconditionerFactors.zeta_indices
        • K2TensorMassPreconditionerFactors.zeta_size
      • K2TensorStiffnessPreconditioner
        • K2TensorStiffnessPreconditioner.__init__()
        • K2TensorStiffnessPreconditioner.factors
        • K2TensorStiffnessPreconditioner.surgery
      • MassPreconditionerSpec
        • MassPreconditionerSpec.damping_safety
        • MassPreconditionerSpec.kind
        • MassPreconditionerSpec.lanczos_iterations
        • MassPreconditionerSpec.lanczos_max_eig_inflation
        • MassPreconditionerSpec.lanczos_min_eig_deflation
        • MassPreconditionerSpec.lanczos_min_eig_floor_fraction
        • MassPreconditionerSpec.min_eig_fraction
        • MassPreconditionerSpec.power_iterations
        • MassPreconditionerSpec.schur_diag_mode
        • MassPreconditionerSpec.smoother
        • MassPreconditionerSpec.steps
        • MassPreconditionerSpec.surgery_schur
      • MassPreconditioners
        • MassPreconditioners.__init__()
        • MassPreconditioners.jacobi
        • MassPreconditioners.surgery
        • MassPreconditioners.tensor
      • MatrixFreeExtraction
        • MatrixFreeExtraction.T
        • MatrixFreeExtraction.__init__()
        • MatrixFreeExtraction.cols
        • MatrixFreeExtraction.data
        • MatrixFreeExtraction.dtype
        • MatrixFreeExtraction.forward_shape
        • MatrixFreeExtraction.from_bcoo()
        • MatrixFreeExtraction.indices
        • MatrixFreeExtraction.restrict_cols()
        • MatrixFreeExtraction.restrict_rows()
        • MatrixFreeExtraction.rows
        • MatrixFreeExtraction.shape
        • MatrixFreeExtraction.to_bcoo()
        • MatrixFreeExtraction.todense()
        • MatrixFreeExtraction.transposed
        • MatrixFreeExtraction.vals
      • NamedTuple()
      • PolarExtractionOperator
        • PolarExtractionOperator.k
        • PolarExtractionOperator.Λ
        • PolarExtractionOperator.xi
        • PolarExtractionOperator.nr
        • PolarExtractionOperator.nt
        • PolarExtractionOperator.nz
        • PolarExtractionOperator.dr
        • PolarExtractionOperator.dt
        • PolarExtractionOperator.dz
        • PolarExtractionOperator.o
        • PolarExtractionOperator.n1
        • PolarExtractionOperator.n2
        • PolarExtractionOperator.n3
        • PolarExtractionOperator.n
        • PolarExtractionOperator.__init__()
        • PolarExtractionOperator._element()
        • PolarExtractionOperator._inner_zeroform()
        • PolarExtractionOperator._outer_zeroform()
        • PolarExtractionOperator._threeform()
        • PolarExtractionOperator.build_extraction()
        • PolarExtractionOperator.inner_oneform_r()
        • PolarExtractionOperator.inner_oneform_θ()
      • Pullback
        • Pullback.__call__()
        • Pullback.__init__()
      • Pushforward
        • Pushforward.__call__()
        • Pushforward.__init__()
      • QuadratureRule
        • QuadratureRule.x_x
        • QuadratureRule.x_y
        • QuadratureRule.x_z
        • QuadratureRule.w_x
        • QuadratureRule.w_y
        • QuadratureRule.w_z
        • QuadratureRule.x
        • QuadratureRule.w
        • QuadratureRule.__init__()
      • SaddlePointPreconditionerSpec
        • SaddlePointPreconditionerSpec.coupled
        • SaddlePointPreconditionerSpec.mass
        • SaddlePointPreconditionerSpec.schur
      • SchurPreconditionerSpec
        • SchurPreconditionerSpec.inner
        • SchurPreconditionerSpec.outer
      • SequenceGeometry
