sfepy.terms.terms_basic module¶

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

Evaluate material parameter $m$ in a surface region.

Depending on evaluation mode, integrate a material parameter over a surface region (‘eval’), average it in faces (‘el_avg’) or interpolate it into surface quadrature points (‘qp’).

Uses reference mapping of $y$ variable.

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition

$\int_\Gamma m$

$\mbox{vector for } K \from \Ical_h: \int_{T_K} m / \int_{T_K} 1$

$m|_{qp}$

Call signature

ev_surface_integrate_mat

(material, parameter)

Arguments

material : $m$ (can have up to two dimensions)
parameter : $y$

arg_shapes = [{'material': 'N, N', 'parameter': 'N'}]¶

arg_types = ('material', 'parameter')¶

integration = 'surface'¶

name = 'ev_surface_integrate_mat'¶

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

Surface integral of a test function weighted by a scalar function $c$ .

Definition

$\int_{\Gamma} q \mbox{ or } \int_\Gamma c q$

Call signature

dw_surface_integrate

(opt_material, virtual)

Arguments

material : $c$ (optional)
virtual : $q$

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

arg_types = ('opt_material', 'virtual')¶

integration = 'surface'¶

name = 'dw_surface_integrate'¶

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

Evaluate (weighted) variable in a surface region.

Depending on evaluation mode, integrate a variable over a surface region (‘eval’), average it in element faces (‘el_avg’) or interpolate it into surface quadrature points (‘qp’). For vector variables, setting term_mode to ‘flux’ leads to computing corresponding fluxes for the three modes instead.

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition

$\int_\Gamma y \mbox{ , } \int_\Gamma \ul{y} \mbox{ , } \int_\Gamma \ul{y} \cdot \ul{n} \\ \int_\Gamma c y \mbox{ , } \int_\Gamma c \ul{y} \mbox{ , } \int_\Gamma c \ul{y} \cdot \ul{n} \mbox{ flux }$

$\mbox{vector for } K \from \Ical_h: \int_{T_K} y / \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (\ul{y} \cdot \ul{n}) / \int_{T_K} 1 \\ \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (c \ul{y} \cdot \ul{n}) / \int_{T_K} 1$

$y|_{qp} \mbox{ , } \ul{y}|_{qp} \mbox{ , } (\ul{y} \cdot \ul{n})|_{qp} \mbox{ flux } \\ c y|_{qp} \mbox{ , } c \ul{y}|_{qp} \mbox{ , } (c \ul{y} \cdot \ul{n})|_{qp} \mbox{ flux }$

Call signature

ev_surface_integrate

(opt_material, parameter)

Arguments

material : $c$ (optional)
parameter : $y$ or $\ul{y}$

arg_shapes = [{'opt_material': '1, 1', 'parameter': 'N'}, {'opt_material': None}]¶

arg_types = ('opt_material', 'parameter')¶

static function(out, val_qp, sg, fmode)[source]¶

get_eval_shape(material, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

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

integration = 'surface'¶

name = 'ev_surface_integrate'¶

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

Evaluate material parameter $m$ in a volume region.

Depending on evaluation mode, integrate a material parameter over a volume region (‘eval’), average it in elements (‘el_avg’) or interpolate it into volume quadrature points (‘qp’).

Uses reference mapping of $y$ variable.

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition

$\int_\Omega m$

$\mbox{vector for } K \from \Ical_h: \int_{T_K} m / \int_{T_K} 1$

$m|_{qp}$

Call signature

ev_volume_integrate_mat

(material, parameter)

Arguments

material : $m$ (can have up to two dimensions)
parameter : $y$

arg_shapes = [{'material': 'N, N', 'parameter': 'N'}]¶

arg_types = ('material', 'parameter')¶

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

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

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

name = 'ev_volume_integrate_mat'¶

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

Volume integral of a test function weighted by a scalar function $c$ .

