Skip to content

Commit

Permalink
update documentation of bilinear forms
Browse files Browse the repository at this point in the history
  • Loading branch information
PetrKryslUCSD committed Jun 10, 2023
1 parent 2a5df37 commit fcd282c
Showing 1 changed file with 13 additions and 6 deletions.
19 changes: 13 additions & 6 deletions src/FEMMBaseModule.jl
Original file line number Diff line number Diff line change
Expand Up @@ -1305,6 +1305,9 @@ function (data). Both functions are assumed to be vectors (even if of length
1). ``f`` is represented with `DataCache`, and needs to return a square
matrix.
The integral is with respect to the volume of the domain ``V`` (i.e. a three
dimensional integral).
# Arguments
- `self` = finite element machine;
- `assembler` = assembler of the global object;
Expand Down Expand Up @@ -1411,17 +1414,21 @@ Compute the sparse matrix implied by the bilinear form of the "diffusion" type.
\\int_{V} \\nabla\\vartheta \\cdot c \\cdot \\nabla u \\; \\mathrm{d} V
```
Here ``\\nabla\\vartheta`` is the gradient of the test function, ``\\nabla u``
is the gradient of the trial function, ``c`` is a square matrix of
coefficients; ``c`` is computed by ``f``, which is a given function(data). Both
functions are assumed to be vectors (even if of length 1). ``f`` is represented
with `DataCache`, and needs to return a symmetric square matrix (to represent
general anisotropic diffusion) or a scalar (to represent isotropic diffusion).
Here ``\\nabla\\vartheta`` is the gradient of the scalar test function,
``\\nabla u`` is the gradient of the scalar trial function, ``c`` is a square
symmetric matrix of coefficients (or a scalar); ``c`` is computed by ``f``,
which is a given function (data). Both test and trial functions are assumed to
be from the same approximation space. ``f`` is represented with `DataCache`,
and needs to return a symmetric square matrix (to represent general anisotropic
diffusion) or a scalar(to represent isotropic diffusion).
The coefficient matrix ``c`` can be given in the so-called local material
coordinates: coordinates that are attached to a material point and are
determined by a local cartesian coordinates system (`mcsys`).
The integral is with respect to the volume of the domain ``V`` (i.e. a three
dimensional integral).
# Arguments
- `self` = finite element machine;
- `assembler` = assembler of the global object;
Expand Down

2 comments on commit fcd282c

@PetrKryslUCSD
Copy link
Owner Author

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

@JuliaRegistrator
Copy link

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Registration pull request created: JuliaRegistries/General/85274

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

git tag -a v6.2.0 -m "<description of version>" fcd282c8cbe88b64d04046b99e6dfa09d4df60ca
git push origin v6.2.0

Please sign in to comment.