        • SequenceGeometry.__init__()
        • SequenceGeometry.from_map()
        • SequenceGeometry.from_spline_map()
        • SequenceGeometry.jacobian_j
        • SequenceGeometry.map
        • SequenceGeometry.metric_inv_jkl
        • SequenceGeometry.metric_jkl
      • SequenceOperators
        • SequenceOperators.__init__()
        • SequenceOperators.curl_curl
        • SequenceOperators.d0
        • SequenceOperators.d0_T
        • SequenceOperators.d1
        • SequenceOperators.d1_T
        • SequenceOperators.d2
        • SequenceOperators.d2_T
        • SequenceOperators.dd0_diaginv
        • SequenceOperators.dd0_diaginv_dbc
        • SequenceOperators.dd1_diaginv
        • SequenceOperators.dd1_diaginv_dbc
        • SequenceOperators.dd2_diaginv
        • SequenceOperators.dd2_diaginv_dbc
        • SequenceOperators.dd3_diaginv
        • SequenceOperators.dd3_diaginv_dbc
        • SequenceOperators.dense
        • SequenceOperators.div_div
        • SequenceOperators.e0
        • SequenceOperators.e0_T
        • SequenceOperators.e0_bc
        • SequenceOperators.e0_bc_T
        • SequenceOperators.e0_dbc
        • SequenceOperators.e0_dbc_T
        • SequenceOperators.e1
        • SequenceOperators.e1_T
        • SequenceOperators.e1_bc
        • SequenceOperators.e1_bc_T
        • SequenceOperators.e1_dbc
        • SequenceOperators.e1_dbc_T
        • SequenceOperators.e2
        • SequenceOperators.e2_T
        • SequenceOperators.e2_bc
        • SequenceOperators.e2_bc_T
        • SequenceOperators.e2_dbc
        • SequenceOperators.e2_dbc_T
        • SequenceOperators.e3
        • SequenceOperators.e3_T
        • SequenceOperators.e3_bc
        • SequenceOperators.e3_bc_T
        • SequenceOperators.e3_dbc
        • SequenceOperators.e3_dbc_T
        • SequenceOperators.g0
        • SequenceOperators.g0_T
        • SequenceOperators.g0_grad_00
        • SequenceOperators.g0_grad_00_T
        • SequenceOperators.g0_grad_01
        • SequenceOperators.g0_grad_01_T
        • SequenceOperators.g0_grad_10
        • SequenceOperators.g0_grad_10_T
        • SequenceOperators.g0_grad_11
        • SequenceOperators.g0_grad_11_T
        • SequenceOperators.g1
        • SequenceOperators.g1_T
        • SequenceOperators.g1_curl_00
        • SequenceOperators.g1_curl_00_T
        • SequenceOperators.g1_curl_01
        • SequenceOperators.g1_curl_01_T
        • SequenceOperators.g1_curl_10
        • SequenceOperators.g1_curl_10_T
        • SequenceOperators.g1_curl_11
        • SequenceOperators.g1_curl_11_T
        • SequenceOperators.g2
        • SequenceOperators.g2_T
        • SequenceOperators.get_laplacian_diaginv()
        • SequenceOperators.grad_grad
        • SequenceOperators.inc_gram_inv_1
        • SequenceOperators.inc_gram_inv_1_dbc
        • SequenceOperators.inc_gram_inv_2
        • SequenceOperators.inc_gram_inv_2_dbc
        • SequenceOperators.inc_gram_inv_3
        • SequenceOperators.inc_gram_inv_3_dbc
        • SequenceOperators.k0_tensor_hodge_precond
        • SequenceOperators.k1_tensor_stiff_model
        • SequenceOperators.k1_tensor_stiff_precond
        • SequenceOperators.k2_tensor_stiff_model
        • SequenceOperators.k2_tensor_stiff_precond
        • SequenceOperators.laplacian0_diaginv
        • SequenceOperators.laplacian0_diaginv_dbc
        • SequenceOperators.laplacian1_diaginv
        • SequenceOperators.laplacian1_diaginv_dbc
        • SequenceOperators.laplacian2_diaginv
