# sfepy.terms.terms_dot module

class sfepy.terms.terms_dot.BCNewtonTerm(name, arg_str, integral, region, **kwargs)

  Newton boundary condition term.

  Definition:

  \int_{\Gamma} \alpha q (p - p_{\rm outer})

  Call signature:

  dw_bc_newton | `(material_1, material_2, virtual, state)`

  Arguments:

    - material_1 : \alpha

    - material_2 : p_{\rm outer}

    - virtual : q

    - state : p

  arg_shapes = {'material_1': '1, 1', 'material_2': '1, 1', 'state': 1, 'virtual': (1, 'state')}
  arg_shapes_dict = None
  arg_types = ('material_1', 'material_2', 'virtual', 'state')
  get_fargs(alpha, p_outer, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)
  integration = 'facet'
  mode = 'weak'
  name = 'dw_bc_newton'

class sfepy.terms.terms_dot.DotProductTerm(name, arg_str, integral, region, **kwargs)

  Volume and surface L^2() weighted dot product for both scalar and vector fields. If the region is a surface and either virtual or state variable is a vector, the orientation of the normal vectors is outwards to the parent region of the virtual variable. Can be evaluated. Can use derivatives.

  Definition:

  \int_{\cal{D}} q p \mbox{ , } \int_{\cal{D}} \ul{v} \cdot \ul{u}\\ \int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , } \int_\Gamma q \ul{n} \cdot \ul{u} \mbox{ , }\\ \int_{\cal{D}} c q p \mbox{ , } \int_{\cal{D}} c \ul{v} \cdot \ul{u} \mbox{ , } \int_{\cal{D}} \ul{v} \cdot \ull{c} \cdot \ul{u}

  Call signature:

  dw_dot | `(opt_material, virtual, state)`
  | `(opt_material, parameter_1, parameter_2)`

  Arguments:

    - material: c or \ull{c} (optional)

    - virtual/parameter_1: q or \ul{v}

    - state/parameter_2: p or \ul{u}

  arg_shapes_dict = {'cell': [{'opt_material': '1, 1', 'parameter_1': 1, 'parameter_2': 1, 'state': 1, 'virtual': (1, 'state')}, {'opt_material': None}, {'opt_material': '1, 1', 'parameter_1': 'D', 'parameter_2': 'D', 'state': 'D', 'virtual': ('D', 'state')}, {'opt_material': 'D, D'}, {'opt_material': None}], 'facet': [{'opt_material': '1, 1', 'parameter_1': 1, 'parameter_2': 1, 'state': 1, 'virtual': (1, 'state')}, {'opt_material': None}, {'opt_material': '1, 1', 'state': 'D', 'virtual': (1, None)}, {'opt_material': None}, {'opt_material': '1, 1', 'state': 1, 'virtual': ('D', None)}, {'opt_material': None}, {'opt_material': '1, 1', 'parameter_1': 'D', 'parameter_2': 'D', 'state': 'D', 'virtual': ('D', 'state')}, {'opt_material': 'D, D'}, {'opt_material': None}]}
  arg_types = (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))
  static d_dot(out, mat, val1_qp, val2_qp, geo)
  static dw_dot(out, mat, val_qp, vgeo, sgeo, fun, fmode)
  get_eval_shape(mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)
  get_fargs(mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)
  integration = ('cell', 'facet')
  modes = ('weak', 'eval')
  name = 'dw_dot'
  set_arg_types()

class sfepy.terms.terms_dot.DotSProductVolumeOperatorWETHTerm(name, arg_str, integral, region, **kwargs)

  Fading memory volume L^2(\Omega) weighted dot product for scalar fields. This term has the same definition as dw_volume_dot_w_scalar_th, but assumes an exponential approximation of the convolution kernel resulting in much higher efficiency. Can use derivatives.

  Definition:

  \int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q

  Call signature:

  dw_volume_dot_w_scalar_eth | `(ts, material_0, material_1, virtual, state)`

  Arguments:

    - ts : `TimeStepper` instance

    - material_0 : \Gcal(0)

    - material_1 : \exp(-\lambda \Delta t) (decay at t_1)

    - virtual : q

    - state : p

  arg_shapes = {'material_0': '1, 1', 'material_1': '1, 1', 'state': 1, 'virtual': (1, 'state')}
  arg_types = ('ts', 'material_0', 'material_1', 'virtual', 'state')
  static function(out, coef, val_qp, rcmap, ccmap, is_diff)
  get_fargs(ts, mat0, mat1, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)
  name = 'dw_volume_dot_w_scalar_eth'

class sfepy.terms.terms_dot.DotSProductVolumeOperatorWTHTerm(name, arg_str, integral, region, **kwargs)

  Fading memory volume L^2(\Omega) weighted dot product for scalar fields. Can use derivatives.

