2010/01/01 by Fred W. Wubs, Wubs, Fred, Jonas Thies +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1006.1874
openalex publication_date 2010/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a new hybrid direct/iterative approach to the solution of a\nspecial class of saddle point matrices arising from the discretization of the\nsteady incompressible Navier-Stokes equations on an Arakawa C-grid. The\ntwo-level method introduced here has the following properties: (i) it is very\nrobust, even close to the point where the solution becomes unstable; (ii) a\nsingle parameter controls fill and convergence, making the method\nstraightforward to use; (iii) the convergence rate is independent of the number\nof unknowns; (iv) it can be implemented on distributed memory machines in a\nnatural way; (v) the matrix on the second level has the same structure and\nnumerical properties as the original problem, so the method can be applied\nrecursively; (vi) the iteration takes place in the divergence- free space, so\nthe method qualifies as a 'constraint preconditioner'; (vii) the approach can\nalso be applied to Poisson problems.\n This work is also relevant for problems in which similar saddle point\nmatrices occur, for instance when simulating electrical networks, where one has\nto satisfy Kirchhoff's conservation law for currents.\n