SP_N Properties

• SP₁ and P₁ equations are identical.
• SP_N and P_N equations are identical in 1-D slab geometry.
• Rotationally invariant $\longrightarrow$ no ray effects.
• SP_N is a non-convergent method. It is an asymptotic approximation associated with the diffusion limit. As N $\longrightarrow$ $\infty$ , the solution doesn't necessarily converge to the true answer.
• SP_N has almost the same accuracy for lower orders as S_N if the solution is approximately locally 1-D, but is much cheaper.
• With DSA and LMFG acceleration, SP_N costs MG + G + 1 diffusion solutions for every outer iteration.
• Unlike the diffusion equation, the SP_N equations propagate information at a finite speed. For radiation, this speed approaches c from below as the order of approximation is increased.
• Order N unknowns for SP_N , vs. order N² unknowns for P_N and S_N .
• In a homogeneous region, SP_N and P_N scalar flux solutions satisfy same equation, except with different boundary conditions.