A survey of preconditioned iterative methods

Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries

“…9, confirm the optimal approximation order with respect to H i -norms, i = 0, 1, and indicate an estimated growth rate of O(h −2 ) for the condition numbers of the diagonally scaled system matrices, cf. [27].…”

“…The numerical results indicate optimal convergence rates in the H i norms, i = 0, 1, 2, and show an estimated growth rate of O(h −4 ) for the condition numbers of the diagonally scaled system matrices (cf. [27]), see Fig. 10 and Table 1.…”

A deep non-hydrostatic compressible atmospheric model on a Yin-Yang grid

“…The overlap/boundary terms are incorporated into the L operator by exchanging the field (i.e., overlap filling) before the action of the operators is applied to the field. The linear solver used herein is the postconditioned version of van der Vorst's [13] Bi-CGSTAB algorithm developed by Brusaet [14]. For the preconditioner a single application of the rotationally invariant part of the vertical (tridiagonal) part of the of the Helmholtz operator is used.…”

Solving the triharmonic equation over multi-patch planar domains using isogeometric analysis

“…7 (fourth row) shows the resulting condition numbers κ of the stiffness matrices S by using diagonally scaling (cf. [7]) and by employing no preconditioner.…”