# Source code for sfepy.terms.terms_navier_stokes

    import numpy as nm

    from sfepy.linalg import dot_sequences, insert_strided_axis
    from sfepy.terms.terms import Term, terms

    class DivGradTerm(Term):
        r"""
        Diffusion term.

        :Definition:

        .. math::
            \int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ , }
            \int_{\Omega} \nabla \ul{v} : \nabla \ul{u}

        :Arguments:
            - material: :math:`\nu` (viscosity, optional)
            - virtualparameter_1: :math:`\ul{v}`
            - state/parameter_2: :math:`\ul{u}`
        """
        name = 'dw_div_grad'
        arg_types = (('opt_material', 'virtual', 'state'),
                     ('opt_material', 'parameter_1', 'parameter_2'))
        arg_shapes = [{'opt_material' : '1, 1', 'virtual' : ('D', 'state'),
                       'state' : 'D', 'parameter_1' : 'D', 'parameter_2' : 'D'},
                      {'opt_material' : None}]
        modes = ('weak', 'eval')

        function = staticmethod(terms.term_ns_asm_div_grad)

        def d_div_grad(self, out, grad1, grad2, mat, vg, fmode):
            sh = grad1.shape
            g1 = grad1.reshape((sh[0], sh[1], sh[2] * sh[3]))
            sh = grad2.shape
            g2 = grad2.reshape((sh[0], sh[1], sh[2] * sh[3]))
            aux = mat * dot_sequences(g1[..., None], g2, 'ATB')[..., None]

            if fmode == 2:
                out[:] = aux
                status = 0

            else:
                status = vg.integrate(out, aux, fmode)

            return status

        def get_fargs(self, mat, virtual, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vgs, _ = self.get_mapping(state)
            vgv, _ = self.get_mapping(virtual)

            if mat is None:
                n_el, n_qp, dim, n_en, n_c = self.get_data_shape(state)
                mat = nm.ones((1, n_qp, 1, 1), dtype=nm.float64)

            if mode == 'weak':
                if diff_var is None:
                    grad = self.get(state, 'grad').transpose((0, 1, 3, 2))
                    sh = grad.shape
                    grad = grad.reshape((sh[0], sh[1], sh[2] * sh[3], 1))
                    fmode = 0

                else:
                    grad = nm.array([0], ndmin=4, dtype=nm.float64)
                    fmode = 1

                return grad, mat, vgv, vgs, fmode

            elif mode == 'eval':
                grad1 = self.get(virtual, 'grad')
                grad2 = self.get(state, 'grad')
                fmode = {'eval' : 0, 'el_avg' : 1, 'qp' : 2}.get(mode, 1)

                return grad1, grad2, mat, vgv, fmode

            else:
                raise ValueError('unsupported evaluation mode in %s! (%s)'
                                 % (self.name, mode))

        def get_eval_shape(self, mat, virtual, state,
                           mode=None, term_mode=None, diff_var=None, **kwargs):
            n_el, n_qp, dim, n_en, n_c = self.get_data_shape(state)

            return (n_el, 1, 1, 1), state.dtype

        def set_arg_types(self):
            if self.mode == 'weak':
                self.function = terms.term_ns_asm_div_grad

            else:
                self.function = self.d_div_grad

    class ConvectTerm(Term):
        r"""
        Nonlinear convective term.

        :Definition:

        .. math::
            \int_{\Omega} ((\ul{u} \cdot \nabla) \ul{u}) \cdot \ul{v}

        :Arguments:
            - virtual : :math:`\ul{v}`
            - state   : :math:`\ul{u}`
        """
        name = 'dw_convect'
        arg_types = ('virtual', 'state')
        arg_shapes = {'virtual' : ('D', 'state'), 'state' : 'D'}

        function = staticmethod(terms.term_ns_asm_convect)

        def get_fargs(self, virtual, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(state)

            grad = self.get(state, 'grad').transpose((0, 1, 3, 2)).copy()
            val_qp = self.get(state, 'val')

            fmode = diff_var is not None

            return grad, val_qp, vg, fmode

    class LinearConvectTerm(Term):
        r"""
        Linearized convective term.

