Direction

I am interested in how the structure of a PDE and its discretization determines the solver, preconditioner, and parallel implementation. The current archive establishes mathematical prerequisites and the first iterative-solver notes. It does not yet contain a completed FEM/DD/MPI experiment campaign.

Stage	Current evidence	Next question
Foundations	Measure theory and convergence	Which functional-analytic assumptions are needed for a weak formulation?
Numerical methods	Floating-point arithmetic	How do stability and discretization error interact?
Solvers	Steepest descent and CG	How does preconditioning change convergence and cost?
Parallel computing	Planned sparse-computing project	When do communication and global reductions dominate?

Experimental records

Each experiment should identify the question, mathematical assumptions, code repository and commit, machine and software environment, input data, exact command, accuracy criterion, and measured result. Failed or inconclusive experiments belong in the record too.

Timing results will include the number of repetitions and an aggregation rule. Solver comparisons will report stopping criteria and residual definitions alongside iteration counts. Scaling reports will distinguish strong from weak scaling and computation from communication.

No experiment reports or research logs are published yet. The project indexes identify the planned milestones.