sll_operator_splitting

Operator splitting methods.

Author

Selalib team
Contact: Eric Sonnendrücker

Operator splitting is used to solve equations of the form \(\frac{dU}{dt} = (T+V)U \), where \(T \) and \(V \) are two differential operators by solving successively the simpler equations

The base class in sll_operator_splitting_base.F90 implements the composition form different kinds of composition methods defined by their coefficients.

The application of an operator splitting method to a concrete problem is done by extending the sll_t_operator_splitting splitting base class by a new type containing on the one hand the data on which the operators act and a specific implementation of the two operators

Examples of applications are provided for

• The linear pendulum problem: the type definition is in sll_m_linear_pendulum_operators.F90 and the main program performing the unit tests in unit_test_linear_pendulum.F90
• The Vlasov equation with constant coefficients advection field: type definition in sll_const_coef_adv_2d.F90 and main program in unit_test_const_coef_adv_2d.F90
• The non linear Vlasov-Poisson equations in cartesian coordinates

References

[HLW] E. Hairer, C. Lubich, G. Wanner, Geometrical numerical integration, Springer 2006 Composition of more that two operators can be reduce to the composition ot two operators by taking there first order composition and its adjoint (See (HLW) section II.5)

Modules available

• sll_m_time_splitting
• sll_m_operator_splitting