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An implicit theta (like Heun but corrector stage is implicit/backwards Euler) should be implemented and tested with respect to history implementation. An implicit scheme has better stability, so that larger step sizes can be taken, reducing history memory requirements. Because coupling values are delayed, the solver step for the implicit scheme does not need to recompute the coupling values, only perform fixed point iterations with the Jacobian of the system (which can be expressed as a Jacobian-vector product),
Describe your proposed implementation
Two schemes can be implemented: backwards Euler & theta scheme. Each requires the Jacobian of the scheme update, which in turn requires the Jacobian of the system wrt. the states. The forward Euler predictor stage is used as the guess for the implicit stage solver, which can use a simple technique like fixed point iterations.
The text was updated successfully, but these errors were encountered:
Describe the new feature or enhancement
An implicit theta (like Heun but corrector stage is implicit/backwards Euler) should be implemented and tested with respect to history implementation. An implicit scheme has better stability, so that larger step sizes can be taken, reducing history memory requirements. Because coupling values are delayed, the solver step for the implicit scheme does not need to recompute the coupling values, only perform fixed point iterations with the Jacobian of the system (which can be expressed as a Jacobian-vector product),
Describe your proposed implementation
Two schemes can be implemented: backwards Euler & theta scheme. Each requires the Jacobian of the scheme update, which in turn requires the Jacobian of the system wrt. the states. The forward Euler predictor stage is used as the guess for the implicit stage solver, which can use a simple technique like fixed point iterations.
The text was updated successfully, but these errors were encountered: