Are all the time discretization schemes implemented in Elmer FEM semi-implicit? Also, where can I find the list of time discretization schemes available in Elmer FEM?

I reviewed TimeIntegrators.F90 code in the src folder as well as Chapter 6/Time discretization in Elmer Solver manual.

Thanks for any formation you can provide.

## Time discretization schemes

### Re: Time discretization schemes

Hi,

Unfortunately the documentation of the time stepping algorithms is not fully up to date. It seems that there are some options which are not mentioned in the documentation, so a documentation update would be needed. These include at least some Runge-Kutta methods and a fractional step method. I don't know much about these undocumented options as I haven't used them myself.

Whether one gets a fully implicit or semi-implicit algorithm may depend on how the different iteration controls of the solver are used. Usually fully implicit time stepping is employed by seeking an accurate nonlinear solution before proceeding to the next time step. However, it seems that the Runge-Kutta methods of Elmer can be explicit. In addition, as far as I understand, the predictor-corrector scheme can be defined to combine explicit and semi-implicit schemes.

-- Mika

Unfortunately the documentation of the time stepping algorithms is not fully up to date. It seems that there are some options which are not mentioned in the documentation, so a documentation update would be needed. These include at least some Runge-Kutta methods and a fractional step method. I don't know much about these undocumented options as I haven't used them myself.

Whether one gets a fully implicit or semi-implicit algorithm may depend on how the different iteration controls of the solver are used. Usually fully implicit time stepping is employed by seeking an accurate nonlinear solution before proceeding to the next time step. However, it seems that the Runge-Kutta methods of Elmer can be explicit. In addition, as far as I understand, the predictor-corrector scheme can be defined to combine explicit and semi-implicit schemes.

-- Mika

### Re: Time discretization schemes

Thank you for the information. Is the documentation that you are referring to - Chapter 6/Elmer Solver Manual?

I am assuming the schemes that are not in the documentation are implemented in the source code. Would that code be TimeIntegrate.F90? If yes, then would the schemes listed in that code be a comprehensive list?

I am assuming the schemes that are not in the documentation are implemented in the source code. Would that code be TimeIntegrate.F90? If yes, then would the schemes listed in that code be a comprehensive list?

### Re: Time discretization schemes

Yes

Yes, this is the common place for time stepping subroutines. The subroutine names used there are quite descriptive:

Code: Select all

```
SUBROUTINE RungeKutta
SUBROUTINE NewmarkBeta
SUBROUTINE AdamsBashforth
SUBROUTINE AdamsMoulton
SUBROUTINE BDFLocal
SUBROUTINE VBDFLocal
SUBROUTINE Bossak2ndOrder
SUBROUTINE FractionalStep
SUBROUTINE Newmark2ndOrder
SUBROUTINE RungeKutta_CRS
SUBROUTINE NewmarkBeta_CRS
SUBROUTINE BDF_CRS
SUBROUTINE VBDF_CRS
SUBROUTINE FractionalStep_CRS
```

-- Mika