        :Definition:

        .. math::
            \int_{\Omega} ((\ul{w} \cdot \nabla) \ul{u}) \cdot \ul{v}

        .. math::
            ((\ul{w} \cdot \nabla) \ul{u})|_{qp}

        :Arguments:
            - virtual   : :math:`\ul{v}`
            - parameter : :math:`\ul{w}`
            - state     : :math:`\ul{u}`
        """
        name = 'dw_lin_convect'
        arg_types = ('virtual', 'parameter', 'state')
        arg_shapes = {'virtual' : ('D', 'state'), 'parameter' : 'D', 'state' : 'D'}

        function = staticmethod(terms.dw_lin_convect)

        def get_fargs(self, virtual, parameter, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(state)

            val_qp = self.get(parameter, 'val')

            if mode == 'weak':
                if diff_var is None:
                    grad = self.get(state, 'grad').transpose((0, 1, 3, 2)).copy()
                    fmode = 0

                else:
                    grad = nm.array([0], ndmin=4, dtype=nm.float64)
                    fmode = 1

                return grad, val_qp, vg, fmode

            elif mode == 'qp':
                grad = self.get(state, 'grad').transpose((0, 1, 3, 2)).copy()
                fmode = 2

                return grad, val_qp, vg, fmode

            else:
                raise ValueError('unsupported evaluation mode in %s! (%s)'
                                 % (self.name, mode))

    class LinearConvect2Term(Term):
        r"""
        Linearized convective term with the convection velocity given as a material
        parameter.

        :Definition:

        .. math::
            \int_{\Omega} ((\ul{c} \cdot \nabla) \ul{u}) \cdot \ul{v}

        .. math::
            ((\ul{c} \cdot \nabla) \ul{u})|_{qp}

        :Arguments:
            - material : :math:`\ul{c}`
            - virtual  : :math:`\ul{v}`
            - state    : :math:`\ul{u}`
        """
        name = 'dw_lin_convect2'
        arg_types = ('material', 'virtual', 'state')
        arg_shapes = {'material' : 'D, 1',
                      'virtual' : ('D', 'state'), 'state' : 'D'}

        function = staticmethod(terms.dw_lin_convect)

        def get_fargs(self, material, virtual, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(state)

            if mode == 'weak':
                if diff_var is None:
                    grad = self.get(state, 'grad').transpose((0, 1, 3, 2)).copy()
                    fmode = 0

                else:
                    grad = nm.array([0], ndmin=4, dtype=nm.float64)
                    fmode = 1

                return grad, material, vg, fmode

            elif mode == 'qp':
                grad = self.get(state, 'grad').transpose((0, 1, 3, 2)).copy()
                fmode = 2

                return grad, material, vg, fmode

            else:
                raise ValueError('unsupported evaluation mode in %s! (%s)'
                                 % (self.name, mode))

    class StokesTerm(Term):
        r"""
        Stokes problem coupling term. Corresponds to weak forms of gradient and
        divergence terms. Can be evaluated.

        :Definition:

        .. math::
            \int_{\Omega} p\ \nabla \cdot \ul{v} \mbox{ , }
            \int_{\Omega} q\ \nabla \cdot \ul{u}\\
            \mbox{ or }
            \int_{\Omega} c\ p\ \nabla \cdot \ul{v} \mbox{ , }
            \int_{\Omega} c\ q\ \nabla \cdot \ul{u}

        :Arguments 1:
            - material: :math:`c` (optional)
            - virtual/parameter_v: :math:`\ul{v}`
            - state/parameter_s: :math:`p`

        :Arguments 2:
            - material : :math:`c` (optional)
            - state    : :math:`\ul{u}`
            - virtual  : :math:`q`
        """
        name = 'dw_stokes'
        arg_types = (('opt_material', 'virtual', 'state'),
                     ('opt_material', 'state', 'virtual'),
                     ('opt_material', 'parameter_v', 'parameter_s'))
        arg_shapes = [{'opt_material' : '1, 1',
                       'virtual/grad' : ('D', None), 'state/grad' : 1,
                       'virtual/div' : (1, None), 'state/div' : 'D',
                       'parameter_v' : 'D', 'parameter_s' : 1},
                      {'opt_material' : None}]
        modes = ('grad', 'div', 'eval')

