We present and analyze an implicit preconditioning strategy specially designed for solving generalized Sylvester equations that uses a preconditioned residual direction at every iteration.
The solver employs an implicit preconditioning algorithm in curvilinear coordinates.
Lv, Y . Zhao et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661–690] based on the immersed membrane method (IMM) [X. Lv, Y . Zhao et al., as mentioned above].
We address temporal stiffness with implicit time stepping, suitably preconditioned.
The convergence of a Runge Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator.
To achieve this goal, the validated FEM was used in combination with an implicit integration scheme and an asynchronous preconditioning technique, as presented in [ 22].
As a result, the discrete equations analytically reduce to the incompressible equations at very low Mach number, i.e., the algorithm overcomes the acoustic time-scale limit without preconditioning or solution of an implicit system of equations.
Effective preconditioning schemes are available in context with implicit and multi-grid iterative algorithms for the nonlinear equation system.
Being that this preconditioner was designed to attack the fastest waves in the system and not other features in the implicit system such as advection or turbulent diffusion, the preconditioning technique is labeled as a physics-based preconditioner.
Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation.