        • SequenceOperators.laplacian2_diaginv_dbc
        • SequenceOperators.laplacian3_diaginv
        • SequenceOperators.laplacian3_diaginv_dbc
        • SequenceOperators.m0
        • SequenceOperators.m1
        • SequenceOperators.m2
        • SequenceOperators.m3
        • SequenceOperators.mass_preconds
        • SequenceOperators.null_0
        • SequenceOperators.null_0_dbc
        • SequenceOperators.null_1
        • SequenceOperators.null_1_dbc
        • SequenceOperators.null_2
        • SequenceOperators.null_2_dbc
        • SequenceOperators.null_3
        • SequenceOperators.null_3_dbc
        • SequenceOperators.p03
        • SequenceOperators.p12
        • SequenceOperators.p21
        • SequenceOperators.p30
        • SequenceOperators.runtime_tuning
        • SequenceOperators.schur_diaginv_k1
        • SequenceOperators.schur_diaginv_k1_dbc
        • SequenceOperators.schur_diaginv_k2
        • SequenceOperators.schur_diaginv_k2_dbc
        • SequenceOperators.schur_diaginv_k3
        • SequenceOperators.schur_diaginv_k3_dbc
        • SequenceOperators.schur_diaginv_mode_k1
        • SequenceOperators.schur_diaginv_mode_k1_dbc
        • SequenceOperators.schur_diaginv_mode_k2
        • SequenceOperators.schur_diaginv_mode_k2_dbc
        • SequenceOperators.schur_diaginv_mode_k3
        • SequenceOperators.schur_diaginv_mode_k3_dbc
        • SequenceOperators.todense()
        • SequenceOperators.with_laplacian_diaginv()
      • SequenceRuntimeTuning
        • SequenceRuntimeTuning.__init__()
        • SequenceRuntimeTuning.diffusion
        • SequenceRuntimeTuning.mass
        • SequenceRuntimeTuning.scalar_hodge
        • SequenceRuntimeTuning.schur
      • ShiftedIterativeRuntimeTuning
        • ShiftedIterativeRuntimeTuning.__init__()
        • ShiftedIterativeRuntimeTuning.shifted
        • ShiftedIterativeRuntimeTuning.unshifted
      • SplineBasis
        • SplineBasis.n
        • SplineBasis.ns
        • SplineBasis.p
        • SplineBasis.type
        • SplineBasis.T
        • SplineBasis.T
        • SplineBasis.__call__()
        • SplineBasis.__getitem__()
        • SplineBasis.__init__()
        • SplineBasis._const_spline()
        • SplineBasis._evaluate()
        • SplineBasis._init_knots()
        • SplineBasis._p_spline()
        • SplineBasis._safe_divide()
        • SplineBasis.collocation_matrix()
        • SplineBasis.evaluate()
        • SplineBasis.greville_points()
        • SplineBasis.n
        • SplineBasis.ns
        • SplineBasis.p
        • SplineBasis.type
      • SplineMap
        • SplineMap.__init__()
        • SplineMap.basis_0
        • SplineMap.coefficients
        • SplineMap.extraction
        • SplineMap.extraction_T
        • SplineMap.with_coefficients()
      • TensorBasis
        • TensorBasis.bases
        • TensorBasis.shape
        • TensorBasis.n
        • TensorBasis.ns
        • TensorBasis.__call__()
        • TensorBasis.__getitem__()
        • TensorBasis.__init__()
        • TensorBasis.evaluate()
      • apply_derivative_matrix()
      • apply_derivative_matrix_ops()
      • apply_hodge_laplacian()
      • apply_hodge_laplacian_approx()
      • apply_hodge_laplacian_preconditioner()
      • apply_incidence_matrix()
      • apply_incidence_matrix_ops()
      • apply_inverse_hodge_laplacian()
      • apply_inverse_laplacian()
      • apply_inverse_laplacian_ops()
      • apply_inverse_mass_matrix()
      • apply_inverse_mass_matrix_ops()