        @staticmethod
        def d_eval(out, coef, vec_qp, div, vvg):
            out_qp = coef * vec_qp * div

            status = vvg.integrate(out, out_qp)

            return status

        def get_fargs(self, coef, vvar, svar,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            if self.mode == 'grad':
                qp_var, qp_name = svar, 'val'

            else:
                qp_var, qp_name = vvar, 'div'

            n_el, n_qp, dim, n_en, n_c = self.get_data_shape(vvar)
            if coef is None:
                coef = nm.ones((1, n_qp, 1, 1), dtype=nm.float64)

            if mode == 'weak':
                vvg, _ = self.get_mapping(vvar)
                svg, _ = self.get_mapping(svar)

                if diff_var is None:
                    val_qp = self.get(qp_var, qp_name)
                    fmode = 0

                else:
                    val_qp = nm.array([0], ndmin=4, dtype=nm.float64)
                    fmode = 1

                return coef, val_qp, svg, vvg, fmode

            elif mode == 'eval':
                vvg, _ = self.get_mapping(vvar)

                div = self.get(vvar, 'div')
                vec_qp = self.get(svar, 'val')

                return coef, vec_qp, div, vvg

            else:
                raise ValueError('unsupported evaluation mode in %s! (%s)'
                                 % (self.name, mode))

        def get_eval_shape(self, coef, vvar, svar,
                           mode=None, term_mode=None, diff_var=None, **kwargs):
            n_el, n_qp, dim, n_en, n_c = self.get_data_shape(vvar)

            return (n_el, 1, 1, 1), vvar.dtype

        def set_arg_types(self):
            self.function = {
                'grad' : terms.dw_grad,
                'div' : terms.dw_div,
                'eval' : self.d_eval,
            }[self.mode]

    class GradTerm(Term):
        r"""
        Evaluate gradient of a scalar or vector field.

        Supports 'eval', 'el_avg' and 'qp' evaluation modes.

        :Definition:

        .. math::
            \int_{\cal{D}} \nabla p \mbox{ or } \int_{\cal{D}} \nabla \ul{u}\\
            \int_{\cal{D}} c \nabla p \mbox{ or } \int_{\cal{D}} c \nabla \ul{u}

        :Arguments:
            - parameter : :math:`p` or :math:`\ul{u}`
        """
        name = 'ev_grad'
        arg_types = ('opt_material', 'parameter')
        arg_shapes = [{'opt_material': '1, 1', 'parameter': 'N'},
                      {'opt_material': None}]
        integration = ('cell', 'facet_extra')

        @staticmethod
        def function(out, mat, grad, vg, fmode):
            if fmode == 2:
                out[:] = grad if mat is None else mat * grad
                status = 0

            else:
                status = vg.integrate(out, grad, fmode) if mat is None else\
                         vg.integrate(out, mat * grad, fmode)

            return status

        def get_fargs(self, mat, parameter,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(parameter)

            grad = self.get(parameter, 'grad', integration=self.act_integration)

            fmode = {'eval' : 0, 'el_avg' : 1, 'qp' : 2}.get(mode, 1)

            return mat, grad, vg, fmode

        def get_eval_shape(self, mat, parameter,
                           mode=None, term_mode=None, diff_var=None, **kwargs):
            n_el, n_qp, dim, n_en, n_c = self.get_data_shape(parameter)

            if mode != 'qp':
                n_qp = 1

            return (n_el, n_qp, dim, n_c), parameter.dtype

    class DivTerm(Term):
        r"""
        Evaluate divergence of a vector field.

        Supports 'eval', 'el_avg' and 'qp' evaluation modes.