Definition

$\int_\Omega q \mbox{ or } \int_\Omega c q$

Call signature

dw_volume_integrate

(opt_material, virtual)

Arguments

material : $c$ (optional)
virtual : $q$

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

arg_types = ('opt_material', 'virtual')¶

static function(out, material, bf, geo)[source]¶

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

name = 'dw_volume_integrate'¶

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

Evaluate (weighted) variable in a volume region.

Depending on evaluation mode, integrate a variable over a volume region (‘eval’), average it in elements (‘el_avg’) or interpolate it into volume quadrature points (‘qp’).

Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.

Definition

$\int_\Omega y \mbox{ , } \int_\Omega \ul{y} \\ \int_\Omega c y \mbox{ , } \int_\Omega c \ul{y}$

$\mbox{vector for } K \from \Ical_h: \int_{T_K} y / \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \\ \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1$

$y|_{qp} \mbox{ , } \ul{y}|_{qp} \\ c y|_{qp} \mbox{ , } c \ul{y}|_{qp}$

Call signature

ev_volume_integrate

(opt_material, parameter)

Arguments

material : $c$ (optional)
parameter : $y$ or $\ul{y}$

arg_shapes = [{'opt_material': '1, 1', 'parameter': 'N'}, {'opt_material': None}]¶

arg_types = ('opt_material', 'parameter')¶

static function(out, val_qp, vg, fmode)[source]¶

get_eval_shape(material, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

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

name = 'ev_volume_integrate'¶

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

Sum nodal values.

Call signature

d_sum_vals

(parameter)

Arguments

parameter : $p$ or $\ul{u}$

arg_shapes = {'parameter': 'N'}¶

arg_types = ('parameter',)¶

static function(out, vec)[source]¶

get_eval_shape(parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'd_sum_vals'¶

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

Surface integral of the outer product of the unit outward normal $\ul{n}$ and the coordinate $\ul{x}$ shifted by $\ul{x}_0$

Definition

$\int_{\Gamma} \ul{n} (\ul{x} - \ul{x}_0)$

Call signature

d_surface_moment

(material, parameter)

Arguments

material : $\ul{x}_0$ (special)
parameter : any variable

arg_shapes = {'material': '.: D', 'parameter': 'N'}¶

arg_types = ('material', 'parameter')¶

static function()¶

get_eval_shape(material, parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

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

integration = 'surface'¶

name = 'd_surface_moment'¶

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

Surface of a domain. Uses approximation of the parameter variable.

Definition

$\int_\Gamma 1$

Call signature

d_surface

(parameter)

Arguments

parameter : any variable

arg_shapes = {'parameter': 'N'}¶

arg_types = ('parameter',)¶

integration = 'surface'¶

name = 'd_surface'¶

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

Volume of a $D$ -dimensional domain, using a surface integral. Uses approximation of the parameter variable.

Definition

$1 / D \int_\Gamma \ul{x} \cdot \ul{n}$

Call signature

d_volume_surface

(parameter)

Arguments

parameter : any variable

arg_shapes = {'parameter': 'N'}¶

arg_types = ('parameter',)¶

static function()¶

get_eval_shape(parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

integration = 'surface'¶

name = 'd_volume_surface'¶

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

Volume of a domain. Uses approximation of the parameter variable.

Definition

$\int_\Omega 1$

Call signature

d_volume

(parameter)

Arguments

parameter : any variable

arg_shapes = [{'parameter': 'N'}]¶

arg_types = ('parameter',)¶

static function(out, geo)[source]¶

get_eval_shape(parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

get_fargs(parameter, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

name = 'd_volume'¶

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

A do-nothing term useful for introducing additional variables into the equations.

Definition

$0$

Call signature

dw_zero

(virtual, state)

Arguments

virtual : $q$ or $\ul{v}$
state : $p$ or $\ul{u}$

arg_shapes = {'state': 'N', 'virtual': ('N', None)}¶

arg_types = ('virtual', 'state')¶

static function(out)[source]¶

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

name = 'dw_zero'¶