Each project connects a mathematical question to methods, code, and experiments. Study in progress means linked notes exist. Planned means the scope is defined but no project results have been published.

Numerical PDE and FEM

Planned

Connect a boundary-value problem to a weak formulation, finite elements, and a sparse linear system.

PDE → weak formulation → FEM → sparse linear system

Iterative Solvers and Preconditioning

Study in progress

Follow existing steepest-descent and conjugate-gradient notes toward preconditioned Krylov methods.

Ax = b → steepest descent → CG / GMRES → preconditioning

Domain Decomposition

Planned

Study local solves, overlap, and coarse spaces as preconditioners for discretized PDEs.

Block Jacobi → ASM / RAS → two-level methods → coarse space

Parallel Sparse Computing

Planned

Connect distributed sparse operations to communication costs and reproducible scaling measurements.

Domain partition → halo exchange → SpMV → global reductions → scaling