petsc-3.12.4 2020-02-04
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# PCHPDDMShellApply

Applies a (2) deflated, (1) additive, or (3) balanced coarse correction. In what follows, E = Z Pmat Z^T and Q = Z^T E^-1 Z.

       (1) y =                Pmat^-1              x + Q x,
       (2) y =                Pmat^-1 (I - Amat Q) x + Q x (default),
       (3) y = (I - Q Amat^T) Pmat^-1 (I - Amat Q) x + Q x.

### Input Parameters

| pc | - preconditioner context
| x | - input vector
| y | - output vector

Application Interface Routine: PCApply()

### Notes

The options of Pmat^1 = pc(Pmat) are prefixed by -pc_hpddm_levels_1_pc_. Z is a tall-and-skiny matrix assembled by HPDDM. The number of processes on which (Z Pmat Z^T) is aggregated is set via -pc_hpddm_coarse_p. The options of (Z Pmat Z^T)^-1 = ksp(Z Pmat Z^T) are prefixed by -pc_hpddm_coarse_ (KSPPREONLY and PCCHOLESKY by default), unless a multilevel correction is turned on, in which case, this function is called recursively at each level except the coarsest one. (1) and (2) visit the "next" level (in terms of coarsening) once per application, while (3) visits it twice, so it is asymptotically twice costlier. (2) is not symmetric even if both Amat and Pmat are symmetric.

### See Also

PCHPDDM, PCHPDDMCoarseCorrectionType

### Level

none

### Location

src/ksp/pc/impls/hpddm/hpddm.cxx
Index of all PC routines
Table of Contents for all manual pages
Index of all manual pages