# Source code for sfepy.tests.test_laplace_unit_disk

    import pytest

    from sfepy import data_dir
    import sfepy.base.testing as tst

    filename_mesh = data_dir + '/meshes/2d/circle_sym.mesh'

    material_1 = {
        'name' : 'coef',
        'values' : {
            'val' : 1.0,
        },
    }
    material_2 = {
        'name' : 'm',
        'values' : {
            'K' : [[1.0, 0.0], [0.0, 1.0]],
        },
    }

    field_1 = {
        'name' : 'a_harmonic_field',
        'dtype' : 'real',
        'shape' : 'scalar',
        'region' : 'Omega',
        'approx_order' : 2,
    }

    variable_1 = {
        'name' : 't',
        'kind' : 'unknown field',
        'field' : 'a_harmonic_field',
        'order' : 0,
    }
    variable_2 = {
        'name' : 's',
        'kind' : 'test field',
        'field' : 'a_harmonic_field',
        'dual' : 't',
    }

    region_1000 = {
        'name' : 'Omega',
        'select' : 'all',
    }

    region_1 = {
        'name' : 'Centre',
        'select' : 'vertices in (x < 1e-8) & (x > -1e-8) & (y < 1e-8) & (y > -1e-8)',
        'kind' : 'vertex'
    }

    region_2 = {
        'name' : 'Gamma',
        'select' : 'vertices of surface',
        'kind' : 'facet',
    }

    ebc_1 = {
        'name' : 't_centre',
        'region' : 'Centre',
        'dofs' : {'t.0' : 1.0},
    }
    ebc_2 = {
        'name' : 't_gamma',
        'region' : 'Gamma',
        'dofs' : {'t.0' : 0.0},
    }

    integral_1 = {
        'name' : 'i',
        'order' : 2,
    }

    equations = {
        'Temperature' : """dw_laplace.i.Omega(coef.val, s, t) = 0"""
    }

    solution = {
        't' : '- 5.0 * (x - 0.5)',
    }

    solver_0 = {
        'name' : 'ls',
        'kind' : 'ls.scipy_direct',
    }

    solver_1 = {
        'name' : 'newton',
        'kind' : 'nls.newton',

        'i_max'      : 1,
        'eps_a'      : 1e-10,
    }

    @pytest.fixture(scope='module')
    def data():
        import sys
        from sfepy.applications import solve_pde
        from sfepy.base.conf import ProblemConf
        from sfepy.base.base import Struct

        conf = ProblemConf.from_dict(globals(), sys.modules[__name__])
        problem, state = solve_pde(conf, save_results=False)

        return Struct(problem=problem, state=state)

    def test_boundary_fluxes(data):
        from sfepy.discrete import Material
        problem = data.problem

        region_names = ['Gamma']

        variables = problem.get_variables()
        get_state = variables.get_vec_part
        state = data.state.copy()

        problem.time_update(ebcs={}, epbcs={})

        state.apply_ebc()
        nls = problem.get_nls()
        aux = nls.fun(state())

        field = variables['t'].field

        conf_m = problem.conf.get_item_by_name('materials', 'm')
        m = Material.from_conf(conf_m, problem.functions)

        ok = True
        for ii, region_name in enumerate(region_names):
            flux_term = 'ev_surface_flux.1.%s(m.K, t)' % region_name
            val1 = problem.evaluate(flux_term, t=variables['t'], m=m)

            rvec = get_state(aux, 't', True)
            reg = problem.domain.regions[region_name]
            nods = field.get_dofs_in_region(reg, merge=True)
            val2 = rvec[nods].sum() # Assume 1 dof per node.

            eps = 1e-2
            ok = ok and ((abs(val1 - val2) < eps))
            tst.report('%d. %s: |%e - %e| = %e < %.2e'\
                       % (ii, region_name, val1, val2, abs(val1 - val2), eps))

        assert ok