PETSc version v3.15.4941g333c02ea7d
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.
Synopsis
#include "petscpc.h"
static PetscErrorCode PCHPDDMShellApply(PC pc, Vec x, Vec y)
(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

Output Parameter
Application Interface Routine: PCApply()
Notes
The options of Pmat^1 = pc(Pmat) are prefixed by pc_hpddm_levels_1_pc_. Z is a tallandskiny 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
advanced
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