Discretizations

QBX discretization

To compute a layer potential as an an end user, create a meshmode.discretization.Discretization with a InterpolatoryQuadratureSimplexGroupFactory as a discretization for the density.

Then create pytential.qbx.QBXLayerPotentialSource, pytential.bind() a layer potential operator to it, and you can start computing.

class pytential.qbx.QBXLayerPotentialSource(density_discr, fine_order, qbx_order=None, fmm_order=None, fmm_level_to_order=None, to_refined_connection=None, expansion_factory=None, target_association_tolerance=<class 'pytential.qbx._not_provided'>, debug=True, _refined_for_global_qbx=False, _expansions_in_tree_have_extent=True, _expansion_stick_out_factor=0.5, _well_sep_is_n_away=2, _max_leaf_refine_weight=None, _box_extent_norm=None, _from_sep_smaller_crit=None, _from_sep_smaller_min_nsources_cumul=None, _tree_kind='adaptive', _use_target_specific_qbx=None, geometry_data_inspector=None, cost_model=None, fmm_backend='sumpy', target_stick_out_factor=<class 'pytential.qbx._not_provided'>)

A source discretization for a QBX layer potential.

qbx_order

fmm_order

__init__(density_discr, fine_order, qbx_order=None, fmm_order=None, fmm_level_to_order=None, to_refined_connection=None, expansion_factory=None, target_association_tolerance=<class 'pytential.qbx._not_provided'>, debug=True, _refined_for_global_qbx=False, _expansions_in_tree_have_extent=True, _expansion_stick_out_factor=0.5, _well_sep_is_n_away=2, _max_leaf_refine_weight=None, _box_extent_norm=None, _from_sep_smaller_crit=None, _from_sep_smaller_min_nsources_cumul=None, _tree_kind='adaptive', _use_target_specific_qbx=None, geometry_data_inspector=None, cost_model=None, fmm_backend='sumpy', target_stick_out_factor=<class 'pytential.qbx._not_provided'>)

Parameters

• fine_order – The total degree to which the (upsampled) underlying quadrature is exact.

• to_refined_connection – A connection used for resampling from density_discr the fine density discretization. It is assumed that the fine density discretization given by to_refined_connection.to_discr is not already upsampled. May be None.

• fmm_order – False for direct calculation. May not be given if fmm_level_to_order is given.

• fmm_level_to_order – A function that takes arguments of (kernel, kernel_args, tree, level) and returns the expansion order to be used on a given level of tree with kernel, where kernel is the sumpy.kernel.Kernel being evaluated, and kernel_args is a set of (key, value) tuples with evaluated kernel arguments. May not be given if fmm_order is given.

Experimental arguments without a promise of forward compatibility:

Parameters

• _use_target_specific_qbx – Whether to use target-specific acceleration by default if possible. None means “use if possible”.

• cost_model – Either None or instance of CostModel, used for gathering modeled costs (experimental)

with_refinement(target_order=None, kernel_length_scale=None, maxiter=None, visualize=False, refiner=None, _expansion_disturbance_tolerance=None, _force_stage2_uniform_refinement_rounds=None, _scaled_max_curvature_threshold=None)

Parameters

refiner – If the mesh underlying density_discr is itself the result of refinement, then its meshmode.refinement.Refiner instance may need to be reused for continued refinement. This argument provides the opportunity to pass in an existing refiner that should be used for continued refinement.

Returns

a tuple (lpot_src, cnx), where lpot_src is a QBXLayerPotentialSource and cnx is a meshmode.discretization.connection.DiscretizationConnection from the originally given to the refined geometry.

copy(density_discr=None, fine_order=None, qbx_order=None, fmm_order=<class 'pytential.qbx._not_provided'>, fmm_level_to_order=<class 'pytential.qbx._not_provided'>, to_refined_connection=None, target_association_tolerance=<class 'pytential.qbx._not_provided'>, _expansions_in_tree_have_extent=<class 'pytential.qbx._not_provided'>, _expansion_stick_out_factor=<class 'pytential.qbx._not_provided'>, _max_leaf_refine_weight=None, _box_extent_norm=None, _from_sep_smaller_crit=None, _tree_kind=None, _use_target_specific_qbx=<class 'pytential.qbx._not_provided'>, geometry_data_inspector=None, cost_model=<class 'pytential.qbx._not_provided'>, fmm_backend=None, debug=<class 'pytential.qbx._not_provided'>, _refined_for_global_qbx=<class 'pytential.qbx._not_provided'>, target_stick_out_factor=<class 'pytential.qbx._not_provided'>)

stage2_density_discr

quad_stage2_density_discr

See QBX internals for some information on the inner workings of this.

Parameters

• fine_order – The total degree to which the (upsampled) underlying quadrature is exact.

• to_refined_connection – A connection used for resampling from density_discr the fine density discretization. It is assumed that the fine density discretization given by to_refined_connection.to_discr is not already upsampled. May be None.

• fmm_order – False for direct calculation. May not be given if fmm_level_to_order is given.

• fmm_level_to_order – A function that takes arguments of (kernel, kernel_args, tree, level) and returns the expansion order to be used on a given level of tree with kernel, where kernel is the sumpy.kernel.Kernel being evaluated, and kernel_args is a set of (key, value) tuples with evaluated kernel arguments. May not be given if fmm_order is given.

Experimental arguments without a promise of forward compatibility:

Parameters

• _use_target_specific_qbx – Whether to use target-specific acceleration by default if possible. None means “use if possible”.

• cost_model – Either None or instance of CostModel, used for gathering modeled costs (experimental)

class pytential.qbx.QBXTargetAssociationFailedException(refine_flags, failed_target_flags, message)

refine_flags

failed_target_flags

Unregularized discretization

class pytential.unregularized.UnregularizedLayerPotentialSource(density_discr, fmm_order=False, fmm_level_to_order=None, expansion_factory=None, debug=True)

A source discretization for a layer potential discretized with a Nyström method that uses panel-based quadrature and does not modify the kernel.

fmm_level_to_order

Parameters

fmm_order – False for direct calculation.

Sources

class pytential.source.PotentialSource

preprocess_optemplate(name, discretizations, expr)

op_group_features(expr)

Return a characteristic tuple by which operators that can be executed together can be grouped.

expr is a subclass of pytential.symbolic.primitives.IntG.

class pytential.source.PointPotentialSource(cl_context, nodes)

nodes

An pyopencl.array.Array of shape [ambient_dim, nnodes].

nnodes

cost_model_compute_potential_insn(queue, insn, bound_expr, evaluate, costs)

exec_compute_potential_insn(queue, insn, bound_expr, evaluate, return_timing_data)

class pytential.source.LayerPotentialSourceBase(density_discr)

A discretization of a layer potential using panel-based geometry, with support for refinement and upsampling.

Discretizations

density_discr

stage2_density_discr

quad_stage2_density_discr

resampler

Discretization data

cl_context

ambient_dim

dim

real_dtype

complex_dtype

Execution

Targets

Target discretizations are a simpler version of the full pytential.discretization.Discretization interface. They do not provide any evaluation of integrals, norms, or layer potentials, but are instead only geared towards being used as evaluation targets.

class pytential.target.TargetBase

ambient_dim

nodes()

Shape: [ambient_dim, nnodes]

nnodes

class pytential.target.PointsTarget(nodes, normals=None)

The point of this class is to act as a container for some target points while presenting enough of the meshmode.discretization.Discretization interface to not necessitate a lot of special cases in that code path.