KSFD algorithm for Poisson equation with one periodic direction
Authors: A. Gorobets, F. X. Trias, M. Soria
The KrylovSchurFourier Decomposition algorithm (KSFD): Fourier decomposition uncouples 3D problem into set of 2D problems (planes).
The Preconditioned Conjugate Gradient (PCG) Krylov subspace iterative method and the Direct Schur Decomposition (DSD) direct method are used to solve the 2D problems
The KSFD solver is designed for largescale DNS and LES on supercomputers.
 It provides good performance and scalability, can work with large meshes using >10000 CPU
 It performs well on both small "Beowulf" clusters and supercomputers
 The problem to solve must have (at least) one periodic direction, mesh step must be uniform in this direction
 The geometry of 3D obstacles is limited to be a 2D shape extruded along the periodic direction
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Parallel fully3D Poisson solver
Authors: A. Gorobets, F. X. Trias, M. Soria
Multigrid approach is used to extend the KSFD solver to fully 3D cases.
A "2.5D" approximation compatible with KSFD solver is used as a second level.
A simple PCG with a local preconditioner is used as a smoother.
The extended solver is designed for largescale DNS and LES of fully 3D cases (3 wallorthogonal directions, 3D obstacles, non uniform mesh in all 3 directions) on supercomputers.
 It provides reasonable scalability,
can work with moderate meshes (10~50*10^{6}) using >1000 CPU
 But it has some limitations on mesh concentration
 It is still under construction...

