sfepy.terms.terms_jax module¶

Proof-of-concept JAX-based terms supporting automatic differentiation.

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

Homogeneous isotropic linear elasticity term differentiable w.r.t. material parameters $\lambda$ , $\mu$ (Lamé’s parameters).

Definition:

$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})\\ \mbox{ with } \\ D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl}$

Call signature:

dw_lin_elastic_l_ad

(material_1, material_2, virtual, state)

Arguments:

material_1: $\lambda$ (Lamé’s first parameter)
material_2: $\mu$ (Lamé’s second parameter, shear modulus)
virtual/parameter_1: $\ul{v}$
state/parameter_2: $\ul{u}$

arg_shapes = {'material_1': '1, 1', 'material_2': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

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

diff_info = {'material_1': 1, 'material_2': 1}¶

static function(out, fun, fargs)[source]¶

get_fargs(material1, material2, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('weak',)¶

name = 'dw_lin_elastic_l_ad'¶

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

Homogeneous isotropic linear elasticity term differentiable w.r.t. material parameters $E$ (Young’s modulus), $\nu$ (Poisson’s ratio).

Definition:

$\int_{\Omega} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})\\ \mbox{ with } \\ D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) + \lambda \ \delta_{ij} \delta_{kl}, \\ \mbox{ where } \\ \lambda = E \nu / ((1 + \nu)(1 - 2\nu)), \\ \mu = E / 2(1 + \nu)$

Call signature:

dw_lin_elastic_yp_ad

(material_1, material_2, virtual, state)

Arguments:

material_1: $E$
material_2: $\nu$
virtual/parameter_1: $\ul{v}$
state/parameter_2: $\ul{u}$

arg_shapes = {'material_1': '1, 1', 'material_2': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

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

diff_info = {'material_1': 1, 'material_2': 1}¶

static function(out, fun, fargs)[source]¶

get_fargs(material1, material2, virtual, state, mode=None, term_mode=None, diff_var=None, **kwargs)[source]¶

modes = ('weak',)¶

name = 'dw_lin_elastic_yp_ad'¶

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

Homogeneous mass term differentiable w.r.t. the material parameter.

Definition:

$\int_{\cal{D}} \rho \ul{v} \cdot \ul{u}$

Call signature:

dw_mass_ad

(material, virtual, state)

Arguments:

material_1: $\rho$
virtual: $\ul{v}$
state: $\ul{u}$

arg_shapes = {'material': '1, 1', 'state': 'D', 'virtual': ('D', 'state')}¶

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

diff_info = {'material': 1}¶

static function(out, fun, fargs)[source]¶

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

modes = ('weak',)¶

name = 'dw_mass_ad'¶

sfepy.terms.terms_jax.ceval_elasticity_l(lam, mu, vbfg, ubfg, det, cu)[source]¶

sfepy.terms.terms_jax.ceval_elasticity_yp(young, poisson, plane, vbfg, ubfg, det, cu)[source]¶

sfepy.terms.terms_jax.ceval_mass(density, vbf, ubf, det, cu)[source]¶

sfepy.terms.terms_jax.eval_density_mass(density, vbf, ubf, det, cu)¶

Vectorized version of ceval_mass. Takes similar arguments as ceval_mass but with additional array axes over which ceval_mass is mapped.

Original documentation:

Jacobian of ceval_mass with respect to positional argument(s) 0. Takes the same arguments as ceval_mass but returns the jacobian of the output with respect to the arguments at positions 0.

sfepy.terms.terms_jax.eval_elasticity_l(lam, mu, vbfg, ubfg, det, cu)¶: Vectorized version of ceval_elasticity_l. Takes similar arguments as ceval_elasticity_l but with additional array axes over which ceval_elasticity_l is mapped.

sfepy.terms.terms_jax.eval_elasticity_yp(young, poisson, plane, vbfg, ubfg, det, cu)¶: Vectorized version of ceval_elasticity_yp. Takes similar arguments as ceval_elasticity_yp but with additional array axes over which ceval_elasticity_yp is mapped.

sfepy.terms.terms_jax.eval_jac_elasticity_l(lam, mu, vbfg, ubfg, det, cu)¶

Vectorized version of ceval_elasticity_l. Takes similar arguments as ceval_elasticity_l but with additional array axes over which ceval_elasticity_l is mapped.

