petsc-3.12.1 2019-10-22
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# TSBasicSymplectic

ODE solver using basic symplectic integration schemes These methods are intened for separable Hamiltonian systems

     qdot = dH(q,p,t)/dp

     pdot = -dH(q,p,t)/dq

where the Hamiltonian can be split into the sum of kinetic energy and potential energy

     H(q,p,t) = T(p,t) + V(q,t).

As a result, the system can be genearlly represented by

     qdot = f(p,t) = dT(p,t)/dp

     pdot = g(q,t) = -dV(q,t)/dq

and solved iteratively with

     q_new = q_old + d_i*h*f(p_old,t_old)

     t_new = t_old + d_i*h

     p_new = p_old + c_i*h*g(p_new,t_new)

     i=0,1,...,n.

The solution vector should contain both q and p, which correspond to (generalized) position and momentum respectively. Note that the momentum component could simply be velocity in some representations. The symplectic solver always expects a two-way splitting with the split names being "position" and "momentum". Each split is associated with an IS object and a sub-TS that is intended to store the user-provided RHS function.

Reference: wikipedia (https://en.wikipedia.org/wiki/Symplectic_integrator)

### See Also

TSCreate(), TSSetType(), TSRHSSplitSetIS(), TSRHSSplitSetRHSFunction()

### Level

beginner

### Location

src/ts/impls/symplectic/basicsymplectic/basicsymplectic.c
Index of all TS routines
Table of Contents for all manual pages
Index of all manual pages