  Definition:

  \int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q

  Call signature:

  dw_volume_dot_w_scalar_th | `(ts, material, virtual, state)`

  Arguments:

    - ts : `TimeStepper` instance

    - material : \Gcal(\tau)

    - virtual : q

    - state : p

  arg_shapes = {'material': '.: N, 1, 1', 'state': 1, 'virtual': (1, 'state')}
  arg_types = ('ts', 'material', 'virtual', 'state')
  static function(out, coef, val_qp, rcmap, ccmap, is_diff)
  get_fargs(ts, mats, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)
  name = 'dw_volume_dot_w_scalar_th'

class sfepy.terms.terms_dot.ScalarDotGradIScalarTerm(name, arg_str, integral, region, **kwargs)

  Dot product of a scalar and the i-th component of gradient of a scalar. The index should be given as a ‘special_constant’ material parameter.

  Definition:

  Z^i = \int_{\Omega} q \nabla_i p

  Call signature:

  dw_s_dot_grad_i_s | `(material, virtual, state)`

  Arguments:

    - material : i

    - virtual : q

    - state : p

  arg_shapes = {'material': '.: 1, 1', 'state': 1, 'virtual': (1, 'state')}
  arg_types = ('material', 'virtual', 'state')
  static dw_fun(out, bf, vg, grad, idx, fmode)
  get_fargs(material, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)
  name = 'dw_s_dot_grad_i_s'
  set_arg_types()

class sfepy.terms.terms_dot.ScalarDotMGradScalarTerm(name, arg_str, integral, region, **kwargs)

  Volume dot product of a scalar gradient dotted with a material vector with a scalar.

  Definition:

  \int_{\Omega} q \ul{y} \cdot \nabla p \mbox{ , } \int_{\Omega} p \ul{y} \cdot \nabla q

  Call signature:

  dw_s_dot_mgrad_s | `(material, virtual, state)`
  | `(material, state, virtual)`

  Arguments 1:

    - material : \ul{y}

    - virtual : q

    - state : p

  Arguments 2:

    - material : \ul{y}

    - state : p

    - virtual : q

  arg_shapes = [{'material': 'D, 1', 'state/grad_state': 1, 'state/grad_virtual': 1, 'virtual/grad_state': (1, None), 'virtual/grad_virtual': (1, None)}]
  arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'))
  static function(out, out_qp, geo, fmode)
  get_fargs(mat, var1, var2, mode=None, term_mode=None, diff_var=None, **kwargs)
  modes = ('grad_state', 'grad_virtual')
  name = 'dw_s_dot_mgrad_s'

class sfepy.terms.terms_dot.VectorDotGradScalarTerm(name, arg_str, integral, region, **kwargs)

  Volume dot product of a vector and a gradient of scalar. Can be evaluated.

  Definition:

  \int_{\Omega} \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} \ul{u} \cdot \nabla q \\ \int_{\Omega} c \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} c \ul{u} \cdot \nabla q \\ \int_{\Omega} \ul{v} \cdot (\ull{c} \nabla p) \mbox{ , } \int_{\Omega} \ul{u} \cdot (\ull{c} \nabla q)

  Call signature:

  dw_v_dot_grad_s | `(opt_material, virtual, state)`
  | `(opt_material, state, virtual)`
  | `(opt_material, parameter_v, parameter_s)`

  Arguments 1:

    - material: c or \ull{c} (optional)

    - virtual/parameter_v: \ul{v}

    - state/parameter_s: p

  Arguments 2:

    - material : c or \ull{c} (optional)

    - state : \ul{u}

    - virtual : q

  arg_shapes = [{'opt_material': '1, 1', 'parameter_s': 1, 'parameter_v': 'D', 'state/s_weak': 'D', 'state/v_weak': 1, 'virtual/s_weak': (1, None), 'virtual/v_weak': ('D', None)}, {'opt_material': 'D, D'}, {'opt_material': None}]
  arg_types = (('opt_material', 'virtual', 'state'), ('opt_material', 'state', 'virtual'), ('opt_material', 'parameter_v', 'parameter_s'))
  get_eval_shape(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)
  get_fargs(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)
  modes = ('v_weak', 's_weak', 'eval')
  name = 'dw_v_dot_grad_s'
  set_arg_types()

class sfepy.terms.terms_dot.VectorDotScalarTerm(name, arg_str, integral, region, **kwargs)

  Volume dot product of a vector and a scalar. Can be evaluated.

  Definition:

  \int_{\Omega} \ul{v} \cdot \ul{c} p \mbox{ , } \int_{\Omega} \ul{u} \cdot \ul{c} q\\

  Call signature:

  dw_vm_dot_s | `(material, virtual, state)`
  | `(material, state, virtual)`
  | `(material, parameter_v, parameter_s)`

  Arguments 1:

    - material : \ul{c}

    - virtual/parameter_v: \ul{v}

    - state/parameter_s: p

  Arguments 2:

    - material : \ul{c}

    - state : \ul{u}

    - virtual : q

  arg_shapes = [{'material': 'D, 1', 'parameter_s': 1, 'parameter_v': 'D', 'state/s_weak': 'D', 'state/v_weak': 1, 'virtual/s_weak': (1, None), 'virtual/v_weak': ('D', None)}]
  arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_v', 'parameter_s'))
  static d_dot(out, mat, val1_qp, val2_qp, geo)
  static dw_dot(out, mat, val_qp, bfve, bfsc, geo, fmode)
  get_eval_shape(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)
  get_fargs(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)
  modes = ('v_weak', 's_weak', 'eval')
  name = 'dw_vm_dot_s'
  set_arg_types()