Finite element algebraic systems, size 50,000 to 500,000 to be solved on a workstation or PC:
Iterative methods with preconditioning by incomplete decomposition - CNSPACK software. High order of the incomplete decomposition is used for nonsymmetric matricies with CGS (or CG for symmetric case) iterative methods. Typical number of unknowns for solved problems ~ 300,000 for SGI O2 workstations (256Mb), or 100,000 for PCs (128Mb). Typical solution time 1 to 5 mins from zero initial approximation; much less for time stepping intergration for unsteady problems.

EXAMPLE 1. 3D movie for thermal vibrational convection flows in oxide melts, 150 000 unknowns : one frame, full movie at http://uahtitan.uah.edu/alex/cvs_frontx5.html.

Multigrid domain decomposition methods for linear and nonlinear problems and eigenvalue problems for complicated domain geometry, 2D and 3D cases.

EXAMPLE 2. 3D flow in a valve-pipe-outlet configuration (multigrid domain decomposition method, 80 000 unknowns); computations done on PC 486 (8Mb) by S. Purtov et al in 1992): pressure distribution, and velocity field. 3D finite element mesh is generated using the CATIA CAD files as input.

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