PETSc version 3.17.4
Fix/Edit manual page

# PCPBJACOBI

Point block Jacobi preconditioner

### Notes

See PCJACOBI for point Jacobi preconditioning, PCVPBJACOBI for variable size point block Jacobi and PCBJACOBI for large blocks

This works for AIJ and BAIJ matrices and uses the blocksize provided to the matrix

Uses dense LU factorization with partial pivoting to invert the blocks; if a zero pivot is detected a PETSc error is generated.

### Developer Notes

This should support the PCSetErrorIfFailure() flag set to PETSC_TRUE to allow the factorization to continue even after a zero pivot is found resulting in a Nan and hence terminating KSP with a KSP_DIVERGED_NANORIF allowing a nonlinear solver/ODE integrator to recover without stopping the program as currently happens.

Perhaps should provide an option that allows generation of a valid preconditioner even if a block is singular as the PCJACOBI does.

### See Also

PCCreate(), PCSetType(), PCType (for list of available types), PC, PCJACOBI, PCVPBJACOBI, PCBJACOBI

### Level

beginner

### Location

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