Add iterative solver methods to sparse solver module

[krystophny]

Summary

Add iterative solver options (BiCGSTAB, GMRES, IDR(s)) to the sparse solver module as alternatives to direct methods for solving Ax=b systems.

Background

Currently the sparse solver only supports direct methods (UMFPACK/SuperLU). Iterative methods can be more efficient for certain problem types and sizes.

Dependencies

• Depends on Refactor sparse solver modules for better modularity and testability #44 (sparse solver refactoring) for clean modular structure
• Depends on Add testing and code coverage infrastructure #50 (testing infrastructure) for proper test coverage

Tasks

• Add BiCGSTAB implementation for sparse linear systems
• Add GMRES implementation for sparse linear systems
• Add IDR(s) implementation for sparse linear systems
• Add ILU(0) and ILU(k) preconditioning
• Create solver selection interface
• Add convergence monitoring
• Comprehensive testing of each method
• Performance benchmarking vs direct methods

Implementation Strategy

1. Build on top of Refactor sparse solver modules for better modularity and testability #44 (modular sparse solver structure)
2. Add iterative methods one at a time with full test coverage
3. Each method should be drop-in replacement for direct solver
4. Use same sparse matrix format and interface
5. Add solver selection parameter

Benefits

• More efficient for large sparse systems
• Better memory scaling
• User can choose best method for their problem
• Foundation for using these methods in ripple solver (Add iterative solver options (BiCGSTAB, GMRES, IDR(s)) to ripple solver #47, Replace nested sparse solver calls in ripple solver with direct iterative methods #49)

Testing Requirements

• Unit tests for each iterative method
• Convergence tests with different matrix types
• Accuracy comparison with direct methods
• Performance benchmarks
• Code coverage > 90%

Related Work

• Work can be extracted from bicgstab branch (iterative solver implementations)
• Will be used by Add iterative solver options (BiCGSTAB, GMRES, IDR(s)) to ripple solver #47 and Replace nested sparse solver calls in ripple solver with direct iterative methods #49 for ripple solver