CS595. Homework 6 (Oct. 2010)
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1) Build PETSc in debug mode (configure with ‘--with-debugging=1 PETSC_ARCH=arch-cs595’) 
   and in optimized mode (configure with ‘--with-debugging=0 PETSC_ARCH=arch-cs595-o’)

2) Build $PETSC_DIR/src/ksp/ksp/examples/tutorials/ex2.c:
     cd $PETSC_DIR/src/ksp/ksp/examples/tutorials
     make ex2 PETSC_ARCH=arch-cs595 (or make ex2 PETSC_ARCH=arch-cs595-o)

   Run:
     mpiexec –n <np> ./ex2 -m 300 -n 300 –ksp_type <ksp_type> -pc_type <pc_type> -log_summary <log_file>

   Fill the form HW6_report.docx with the result collected from <log_file>.

Methods
1. -ksp_type gmres -pc_type none -ksp_max_it 1000

2. -ksp_type cg -pc_type none -ksp_max_it 1000

3. -ksp_type gmres -pc_type bjacobi -sub_pc_type ilu

4. -ksp_type gmres -pc_type bjacobi -sub_pc_type lu

5. -ksp_type cg -pc_type bjacobi -sub_pc_type icc

6. -ksp_type gmres -pc_type asm -sub_pc_type lu

7. -ksp_type gmres -pc_type asm -sub_pc_type lu -pc_asm_overlap 2

8. -ksp_type cg -pc_type sor -pc_sor_local_symmetric

This is a linear problem. We only consider matrix operations for "Dominating Operation", e.g.,
./ex2 -m 300 -n 300 -ksp_type gmres -pc_type bjacobi -sub_pc_type ilu -log_summary |grep Mat
MatMult        580 1.0 3.9221e+00 1.0 4.68e+08 1.0 0.0e+00 0.0e+00 0.0e+00 21 11 0 0 0 21 11 0 0 0 119
MatSolve       580 1.0 4.0558e+00 1.0 4.68e+08 1.0 0.0e+00 0.0e+00 0.0e+00 21 11 0 0 0 22 11 0 0 0 115
MatLUFactorNum   1 1.0 4.0746e-02 1.0 8.06e+05 1.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 20
MatILUFactorSym  1 1.0 4.9145e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 3.0e+00 0 0 0 0 0 0 0 0 0 0 0
MatGetRowIJ      1 1.0 1.9073e-06 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
MatGetOrdering   1 1.0 3.2486e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 2.0e+00 0 0 0 0 0 0 0 0 0 0 0
MatAssemblyBegin 1 1.0 1.9073e-06 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 0 0 0 0 0 0
MatAssemblyEnd   1 1.0 1.8147e-02 1.0 0.00e+00 0.0 0.0e+00 0.0e+00 0.0e+00 0 0 0 0 0 14 0 0 0 0 0

thus, dominating operations are
MatMult        580 1.0 3.9221e+00 
MatSolve       580 1.0 4.0558e+00

3) $PETSC_DIR/snes/examples/tutorials/ex19.c: 
   First, run following to understand the algorithm
     ./ex19 -dmmg_nlevels 7 -ksp_monitor -snes_monitor -snes_view
   
   Then run   
     mpiexec –n <np> ./ex19  -dmmg_nlevels 7 -log_summary <log_file>

This is non-linear problem. Check matrix operations and following three operations for "Dominating Operation"
SNESLineSearch 
SNESFunctionEval 
SNESJacobianEval