Accelerating the solution of the SN equations with highly anisotropic scattering using the Fokker-Planck approximation

Modified Fokker-Planck Acceleration for Forward-Peaked Transport Problems in Slab Geometry

“…In the FPSA scheme (Patel et al 2020;Patel 2016), the FP approximation is used to synthetically accelerate convergence when solving Equation (2.1) (cf. (Adams and Larsen 2002) for a detailed description of synthetic acceleration).…”

“…The main advantage of setting up the solver in this fashion is that the stiff matrix for LO needs to be setup and inverted only once, just as with FPSA (Patel et al 2020;Patel 2016). This has a significant impact on the method's performance.…”

“…For these problems, solutions of the transport equation converge slowly when using conventional methods such as source iteration (SI) (Adams and Larsen 2002) and the generalized minimal residual method (GMRES) (Saad and Schultz 1986). Moreover, diffusion-based acceleration techniques like diffusion synthetic acceleration (DSA) (Alcouffe 1977) and nonlinear diffusion acceleration (NDA) (Knoll et al 2011) are generally inefficient when tackling these problems, as they only accelerate up to the first moment of the angular flux (Patel et al 2020). Higher order moments carry important information in problems with highly forward-peaked scattering and can be used to further accelerate convergence (Patel 2016).…”

“…One of the most recent convergence methods developed is Fokker-Planck Synthetic Acceleration (FPSA) (Patel et al 2020;Patel 2016). FPSA accelerates up to N moments of the angular flux and has shown significant improvement in the convergence rate for the types of problems described above.…”

“…FPSA accelerates up to N moments of the angular flux and has shown significant improvement in the convergence rate for the types of problems described above. The method returns a speed-up of several orders of magnitude with respect to wall-clock time when compared to DSA (Patel et al 2020).…”