test_grudge.py

__copyright__ = "Copyright (C) 2015 Andreas Kloeckner"

__license__ = """
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
"""

import numpy as np
import numpy.linalg as la

from meshmode import _acf       # noqa: F401
from meshmode.dof_array import flatten, thaw

from pytools.obj_array import flat_obj_array, make_obj_array

from grudge import sym, bind, DGDiscretizationWithBoundaries

import pytest
from meshmode.array_context import (  # noqa
        pytest_generate_tests_for_pyopencl_array_context
        as pytest_generate_tests)

import logging

logger = logging.getLogger(__name__)


# {{{ inverse metric

@pytest.mark.parametrize("dim", [2, 3])
def test_inverse_metric(actx_factory, dim):
    actx = actx_factory()

    from meshmode.mesh.generation import generate_regular_rect_mesh
    mesh = generate_regular_rect_mesh(a=(-0.5,)*dim, b=(0.5,)*dim,
            n=(6,)*dim, order=4)

    def m(x):
        result = np.empty_like(x)
        result[0] = (
                1.5*x[0] + np.cos(x[0])
                + 0.1*np.sin(10*x[1]))
        result[1] = (
                0.05*np.cos(10*x[0])
                + 1.3*x[1] + np.sin(x[1]))
        if len(x) == 3:
            result[2] = x[2]
        return result

    from meshmode.mesh.processing import map_mesh
    mesh = map_mesh(mesh, m)

    discr = DGDiscretizationWithBoundaries(actx, mesh, order=4)

    sym_op = (
            sym.forward_metric_derivative_mat(mesh.dim)
            .dot(
                sym.inverse_metric_derivative_mat(mesh.dim)
                )
            .reshape(-1))

    op = bind(discr, sym_op)
    mat = op(actx).reshape(mesh.dim, mesh.dim)

    for i in range(mesh.dim):
        for j in range(mesh.dim):
            tgt = 1 if i == j else 0

            err = actx.np.linalg.norm(mat[i, j] - tgt, ord=np.inf)
            logger.info("error[%d, %d]: %.5e", i, j, err)
            assert err < 1.0e-12, (i, j, err)

# }}}


# {{{ mass operator trig integration

@pytest.mark.parametrize("ambient_dim", [1, 2, 3])
@pytest.mark.parametrize("quad_tag", [sym.QTAG_NONE, "OVSMP"])
def test_mass_mat_trig(actx_factory, ambient_dim, quad_tag):
    """Check the integral of some trig functions on an interval using the mass
    matrix.
    """
    actx = actx_factory()

    nelements = 17
    order = 4

    a = -4.0 * np.pi
    b = +9.0 * np.pi
    true_integral = 13*np.pi/2 * (b - a)**(ambient_dim - 1)

    from meshmode.discretization.poly_element import QuadratureSimplexGroupFactory
    dd_quad = sym.DOFDesc(sym.DTAG_VOLUME_ALL, quad_tag)
    if quad_tag is sym.QTAG_NONE:
        quad_tag_to_group_factory = {}
    else:
        quad_tag_to_group_factory = {
                quad_tag: QuadratureSimplexGroupFactory(order=2*order)
                }

    from meshmode.mesh.generation import generate_regular_rect_mesh
    mesh = generate_regular_rect_mesh(
            a=(a,)*ambient_dim, b=(b,)*ambient_dim,
            n=(nelements,)*ambient_dim, order=1)
    discr = DGDiscretizationWithBoundaries(actx, mesh, order=order,
            quad_tag_to_group_factory=quad_tag_to_group_factory)

    def _get_variables_on(dd):
        sym_f = sym.var("f", dd=dd)
        sym_x = sym.nodes(ambient_dim, dd=dd)
        sym_ones = sym.Ones(dd)

        return sym_f, sym_x, sym_ones

    sym_f, sym_x, sym_ones = _get_variables_on(sym.DD_VOLUME)
    f_volm = actx.to_numpy(flatten(bind(discr, sym.cos(sym_x[0])**2)(actx)))
    ones_volm = actx.to_numpy(flatten(bind(discr, sym_ones)(actx)))

    sym_f, sym_x, sym_ones = _get_variables_on(dd_quad)
    f_quad = bind(discr, sym.cos(sym_x[0])**2)(actx)
    ones_quad = bind(discr, sym_ones)(actx)

    mass_op = bind(discr, sym.MassOperator(dd_quad, sym.DD_VOLUME)(sym_f))

    num_integral_1 = np.dot(ones_volm, actx.to_numpy(flatten(mass_op(f=f_quad))))
    err_1 = abs(num_integral_1 - true_integral)
    assert err_1 < 1e-9, err_1

    num_integral_2 = np.dot(f_volm, actx.to_numpy(flatten(mass_op(f=ones_quad))))
    err_2 = abs(num_integral_2 - true_integral)
    assert err_2 < 1.0e-9, err_2

    if quad_tag is sym.QTAG_NONE:
        # NOTE: `integral` always makes a square mass matrix and
        # `QuadratureSimplexGroupFactory` does not have a `mass_matrix` method.
        num_integral_3 = bind(discr,
                sym.integral(sym_f, dd=dd_quad))(f=f_quad)
        err_3 = abs(num_integral_3 - true_integral)
        assert err_3 < 5.0e-10, err_3

# }}}


# {{{ mass operator surface area

def _ellipse_surface_area(radius, aspect_ratio):
    # https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.ellipe.html
    eccentricity = 1.0 - (1/aspect_ratio)**2

    if abs(aspect_ratio - 2.0) < 1.0e-14:
        # NOTE: hardcoded value so we don't need scipy for the test
        ellip_e = 1.2110560275684594
    else:
        from scipy.special import ellipe
        ellip_e = ellipe(eccentricity)

    return 4.0 * radius * ellip_e


def _spheroid_surface_area(radius, aspect_ratio):
    # https://en.wikipedia.org/wiki/Ellipsoid#Surface_area
    a = 1.0
    c = aspect_ratio

    if a < c:
        e = np.sqrt(1.0 - (a/c)**2)
        return 2.0 * np.pi * radius**2 * (1.0 + (c/a) / e * np.arcsin(e))
    else:
        e = np.sqrt(1.0 - (c/a)**2)
        return 2.0 * np.pi * radius**2 * (1 + (c/a)**2 / e * np.arctanh(e))


@pytest.mark.parametrize("name", [
    "2-1-ellipse", "spheroid", "box2d", "box3d"
    ])
def test_mass_surface_area(actx_factory, name):
    actx = actx_factory()

    # {{{ cases

    if name == "2-1-ellipse":
        from mesh_data import EllipseMeshBuilder
        builder = EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
        surface_area = _ellipse_surface_area(builder.radius, builder.aspect_ratio)