Original documentation:

Jacobian of ceval_elasticity_l with respect to positional argument(s) -1. Takes the same arguments as ceval_elasticity_l but returns the jacobian of the output with respect to the arguments at positions -1.

sfepy.terms.terms_jax.eval_jac_elasticity_yp(young, poisson, plane, vbfg, ubfg, det, cu)¶

Vectorized version of ceval_elasticity_yp. Takes similar arguments as ceval_elasticity_yp but with additional array axes over which ceval_elasticity_yp is mapped.

Original documentation:

Jacobian of ceval_elasticity_yp with respect to positional argument(s) -1. Takes the same arguments as ceval_elasticity_yp but returns the jacobian of the output with respect to the arguments at positions -1.

sfepy.terms.terms_jax.eval_jac_mass(density, vbf, ubf, det, cu)¶

Vectorized version of ceval_mass. Takes similar arguments as ceval_mass but with additional array axes over which ceval_mass is mapped.

Original documentation:

Jacobian of ceval_mass with respect to positional argument(s) -1. Takes the same arguments as ceval_mass but returns the jacobian of the output with respect to the arguments at positions -1.

sfepy.terms.terms_jax.eval_lam_elasticity_l(lam, mu, vbfg, ubfg, det, cu)¶

Vectorized version of ceval_elasticity_l. Takes similar arguments as ceval_elasticity_l but with additional array axes over which ceval_elasticity_l is mapped.

Original documentation:

Jacobian of ceval_elasticity_l with respect to positional argument(s) 0. Takes the same arguments as ceval_elasticity_l but returns the jacobian of the output with respect to the arguments at positions 0.

sfepy.terms.terms_jax.eval_mass(density, vbf, ubf, det, cu)¶: Vectorized version of ceval_mass. Takes similar arguments as ceval_mass but with additional array axes over which ceval_mass is mapped.

sfepy.terms.terms_jax.eval_mu_elasticity_l(lam, mu, vbfg, ubfg, det, cu)¶

Vectorized version of ceval_elasticity_l. Takes similar arguments as ceval_elasticity_l but with additional array axes over which ceval_elasticity_l is mapped.

Original documentation:

Jacobian of ceval_elasticity_l with respect to positional argument(s) 1. Takes the same arguments as ceval_elasticity_l but returns the jacobian of the output with respect to the arguments at positions 1.

sfepy.terms.terms_jax.eval_poisson_elasticity_yp(young, poisson, plane, vbfg, ubfg, det, cu)¶

Vectorized version of ceval_elasticity_yp. Takes similar arguments as ceval_elasticity_yp but with additional array axes over which ceval_elasticity_yp is mapped.

Original documentation:

Jacobian of ceval_elasticity_yp with respect to positional argument(s) 1. Takes the same arguments as ceval_elasticity_yp but returns the jacobian of the output with respect to the arguments at positions 1.

sfepy.terms.terms_jax.eval_young_elasticity_yp(young, poisson, plane, vbfg, ubfg, det, cu)¶

Vectorized version of ceval_elasticity_yp. Takes similar arguments as ceval_elasticity_yp but with additional array axes over which ceval_elasticity_yp is mapped.

Original documentation:

Jacobian of ceval_elasticity_yp with respect to positional argument(s) 0. Takes the same arguments as ceval_elasticity_yp but returns the jacobian of the output with respect to the arguments at positions 0.

sfepy.terms.terms_jax.get_strain(gu)[source]¶

sfepy.terms.terms_jax.get_stress(lam, mu, gu)[source]¶