puncturedfem.BilinearForm

Bilinear form for a diffusion-reaction equation.

Represents a bilinear form of the form a(u, v) = (D grad u, grad v) + (R u, v) where D is the diffusion constant, R is the reaction constant. Also includes a right-hand side Polynomial f, so that the weak problem is a(u, v) = (D grad u, grad v) + (R u, v) = (f, v) for all v in V.

Attributes:

Name	Type	Description
diffusion_constant	float	Diffusion constant D
reaction_constant	float	Reaction constant R
rhs_poly	Polynomial	Right-hand side Polynomial f

__init__(diffusion_constant, reaction_constant, rhs_poly)

Initialize the BilinearForm object.

Parameters:

Name	Type	Description	Default
diffusion_constant	float	Diffusion constant D	required
reaction_constant	float	Reaction constant R	required
rhs_poly	Polynomial	Right-hand side Polynomial f	required

__str__()

Return a string representation of the bilinear form.

eval(u, v)

Evaluate the bilinear form on two LocalPoissonFunction objects u and v.

Parameters:

Name	Type	Description	Default
u	LocalPoissonFunction	The first LocalPoissonFunction object	required
v	LocalPoissonFunction	The second LocalPoissonFunction object	required

eval_h1(u, v)

Return the H^1 semi-inner product of two LocalPoissonFunction objects u and v.

Parameters:

Name	Type	Description	Default
u	LocalPoissonFunction	The first LocalPoissonFunction object	required
v	LocalPoissonFunction	The second LocalPoissonFunction object	required

eval_l2(u, v)

Return the L^2 inner product of two LocalPoissonFunction objects u and v.

Parameters:

Name	Type	Description	Default
u	LocalPoissonFunction	The first LocalPoissonFunction object	required
v	LocalPoissonFunction	The second LocalPoissonFunction object	required

eval_rhs(v)

Evaluate the right-hand side polynomial f on a LocalPoissonFunction object v.

Parameters:

Name	Type	Description	Default
v	LocalPoissonFunction	The LocalPoissonFunction object against which to integrate f.	required

eval_with_h1_and_l2(h1, l2)

Get the bilinear form a(u,v) given h1 and l2 inner products.

Parameters:

Name	Type	Description	Default
h1	float	The H^1 semi-inner product (grad u, grad v)	required
l2	float	The L^2 inner product (u, v)	required

set_diffusion_constant(diffusion_constant)

Set the diffusion constant D.

Parameters:

Name	Type	Description	Default
diffusion_constant	float	The diffusion constant D	required

set_reaction_constant(reaction_constant)

Set the reaction constant R.

Parameters:

Name	Type	Description	Default
reaction_constant	float	The reaction constant R	required

set_rhs_poly(f_poly)

Set the right-hand side polynomial f.

Parameters:

Name	Type	Description	Default
f_poly	Polynomial	The right-hand side polynomial f	required