2020/12/31 by Maxim Olshanskii, Alexander Zhiliakov · 1 citation
Mathematics · Computer Science · #math.NA #cs.NA
paper · pdf · doi:10.1002/nla.2415
15 pages, 5 figures, 3 tables
arxiv created 2022/01/15 · arxiv updated 2022/01/19
The paper discusses a reuse of matrix factorization as a building block in the Augmented Lagrangian (AL) and modified AL preconditioners for non-symmetric saddle point linear algebraic systems. The strategy is applied to solve two-dimensional incompressible fluid problems with efficiency rates independent of the Reynolds number. The solver is then tested to simulate motion of a surface fluid, an example of a 2D flow motivated by an interest in lateral fluidity of inextensible viscous membranes. Numerical examples include the Kelvin--Helmholtz instability problem posed on the sphere and on the torus. Some new eigenvalue estimates for the AL preconditioner are derived.