test_modal_connections.py

__copyright__ = "Copyright (C) 2021 University of Illinois Board of Trustees"

__license__ = """
Permission is hereby granted, free of charge, to any person obtaining a copy
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"""


from meshmode.array_context import (  # noqa
    pytest_generate_tests_for_pyopencl_array_context
    as pytest_generate_tests
)
from meshmode.discretization.poly_element import (
    # Simplex group factories
    InterpolatoryQuadratureSimplexGroupFactory,
    PolynomialWarpAndBlendGroupFactory,
    PolynomialEquidistantSimplexGroupFactory,
    # Tensor product group factories
    LegendreGaussLobattoTensorProductGroupFactory,
    # Quadrature-based (non-interpolatory) group factories
    QuadratureSimplexGroupFactory
    )
from meshmode.dof_array import thaw
import meshmode.mesh.generation as mgen

from grudge import DiscretizationCollection
import grudge.dof_desc as dof_desc

import pytest


@pytest.mark.parametrize("nodal_group_factory", [
    InterpolatoryQuadratureSimplexGroupFactory,
    PolynomialWarpAndBlendGroupFactory,
    PolynomialEquidistantSimplexGroupFactory,
    LegendreGaussLobattoTensorProductGroupFactory,
    ]
)
def test_inverse_modal_connections(actx_factory, nodal_group_factory):
    actx = actx_factory()
    order = 4

    def f(x):
        return 2*actx.np.sin(20*x) + 0.5*actx.np.cos(10*x)

    # Make a regular rectangle mesh
    mesh = mgen.generate_regular_rect_mesh(
        a=(0, 0), b=(5, 3), npoints_per_axis=(10, 6), order=order,
        group_cls=nodal_group_factory.mesh_group_class
    )

    dcoll = DiscretizationCollection(
        actx, mesh,
        quad_tag_to_group_factory={
            dof_desc.DISCR_TAG_BASE: nodal_group_factory(order)
        }
    )

    dd_modal = dof_desc.DD_VOLUME_MODAL
    dd_volume = dof_desc.DD_VOLUME

    x_nodal = thaw(actx, dcoll.discr_from_dd(dd_volume).nodes()[0])
    nodal_f = f(x_nodal)

    # Map nodal coefficients of f to modal coefficients
    forward_conn = dcoll.connection_from_dds(dd_volume, dd_modal)
    modal_f = forward_conn(nodal_f)
    # Now map the modal coefficients back to nodal
    backward_conn = dcoll.connection_from_dds(dd_modal, dd_volume)
    nodal_f_2 = backward_conn(modal_f)

    # This error should be small since we composed a map with
    # its inverse
    err = actx.np.linalg.norm(nodal_f - nodal_f_2)

    assert err <= 1e-13


def test_inverse_modal_connections_quadgrid(actx_factory):
    actx = actx_factory()
    order = 5

    def f(x):
        return 1 + 2*x + 3*x**2

    # Make a regular rectangle mesh
    mesh = mgen.generate_regular_rect_mesh(
        a=(0, 0), b=(5, 3), npoints_per_axis=(10, 6), order=order,
        group_cls=QuadratureSimplexGroupFactory.mesh_group_class
    )

    dcoll = DiscretizationCollection(
        actx, mesh,
        quad_tag_to_group_factory={
            dof_desc.DISCR_TAG_BASE: PolynomialWarpAndBlendGroupFactory(order),
            dof_desc.DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(2*order)
        }
    )

    # Use dof descriptors on the quadrature grid
    dd_modal = dof_desc.DD_VOLUME_MODAL
    dd_quad = dof_desc.DOFDesc(dof_desc.DTAG_VOLUME_ALL,
                               dof_desc.DISCR_TAG_QUAD)

    x_quad = thaw(actx, dcoll.discr_from_dd(dd_quad).nodes()[0])
    quad_f = f(x_quad)

    # Map nodal coefficients of f to modal coefficients
    forward_conn = dcoll.connection_from_dds(dd_quad, dd_modal)
    modal_f = forward_conn(quad_f)
    # Now map the modal coefficients back to nodal
    backward_conn = dcoll.connection_from_dds(dd_modal, dd_quad)
    quad_f_2 = backward_conn(modal_f)

    # This error should be small since we composed a map with
    # its inverse
    err = actx.np.linalg.norm(quad_f - quad_f_2)

    assert err <= 1e-11