        :Definition:

        .. math::
             \int_{\cal{D}} \nabla \cdot \ul{u} \mbox { , }
             \int_{\cal{D}} c \nabla \cdot \ul{u}

        :Arguments:
            - parameter : :math:`\ul{u}`
        """
        name = 'ev_div'
        arg_types = ('opt_material', 'parameter')
        arg_shapes = [{'opt_material': '1, 1', 'parameter': 'D'},
                      {'opt_material': None}]
        integration = ('cell', 'facet_extra')

        @staticmethod
        def function(out, mat, div, vg, fmode):
            if fmode == 2:
                out[:] = div if mat is None else mat * div
                status = 0

            else:
                status = vg.integrate(out, div, fmode) if mat is None else\
                         vg.integrate(out, mat * div, fmode)

            return status

        def get_fargs(self, mat, parameter,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(parameter)

            div = self.get(parameter, 'div', integration=self.act_integration)

            fmode = {'eval' : 0, 'el_avg' : 1, 'qp' : 2}.get(mode, 1)

            return mat, div, vg, fmode

        def get_eval_shape(self, mat, parameter,
                           mode=None, term_mode=None, diff_var=None, **kwargs):
            n_el, n_qp, dim, n_en, n_c = self.get_data_shape(parameter)

            if mode != 'qp':
                n_qp = 1

            return (n_el, n_qp, 1, 1), parameter.dtype

    class DivOperatorTerm(Term):
        r"""
        Weighted divergence term of a test function.

        :Definition:

        .. math::
            \int_{\Omega} \nabla \cdot \ul{v} \mbox { or } \int_{\Omega} c \nabla
            \cdot \ul{v}

        :Arguments:
            - material : :math:`c` (optional)
            - virtual  : :math:`\ul{v}`
        """
        name = 'dw_div'
        arg_types = ('opt_material', 'virtual')
        arg_shapes = [{'opt_material' : '1, 1', 'virtual' : ('D', None)},
                      {'opt_material' : None}]

        @staticmethod
        def function(out, mat, vg):
            div_bf = vg.bfg

            n_el, n_qp, dim, n_ep = div_bf.shape
            div_bf = div_bf.reshape((n_el, n_qp, dim * n_ep, 1))
            div_bf = nm.ascontiguousarray(div_bf)

            if mat is not None:
                status = vg.integrate(out, mat * div_bf)
            else:
                status = vg.integrate(out, div_bf)

            return status

        def get_fargs(self, mat, virtual,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(virtual)

            return mat, vg

    class StokesWaveTerm(Term):
        r"""
        Stokes dispersion term with the wave vector :math:`\ul{\kappa}`.

        :Definition:

        .. math::
            \int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\ul{\kappa} \cdot \ul{u})

        :Arguments:
            - material : :math:`\ul{\kappa}`
            - virtual  : :math:`\ul{v}`
            - statee   : :math:`\ul{u}`
        """
        name = 'dw_stokes_wave'
        arg_types = ('material', 'virtual', 'state')
        arg_shapes = {'material' : '.: D',
                      'virtual' : ('D', 'state'), 'state' : 'D'}
        geometries = ['2_3', '2_4', '3_4', '3_8']

        @staticmethod
        def function(out, out_qp, geo, fmode):
            status = geo.integrate(out, out_qp)
            return status

        def get_fargs(self, kappa, virtual, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            from sfepy.discrete.variables import create_adof_conn, expand_basis

            geo, _ = self.get_mapping(state)

            n_el, n_qp, dim, n_en, n_c = self.get_data_shape(virtual)

            ebf = expand_basis(geo.bf, dim)

            aux = nm.einsum('i,...ij->...j', kappa, ebf)[0, :, None, :]
            kebf = insert_strided_axis(aux, 0, n_el)

            if diff_var is None:
                econn = state.field.get_econn('cell', self.region)
                adc = create_adof_conn(nm.arange(state.n_dof, dtype=nm.int32),
                                       econn, n_c, 0)
                vals = state()[adc]
                aux = dot_sequences(kebf, vals[:, None, :, None])
                out_qp = dot_sequences(kebf, aux, 'ATB')
                fmode = 0

            else:
                out_qp = dot_sequences(kebf, kebf, 'ATB')
                fmode = 1

            return out_qp, geo, fmode

    class StokesWaveDivTerm(Term):
        r"""
        Stokes dispersion term with the wave vector :math:`\ul{\kappa}` and the
        divergence operator.

