Special Partitioned Additive Runge-Kutta Integrators
SPARK or Special Partitioned Additive Runge-Kutta Integrators are a family of integrators that have been introduced by Laurent O. Jay for the integration of differential algebraic equations and in particular systems subject to holonomic and nonholonomic constraints [Laurent O. Jay (1998), Laurent O. Jay (2003), Laurent O. Jay (2006), Laurent O. Jay (2007), Laurent O. Jay (2007)]. Recently, the idea of SPARK methods has been generalized and adapted to facilitate the integration of degenerate Lagrangian systems as well as Hamiltonian systems subject to Dirac constraints [Michael Kraus (2020)].
GeometricIntegrators.jl provides several flavours of such SPARK methods (some are still experimental):
| Integrator | Description |
|---|---|
IntegratorHPARK | Partitioned additive methods for Hamiltonian system subject to a general constraint $\phi(q,p) = 0$ |
IntegratorVPARK | Partitioned additive methods for Lagrangian system subject to a general constraint $\phi(q,p) = 0$ |
IntegratorSPARK | SPARK methods for general index-two differential algebraic equations |
IntegratorHSPARK | Hamiltonian system subject to a general constraint $\phi(q,p) = 0$ |
IntegratorHSPARKprimary | Hamiltonian system subject primary constraint in the sense of Dirac |
IntegratorHSPARKsecondary | Hamiltonian system enforcing primary & secondary Dirac constraint |
IntegratorVSPARK | Lagrangian system in implicit form subject to a general constraint $\phi(q,p) = 0$ |
IntegratorVSPARKprimary | Degenerate Lagrangian system subject primary constraint in the sense of Dirac |
IntegratorVSPARKsecondary | Degenerate Lagrangian system enforcing primary & secondary Dirac constraint |
These integrators are applied to either an IDAE, HDAE or VDAE.