A parallel two-level hybrid method for diagonal dominant tridiagonal systems

A new method, namely the Parallel Two-Level Hybrid (PTH) method, is developed to solve tridiagonal systems on parallel computers. PTH is designed based on Parallel Diagonal Dominant (PDD) algorithm. Like PDD, PTH is highly scalable. It provides accurate solutions when PDD may not be applicable and maintains a near PDD performance when the underlying machine ensemble size is large. By controlling its two-level partition, PTH can deliver optimal performance for different machine ensemble and problem sizes. Theoretical analyses and numerical experiments indicate that PTH is significantly better than existing methods for many scientific and engineering applications.