      • apply_inverse_mass_plus_eps_laplace_matrix()
      • apply_inverse_mass_plus_eps_laplace_matrix_ops()
      • apply_inverse_shifted_hodge_laplacian()
      • apply_inverse_shifted_laplacian()
      • apply_inverse_shifted_laplacian_ops()
      • apply_laplacian()
      • apply_laplacian_approx()
      • apply_laplacian_approx_ops()
      • apply_laplacian_ops()
      • apply_laplacian_preconditioner()
      • apply_laplacian_preconditioner_ops()
      • apply_mass_matrix()
      • apply_mass_matrix_ops()
      • apply_mass_matrix_preconditioner()
      • apply_mass_matrix_preconditioner_ops()
      • apply_mass_tensor_forward_model()
      • apply_mass_tensor_forward_model_ops()
      • apply_mass_tensor_preconditioner()
      • apply_mass_tensor_preconditioner_ops()
      • apply_projection_matrix()
      • apply_projection_matrix_ops()
      • apply_stiffness()
      • apply_stiffness_ops()
      • apply_stiffness_tensor_forward_model()
      • apply_stiffness_tensor_preconditioner()
      • approx_inverse_map()
      • assemble_all_dense_operators()
      • assemble_all_operators()
      • assemble_derivative_operators()
      • assemble_hodge_operators()
      • assemble_incidence_operators()
      • assemble_laplacian_operators()
      • assemble_leray_projection()
      • assemble_mass_jacobi_preconditioner()
      • assemble_mass_local()
      • assemble_mass_operators()
      • assemble_mass_surgery_preconditioner()
      • assemble_projection_operators()
      • assemble_schur_jacobi_preconditioner()
      • assemble_tensor_hodge_preconditioner()
      • assemble_tensor_laplacian_preconditioner()
      • assemble_tensor_mass_preconditioner()
      • assemble_tensor_stiffness_models()
      • assemble_tensor_stiffness_preconditioner()
      • assemble_vectorial()
      • backtracking_line_search()
      • bc_extraction_op()
      • build_curl_stencil_g1()
      • build_grad_stencil_g0()
      • build_mass_surgery_preconditioner()
      • build_mass_tensor_preconditioner()
      • build_matrixfree_mass_apply()
      • cg()
      • classify_uniformity()
      • composite_quad()
      • compute_geometry_terms()
      • compute_nullspaces()
      • compute_nullspaces_iterative()
      • cos()
      • curl()
      • cylinder_map()
      • default_mass_preconditioner()
      • default_saddle_preconditioner()
      • dense_derivative_matrix()
      • dense_hodge_laplacian()
      • dense_laplacian()
      • dense_mass_matrix()
      • dense_projection_matrix()
      • dense_stiffness_matrix()
      • det33()
      • diag_EAET()
      • diag_EAET_direct()
      • diag_EAET_matvec()
      • diag_EGtMGEt_direct()
      • diag_matvec()
      • diag_schur_complement()
      • div()
      • double_map()
      • eval_basis_0_ijk()
      • eval_basis_1_ijk()
      • eval_basis_2_ijk()
      • eval_basis_3_ijk()
      • eval_d_basis_0_ijk()
      • eval_d_basis_1_ijk()
      • eval_d_basis_2_ijk()
      • evaluate_at_xq()
      • evaluate_at_xq_deprecated()
      • extend_map_nfp()
      • extract_diag_vector()
      • find_nullspace_vectors()
      • get_1d_grids()
      • get_2d_grids()
      • get_3d_grids()
      • get_iota()
      • get_iota_log()
      • get_mass_jacobi_diaginv()
      • get_nullspace()
      • get_periodic_intersections()
      • get_saddle_point_nullspaces()
      • get_smallest_ev_pair()
      • get_xi()
      • grad()
      • grad_1d()
      • greville_interpolate_map()
