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_types = ('material_1', 'material_2', 'virtual', 'state')¶

check_shapes(alpha, p_outer, virtual, state)[source]¶

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

mode = 'weak'¶

name = 'dw_bc_newton'¶

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

Surface $L^2(\Gamma)$ dot product for both scalar and vector fields.

Definition :

$\int_\Gamma q p \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , } \int_\Gamma q \ul{n} \cdot \ul{u} \mbox{ , } \int_\Gamma p r \mbox{ , } \int_\Gamma \ul{u} \cdot \ul{w} \mbox{ , } \int_\Gamma \ul{w} \cdot \ul{n} p \\ \int_\Gamma c q p \mbox{ , } \int_\Gamma c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma c p r \mbox{ , } \int_\Gamma c \ul{u} \cdot \ul{w} \\ \int_\Gamma \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{u} \cdot \ull{M} \cdot \ul{w}$

Call signature:

dw_surface_dot	`(opt_material, virtual, state)`
	`(opt_material, parameter_1, parameter_2)`

Arguments 1:	material : $c$ or $\ull{M}$ (optional) virtual : $q$ or $\ul{v}$ state : $p$ or $\ul{u}$
Arguments 2:	material : $c$ or $\ull{M}$ (optional) parameter_1 : $p$ or $\ul{u}$ parameter_2 : $r$ or $\ul{w}$

arg_types = (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶

integration = 'surface'¶

modes = ('weak', 'eval')¶

name = 'dw_surface_dot'¶

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

Volume $L^2(\Omega)$ weighted dot product for both scalar and vector fields. Can be evaluated. Can use derivatives.

Definition :

$\int_\Omega q p \mbox{ , } \int_\Omega \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega p r \mbox{ , } \int_\Omega \ul{u} \cdot \ul{w} \\ \int_\Omega c q p \mbox{ , } \int_\Omega c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega c p r \mbox{ , } \int_\Omega c \ul{u} \cdot \ul{w} \\ \int_\Omega \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_\Omega \ul{u} \cdot \ull{M} \cdot \ul{w}$

Call signature:

dw_volume_dot	`(opt_material, virtual, state)`
	`(opt_material, parameter_1, parameter_2)`

Arguments 1:	material : $c$ or $\ull{M}$ (optional) virtual : $q$ or $\ul{v}$ state : $p$ or $\ul{u}$
Arguments 2:	material : $c$ or $\ull{M}$ (optional) parameter_1 : $p$ or $\ul{u}$ parameter_2 : $r$ or $\ul{w}$

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

arg_types = (('opt_material', 'virtual', 'state'), ('opt_material', 'parameter_1', 'parameter_2'))¶

check_shapes(mat, virtual, state)[source]¶

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]¶

modes = ('weak', 'eval')¶

name = 'dw_volume_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_types = ('ts', 'material_0', 'material_1', 'virtual', 'state')¶

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_types = ('ts', 'material', 'virtual', 'state')¶

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 = {'state': 1, 'material': '1, 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.VectorDotGradScalarTerm(name, arg_str, integral, region, **kwargs)[source]¶

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

Definition :

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

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 $\ull{M}$ (optional) virtual : $\ul{v}$ state : $p$
Arguments 2:	material : $c$ or $\ull{M}$ (optional) state : $\ul{u}$ virtual : $q$
Arguments 3:	material : $c$ or $\ull{M}$ (optional) parameter_v : $\ul{u}$ parameter_s : $p$

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

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

check_shapes(coef, vvar, svar)[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_v_dot_grad_s'¶

set_arg_types()[source]¶

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