        :Definition:

        .. math::
            \int_{\Omega} (\ul{\kappa} \cdot \ul{v}) (\nabla \cdot \ul{u}) \;,
            \int_{\Omega} (\ul{\kappa} \cdot \ul{u}) (\nabla \cdot \ul{v})

        :Arguments 1:
            - material : :math:`\ul{\kappa}`
            - virtual  : :math:`\ul{v}`
            - state    : :math:`\ul{u}`

        :Arguments 2:
            - material : :math:`\ul{\kappa}`
            - state    : :math:`\ul{u}`
            - virtual  : :math:`\ul{v}`
        """
        name = 'dw_stokes_wave_div'
        arg_types = (('material', 'virtual', 'state'),
                     ('material', 'state', 'virtual'))
        arg_shapes = {'material' : '.: D',
                      'virtual' : ('D', 'state'), 'state' : 'D'}
        geometries = ['2_3', '2_4', '3_4', '3_8']
        modes = ('kd', 'dk')

        @staticmethod
        def function(out, out_qp, geo, fmode):
            status = geo.integrate(out, out_qp)
            return status

        def get_fargs(self, kappa, kvar, dvar,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            from sfepy.discrete.variables import create_adof_conn, expand_basis

            geo, _ = self.get_mapping(dvar)

            n_el, n_qp, dim, n_en, n_c = self.get_data_shape(kvar)

            ebf = expand_basis(geo.bf, dim)

            aux = nm.einsum('i,...ij->...j', kappa, ebf)[0, :, None, :]
            kebf = insert_strided_axis(aux, 0, n_el)

            div_bf = geo.bfg

            div_bf = div_bf.reshape((n_el, n_qp, 1, dim * n_en))
            div_bf = nm.ascontiguousarray(div_bf)

            if diff_var is None:
                avar = dvar if self.mode == 'kd' else kvar
                econn = avar.field.get_econn('cell', self.region)
                adc = create_adof_conn(nm.arange(avar.n_dof, dtype=nm.int32),
                                       econn, n_c, 0)
                vals = avar()[adc]

                if self.mode == 'kd':
                    aux = dot_sequences(div_bf, vals[:, None, :, None])
                    out_qp = dot_sequences(kebf, aux, 'ATB')

                else:
                    aux = dot_sequences(kebf, vals[:, None, :, None])
                    out_qp = dot_sequences(div_bf, aux, 'ATB')

                fmode = 0

            else:
                if self.mode == 'kd':
                    out_qp = dot_sequences(kebf, div_bf, 'ATB')

                else:
                    out_qp = dot_sequences(div_bf, kebf, 'ATB')

                fmode = 1

            return out_qp, geo, fmode

    class GradDivStabilizationTerm(Term):
        r"""
        Grad-div stabilization term ( :math:`\gamma` is a global stabilization
        parameter).

        :Definition:

        .. math::
            \gamma \int_{\Omega} (\nabla\cdot\ul{u}) \cdot (\nabla\cdot\ul{v})

        :Arguments:
            - material : :math:`\gamma`
            - virtual  : :math:`\ul{v}`
            - state    : :math:`\ul{u}`
        """
        name = 'dw_st_grad_div'
        arg_types = ('material', 'virtual', 'state')
        arg_shapes = {'material' : '1, 1', 'virtual' : ('D', 'state'),
                      'state' : 'D'}

        function = staticmethod(terms.dw_st_grad_div)

        def get_fargs(self, gamma, virtual, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(state)

            if diff_var is None:
                div = self.get(state, 'div')
                fmode = 0

            else:
                div = nm.array([0], ndmin=4, dtype=nm.float64)
                fmode = 1

            return div, gamma, vg, fmode

    from sfepy.terms.terms_diffusion import LaplaceTerm

    class PSPGPStabilizationTerm(LaplaceTerm):
        r"""
        PSPG stabilization term, pressure part ( :math:`\tau` is a local
        stabilization parameter), alias to Laplace term dw_laplace.

