DG Discretizations and related services

class hedge.discretization.Discretization

Discretization.close()

Discretization.add_instrumentation(mgr)

Discretization.is_boundary_tag_nonempty(tag)

Discretization.all_debug_flags()

classmethod Discretization.noninteractive_debug_flags()

Return all debug flags that do not entail user interaction (such as key presses or console output).

Vector Kinds

When computing on GPU hardware, the :class`Discretization` operates on fields that are not represented by numpy arrays. Vector kinds make this explicit. Every discretization is guaranteed to support converting its preferred vector kind, given by Discretization.compute_kind, to the kind “numpy”.

Discretization.compute_kind

The array kind that this discretization can evaluate operators on.

Discretization.convert_volume(field, kind)

Discretization.convert_boundary(field, tag, kind)

Vector Creation

Discretization.volume_empty(shape=(), dtype=None, kind=None)

Discretization.volume_zeros(shape=(), dtype=None, kind=None)

Discretization.interpolate_volume_function(f, dtype=None, kind=None)

Discretization.boundary_empty(tag, shape=(), dtype=None, kind=None)

Discretization.boundary_zeros(tag, shape=(), dtype=None, kind=None)

Discretization.interpolate_boundary_function(f, tag, dtype=None, kind=None)

Discretization.boundary_normals(tag, dtype=None, kind=None)

Vector Conversion

Discretization.volumize_boundary_field(bfield, tag, kind=None)

Discretization.boundarize_boundary_field(bfield, tag, kind=None)

Vector Reductions

Discretization.nodewise_dot_product(a, b)

Discretization.mesh_volume()

Discretization.integral(volume_vector)

Discretization.norm(volume_vector, p=2)

Discretization.inner_product(a, b)

Miscellanea

Discretization.dt_factor(max_system_ev, stepper_class, *stepper_args)

Discretization.get_point_evaluator(point)

Compilation of operator templates

Discretization.compile(optemplate, post_bind_mapper=lambda x: x)

Discretization.add_function(name, func)

Projection between Discretization instances

class hedge.discretization.Projector(from_discr, to_discr)

__call__(self, from_vec)

Filtering

class hedge.discretization.ExponentialFilterResponseFunction(min_amplification=0.1, order=6)

A typical exponential-falloff mode response filter function.

See description in Section 5.6.1 of Hesthaven/Warburton.

__init__(min_amplification=0.1, order=6)

Construct the filter function.

The amplification factor of the lowest-order (constant) mode is always 1.

Parameters:

• min_amplification – The amplification factor applied to the highest mode.
• order – The order of the filter. This controls how fast (or slowly) the min_amplification is reached.

class hedge.discretization.Filter

__init__(discr, mode_response_func)

Construct a filter.

Parameters:

• discr – The Discretization for which the filter is to be constructed.
• mode_response_func – A function mapping (mode_tuple, local_discretization) to a float indicating the factor by which this mode is to be multiplied after filtering. (For example an instance of ExponentialFilterResponseFunction.