Add Preconditioned Conjugate Gradient Method

[julianlitz]

Add Preconditioned Conjugate Gradient (PCG)

Rather than running GMGPolar as a standalone iterative solver, we can exploit it as a preconditioner for CG.

Each PCG iteration approximates the action of A^{-1} by running a cheap FMG approximation followed by one multigrid cycle. Good enough to serve as a preconditioner, but much cheaper than iterating GMGPolar to full convergence.

The non-extrapolated operator A is used as the preconditioner M, even when solving the extrapolated system (see Litz et al.). The extrapolated operator A_ex cannot serve as preconditioner because its right-hand side requires evaluating a source term function, whereas PCG only has access to a discretized residual vector at each iteration. This was validated on the paper_v2_conjugate_gradient branch.

The implementation is tightly integrated with the existing solver, so the additional memory cost is just two vectors. The three PCG work vectors (r, z, A*p) are aliased onto storage that already exists (level.rhs(), level.solution(), level.residual()), and only the solution x and search direction p require fresh allocations.

When combined with extrapolation, the PCG solver converges in up to 4× fewer iterations than standalone GMGPolar and runs up to 2× faster end-to-end. A significant gain for a minimal implementation cost.

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[codecov]

Codecov Report

❌ Patch coverage is 78.30882% with 59 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.91%. Comparing base (aac9b10) to head (e8d7055).

Files with missing lines	Patch %	Lines
src/GMGPolar/setup.cpp	8.82%	31 Missing ⚠️
src/ConfigParser/config_parser.cpp	52.94%	16 Missing ⚠️
src/GMGPolar/solver.cpp	92.98%	8 Missing ⚠️
src/GMGPolar/gmgpolar.cpp	94.44%	3 Missing ⚠️
src/Level/level.cpp	85.71%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #188      +/-   ##
==========================================
- Coverage   95.28%   94.91%   -0.38%     
==========================================
  Files          94       94              
  Lines        9316     9517     +201     
==========================================
+ Hits         8877     9033     +156     
- Misses        439      484      +45     

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