# Module: Ferroelectric

Semi-implicit thin film solver for second order differential equations of form:

$$
    \frac{\eta}{\Delta t} - G_{ij} \eta_{,ij}= rhs
$$

:Name: mod_mupro_msolve
:Depends on: [mod_mupro_base](base.md), [mod_mupro_fft](fft.md), [mod_mupro_log](log.md)
:Defined variables: None
:Defined types: - [type_mupro_FerroelectricContext](#type_mupro_FerroelectricContext)

<!-- :Defined subroutines: - [mupro_ferroelectric_setup](#mupro_ferroelectric_setup) -->

## Defined Types

### type_mupro_FerroelectricContext

#### Variables
|        Variable         |  Type  | Dimension | Meaning                 |
| :---------------------: | :----: | :-------: | ----------------------- |
|        stiffness        | real64 |   (6,6)   | Elastic stiffness       |
|    electrostrictive     | real64 |   (6,6)   | Electrostrictive tensor |
|       eigenstrain       | real64 | (6,z,y,x) | Eigenstrain             |
|          elast          | real64 | (3,z,y,x) | Elastic driving force   |
|          elec           | real64 | (3,z,y,x) | Electric driving force  |
|           lan           | real64 | (3,z,y,x) | Landau driving force  |
|           op            | real64 | (3,z,y,x) | Order parameter  |
|       boundCharge       | real64 | (3,z,y,x) | Bound charge  |
|      landau_energy      | real64 | (3,z,y,x) | Landau energy  |
|       grad_energy       | real64 | (3,z,y,x) | gradient energy  |
|        a1,a2,a3         | real64 | - | Landau coefficient  |
|       a11,a22,a33       | real64 | - | Landau coefficient  |
|       a11,a22,a33       | real64 | - | Landau coefficient  |
|       a23,a13,a12       | real64 | - | Landau coefficient  |
|     a111,a112,a123      | real64 | - | Landau coefficient  |
| a1111,a1112,a1122,a1123 | real64 | - | Landau coefficient  |

#### Procedures

##### setup

##### get_polarization_bound_charge

##### get_eigenstrain

##### get_elastic_driving_force

##### get_landau_driving_force