Algebraic Solution

• Main Matrix System (Asymmetric Method):
  • Asymmetric - must use an asymmetric solver like GMRES, BCGS or TFQMR
  • Size is $\left(\vphantom{ 3 n_c + n_b/2 }\right.$3n_c + n_b/2$\left.\vphantom{ 3 n_c + n_b/2 }\right)$ squared
  • Maximum of 7 non-zero elements per row
• Main Matrix System (Support Operator Method):
  • Symmetric - can use CG to solve
  • Size is $\left(\vphantom{ 3 n_c + n_b/2 }\right.$3n_c + n_b/2$\left.\vphantom{ 3 n_c + n_b/2 }\right)$ squared
  • Maximum of 9 non-zero elements per row
• Preconditioner for Krylov Space methods is a Low-Order Matrix System:
  • Assume orthogonal: drop out minor directions in flux terms
  • Symmetric - can use standard CG solver
  • Size is n_c squared
  • Maximum of 5 non-zero elements per row