Semi-implicit time integrator for level-set advection

[Fastaxx]

Description

Semi-implicit time integrator (Mikula et al.)

Hi @maltezfaria 👋

I’ve been experimenting with a semi-implicit time integrator for the level-set advection equation, inspired by the I2OE-schemes of Mikula et al.

The motivation is to relax the CFL restriction of the current explicit RK schemes when solving:

$\phi_t + \mathbf{u}\cdot\nabla \phi = 0$

I implemented a prototype integrator (SemiImplicitI2OE) in my fork:

https://github.com/Fastaxx/LevelSetMethods.jl/tree/feature/semi-implicit-scheme-tests

At the moment it:

• targets problems with an AdvectionTerm
• allows larger stable time steps than explicit RK
• works with existing grid/BC infrastructure

Would you be open to integrating a semi-implicit time integrator in the package?

Ref :
10.1016/j.apnum.2014.06.002

Validation and testing

No response

Motivation

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Target audience

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Can you help?

No response

[maltezfaria]

Sounds like a good idea, so yeah, it would be great to integrate this :-)

Would you mind creating a PR so that we can discuss some details and eventually merge it? I am not familiar with the details in the paper, but I will try to take a look. The most important thing would be to have some tests that e.g. the time-step restrictions are indeed less severe than using the fully explicit schemes currently available.

Thanks!