        :Definition:

        .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ \nabla p \cdot \nabla q

        :Arguments:
            - material : :math:`\tau_K`
            - virtual  : :math:`q`
            - state    : :math:`p`
        """
        name = 'dw_st_pspg_p'

    class PSPGCStabilizationTerm(Term):
        r"""
        PSPG stabilization term, convective part ( :math:`\tau` is a local
        stabilization parameter).

        :Definition:

        .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \tau_K\ ((\ul{b} \cdot \nabla) \ul{u})
            \cdot \nabla q

        :Arguments:
            - material  : :math:`\tau_K`
            - virtual   : :math:`q`
            - parameter : :math:`\ul{b}`
            - state     : :math:`\ul{u}`
        """
        name = 'dw_st_pspg_c'
        arg_types = ('material', 'virtual', 'parameter', 'state')
        arg_shapes = {'material' : '1, 1', 'virtual' : (1, None),
                      'parameter' : 'D', 'state' : 'D'}

        function = staticmethod(terms.dw_st_pspg_c)

        def get_fargs(self, tau, virtual, parameter, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            svg, _ = self.get_mapping(virtual)
            vvg, _ = self.get_mapping(state)

            val_qp = self.get(parameter, 'val')
            conn = state.field.get_econn(self.act_integration, self.region)

            if diff_var is None:
                fmode = 0

            else:
                fmode = 1

            return val_qp, state(), tau, svg, vvg, conn, fmode

    class SUPGPStabilizationTerm(Term):
        r"""
        SUPG stabilization term, pressure part ( :math:`\delta` is a local
        stabilization parameter).

        :Definition:

        .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ \nabla p\cdot ((\ul{b} \cdot
            \nabla) \ul{v})

        :Arguments:
            - material  : :math:`\delta_K`
            - virtual   : :math:`\ul{v}`
            - parameter : :math:`\ul{b}`
            - state     : :math:`p`
        """
        name = 'dw_st_supg_p'
        arg_types = ('material', 'virtual', 'parameter', 'state')
        arg_shapes = {'material' : '1, 1', 'virtual' : ('D', None),
                      'parameter' : 'D', 'state' : 1}

        function = staticmethod(terms.dw_st_supg_p)

        def get_fargs(self, delta, virtual, parameter, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vvg, _ = self.get_mapping(virtual)
            svg, _ = self.get_mapping(state)

            val_qp = self.get(parameter, 'val')

            if diff_var is None:
                grad = self.get(state, 'grad')
                fmode = 0

            else:
                grad = nm.array([0], ndmin=4, dtype=nm.float64)
                fmode = 1

            return val_qp, grad, delta, vvg, svg, fmode

    class SUPGCStabilizationTerm(Term):
        r"""
        SUPG stabilization term, convective part ( :math:`\delta` is a local
        stabilization parameter).

        :Definition:

        .. math::
            \sum_{K \in \Ical_h}\int_{T_K} \delta_K\ ((\ul{b} \cdot \nabla)
            \ul{u})\cdot ((\ul{b} \cdot \nabla) \ul{v})

        :Arguments:
            - material  : :math:`\delta_K`
            - virtual   : :math:`\ul{v}`
            - parameter : :math:`\ul{b}`
            - state     : :math:`\ul{u}`
        """
        name = 'dw_st_supg_c'
        arg_types = ('material', 'virtual', 'parameter', 'state')
        arg_shapes = {'material' : '1, 1', 'virtual' : ('D', 'state'),
                      'parameter' : 'D', 'state' : 'D'}

        function = staticmethod(terms.dw_st_supg_c)

        def get_fargs(self, delta, virtual, parameter, state,
                      mode=None, term_mode=None, diff_var=None, **kwargs):
            vg, _ = self.get_mapping(virtual)

            val_qp = self.get(parameter, 'val')
            conn = virtual.field.get_econn(self.act_integration, self.region)

            if diff_var is None:
                fmode = 0

            else:
                fmode = 1

            return val_qp, state(), delta, vg, conn, fmode