sfepy.terms.terms_dot module¶

class sfepy.terms.terms_dot.BCNewtonTerm(name, arg_str, integral, region, **kwargs)[source]¶

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)[source]¶

integration = 'facet'¶

mode = 'weak'¶

name = 'dw_bc_newton'¶

class sfepy.terms.terms_dot.DotProductTerm(name, arg_str, integral, region, **kwargs)[source]¶

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', 'virtual': (1, 'state'), 'state': 1, 'parameter_1': 1, 'parameter_2': 1}, {'opt_material': None}, {'opt_material': '1, 1', 'virtual': ('D', 'state'), 'state': 'D', 'parameter_1': 'D', 'parameter_2': 'D'}, {'opt_material': 'D, D'}, {'opt_material': None}], 'facet': [{'opt_material': '1, 1', 'virtual': (1, 'state'), 'state': 1, 'parameter_1': 1, 'parameter_2': 1}, {'opt_material': None}, {'opt_material': '1, 1', 'virtual': (1, None), 'state': 'D'}, {'opt_material': None}, {'opt_material': '1, 1', 'virtual': ('D', None), 'state': 1}, {'opt_material': None}, {'opt_material': '1, 1', 'virtual': ('D', 'state'), 'state': 'D', 'parameter_1': 'D', 'parameter_2': 'D'}, {'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)[source]¶

static dw_dot(out, mat, val_qp, vgeo, sgeo, fun, fmode)[source]¶

get_eval_shape(mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(mat, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

integration = ('cell', 'facet')¶

modes = ('weak', 'eval')¶

name = 'dw_dot'¶

set_arg_types()[source]¶

class sfepy.terms.terms_dot.DotSProductVolumeOperatorWETHTerm(name, arg_str, integral, region, **kwargs)[source]¶

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()¶

get_fargs(ts, mat0, mat1, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_volume_dot_w_scalar_eth'¶

class sfepy.terms.terms_dot.DotSProductVolumeOperatorWTHTerm(name, arg_str, integral, region, **kwargs)[source]¶

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()¶

get_fargs(ts, mats, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_volume_dot_w_scalar_th'¶

class sfepy.terms.terms_dot.ScalarDotGradIScalarTerm(name, arg_str, integral, region, **kwargs)[source]¶

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)[source]¶

get_fargs(material, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'dw_s_dot_grad_i_s'¶

set_arg_types()[source]¶

class sfepy.terms.terms_dot.ScalarDotMGradScalarTerm(name, arg_str, integral, region, **kwargs)[source]¶

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', 'virtual/grad_state': (1, None), 'state/grad_state': 1, 'virtual/grad_virtual': (1, None), 'state/grad_virtual': 1}]¶

arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'))¶

static function(out, out_qp, geo, fmode)[source]¶

get_fargs(mat, var1, var2, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('grad_state', 'grad_virtual')¶

name = 'dw_s_dot_mgrad_s'¶

class sfepy.terms.terms_dot.VectorDotGradScalarTerm(name, arg_str, integral, region, **kwargs)[source]¶

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', 'virtual/v_weak': ('D', None), 'state/v_weak': 1, 'virtual/s_weak': (1, None), 'state/s_weak': 'D', 'parameter_v': 'D', 'parameter_s': 1}, {'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)[source]¶

get_fargs(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('v_weak', 's_weak', 'eval')¶

name = 'dw_v_dot_grad_s'¶

set_arg_types()[source]¶

class sfepy.terms.terms_dot.VectorDotScalarTerm(name, arg_str, integral, region, **kwargs)[source]¶

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', 'virtual/v_weak': ('D', None), 'state/v_weak': 1, 'virtual/s_weak': (1, None), 'state/s_weak': 'D', 'parameter_v': 'D', 'parameter_s': 1}]¶

arg_types = (('material', 'virtual', 'state'), ('material', 'state', 'virtual'), ('material', 'parameter_v', 'parameter_s'))¶

static d_dot(out, mat, val1_qp, val2_qp, geo)[source]¶

static dw_dot(out, mat, val_qp, bfve, bfsc, geo, fmode)[source]¶

get_eval_shape(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(coef, vvar, svar, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('v_weak', 's_weak', 'eval')¶

name = 'dw_vm_dot_s'¶

set_arg_types()[source]¶