      • greville_interpolate_stellarator_map()
      • init_nullspaces()
      • integrate_against()
      • integrate_against_deprecated()
      • integrate_fieldlines()
      • interpolate()
      • interpolate_map()
      • inv33()
      • invert_map()
      • is_running_in_github_actions()
      • jacobian_determinant()
      • l2_product()
      • load()
      • mass_core_apply()
      • mass_surgery_available()
      • mass_tensor_available()
      • minres()
      • newton_solver()
      • one_size_fits_all_map()
      • operators_from_coeffs()
      • picard_solver()
      • plot_crossections_separate()
      • plot_torus()
      • plot_twin_axis()
      • poincare_plot()
      • preconditioned_cg()
      • rotating_ellipse_map()
      • run_relaxation_loop()
      • safe_inv33()
      • select_boundary_data()
      • select_quadrature()
      • set_axes_equal()
      • set_mass_jacobi_pair()
      • set_mass_surgery()
      • set_mass_tensor()
      • sin()
      • solve_saddle_point_minres()
      • solve_singular_cg()
      • spectral_quad()
      • stellarator_map()
      • stiffness_tensor_preconditioner_available()
      • surface_integral()
      • tensor_stiffness_model_available()
      • toroid_map()
      • trace_plot()
      • update_config()
      • update_derivative_operator()
      • update_diffusion_runtime_tuning()
      • update_diffusion_runtime_tuning_ops()
      • update_hodge_operator()
      • update_incidence_operator()
      • update_mass_operator()
      • update_mass_runtime_tuning()
      • update_mass_runtime_tuning_ops()
      • update_projection_operator()
      • update_scalar_hodge_runtime_tuning()
      • update_scalar_laplacian_runtime_tuning()
      • update_scalar_laplacian_runtime_tuning_ops()
      • update_schur_runtime_tuning()
      • update_schur_runtime_tuning_ops()

Tutorials:

  • Poisson equation on the unit disk
    • Mapping
    • Manufactured solution
    • Resolution and periodicity
    • de Rham sequence
    • Matrix assembly
    • Differential forms
    • Handling the polar singularity and boundary conditions
    • Pre-computations
    • Matrix solve
  • Mixed Poisson equation on the unit disk
    • Mixed formulation
    • Discrete formulation
    • Strong and weak operators
    • Manufactured solution
    • Code
  • Poisson equation on a toroid
  • Harmonic fields in a hollow torus
    • Parameters
    • de Rham sequence
    • Harmonic fields
    • Ampère’s law
    • Final checks
  • GVEC mappings
    • GVEC
    • Input
    • Approximating the mapping in spline space
    • Verifying the mapping
  • A simple tokamak equilibrium
  • Helicity minimization

Tutorial Scripts:

  • Poisson Problem on a disc
    • Code Walkthrough
  • Mixed Polar Poisson Problem
    • Code Walkthrough
  • Toroid Poisson Problem
    • Code Walkthrough

Configuration Scripts:

  • Solovev Configuration
    • Code Walkthrough
  • Stellarator Configuration
    • Code Walkthrough
  • Iterative Island Calculation
    • Code Walkthrough
  • Hopf Configuration
    • Code Walkthrough

Interactive Scripts:

  • GVEC Tokamak Interface Test
    • Code Walkthrough
  • GVEC Stellarator Interface Test
    • Code Walkthrough
  • Toroid Poisson (Interactive)
    • Code Walkthrough
  • Toroid Cavity
    • Code Walkthrough
  • Cylinder Cavity
    • Code Walkthrough
  • Cylinder Vector Poisson
    • Code Walkthrough
  • Drum Shape Optimization
    • Code Walkthrough
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