[kakeueda]

Description

GMRES previously failed during solve() when the preconditioner was set to "none". This adds an identity preconditioner (M = I) to support unpreconditioned GMRES.

Coses #467

Proposed changes

• Added an identity preconditioner derived from the preconditioner interface.
• Updated SystemSolver to instantiate the identity preconditioner when "none" is selected.
• Added unit tests.

GMRES iterations: 19 (none) → 8 (ILU0).

ku@kakeru:~/dev/ReSolve$ ./build/examples/sysGmres.exe \
  -b cuda -i fgmres -x no -g cgs2 -c none \
  -m tests/functionality/data/A_asymmetric01.mtx \
  -r tests/functionality/data/b_asymmetric01.mtx
Matrix file: tests/functionality/data/A_asymmetric01.mtx
RHS file: tests/functionality/data/b_asymmetric01.mtx
Preconditioner: none (identity)
sysGmres with CUDA backend
solver.setMatrix returned status: 0
solver.solve returned status: 0
         Initial relative residual norm ||b-A*x||/||b|| : 1.0000000000000000e+00
         Final relative residual norm   ||b-A*x||/||b|| : 4.6914933872622074e-13
         Number of iterations                           : 19

ku@kakeru:~/dev/ReSolve$ ./build/examples/sysGmres.exe \
  -b cuda -i fgmres -x no -g cgs2 -c ilu0 \
  -m tests/functionality/data/A_asymmetric01.mtx \
  -r tests/functionality/data/b_asymmetric01.mtx
Matrix file: tests/functionality/data/A_asymmetric01.mtx
RHS file: tests/functionality/data/b_asymmetric01.mtx
Preconditioner: ILU0
sysGmres with CUDA backend
solver.setMatrix returned status: 0
solver.preconditionerSetup returned status: 0
solver.solve returned status: 0
         Initial relative residual norm ||b-A*x||/||b|| : 1.0000000000000000e+00
         Final relative residual norm   ||b-A*x||/||b|| : 3.7609434128388183e-14
         Number of iterations                           : 8

Checklist

• All tests pass (make test and make test_install per testing instructions). Code tested on
  • CPU backend
  • CUDA backend
  • HIP backend
• I have manually run the non-experimental examples and verified that residuals are close to machine precision. (In your build directory run: ./examples/<your_example>.exe -h to get instructions how to run examples). Code tested on:
  • CPU backend
  • CUDA backend
  • HIP backend
• Code compiles cleanly with flags -Wall -Wpedantic -Wconversion -Wextra.
• The new code follows Re::Solve style guidelines.
• There are unit tests for the new code.
• The new code is documented.
• [N/A] The feature branch is rebased with respect to the target branch.
• I have updated CHANGELOG.md to reflect the changes in this PR. If this is a minor PR that is part of a larger fix already included in the file, state so.