Linear-forms

A linear form is defined by

define linearform <name> <flaglist>
integrator1
integrator2
integrator3
...

Example

define linearform f -fespace=v
source coef_f
neumann coef_g

A linear-form is always defined as sum over integrators. A linear-form maintains the right hand side vector.

The following flags are defined

-fespace=<name>

bilinear form is defined on fe space <name>

An integrator is defined as

token <coef1> <coef2> ... <flaglist>

Example:

source coef_fy -comp=2

The <coefi> refers to a coefficient function defined above. It provides the coefficients defined sub-domain by dub-domain for integrators defined on the domain (e.g., source), or, the coefficient boundary-patch by boundary-patch for integrators defined on the surface (e.g., neumann).

Allowed flags are

-order=num	use integration rule of order num. Default order is computed form element order.
-comp=num	use scalar integrator as component num for system (e.g., penalty term for y-displacement). num=0 adds integrator to all components.
-normal	add integrator in normal direction (surface load in normal direction)

The integrator tokens are

source f	$\int_\Omega f v dx$
neumann g	$\int_\Gamma g v ds$
sourceedge jx jy jz	$\int_\Omega j \cdot v dx$ for 3D $H(curl)$ spaces
neumannedge jx jy jz	$\int_\Gamma (n \times j) \cdot (n \times v) ds$ for 3D $H(curl)$ spaces
curledge f	$\int_\Omega f (\nabla \times v_z) dx$ for 2D $H(curl)$ spaces
curlboundaryedge f	$\int_\Gamma f n \cdot (\nabla \times v) ds$ for 3D $H(curl)$ spaces