The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems.
We combine the adaptive and multilevel approaches to the BDDC and formulate a
method which allows an adaptive selection of constraints on each decomposition
level. We also present a strategy for the solution of local eigenvalue problems
in the adaptive algorithm using the LOBPCG method with a preconditioner based
on standard components of the BDDC. The effectiveness of the method is
illustrated on several engineering problems. It appears that the
Adaptive-Multilevel BDDC algorithm is able to effectively detect troublesome
parts on each decomposition level and improve convergence of the method. The
developed open-source parallel implementation shows a good scalability as well
as applicability to very large problems and core counts.Comment: 37 pages, 10 figures, 13 table
An easy-to-interpret kinematic quantity measuring the average corotation of material line segments near a point is introduced and applied to vortex identification. At a given point, the vector of average corotation of line segments is defined as the average of the instantaneous local rigid-body rotation over 'all planar cross-sections' passing through the examined point. The vortex identification method based on average corotation is a one-parameter, region-type local method sensitive to the axial stretching rate as well as to the inner configuration of the velocity gradient tensor. The method is derived from a well-defined interpretation of the local flow kinematics to determine the 'plane of swirling' and is also applicable to compressible and variable-density flows. Practical application to DNS data sets includes a hairpin vortex of boundary-layer transition, the reconnection process of two Burgers vortices, a flow around an inclined flat plate, and a flow around a revolving insect wing. The results agree well with some popular local methods and perform better in regions of strong shearing.
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