Fast convergence of SPH numerical solutions using robust algebraic multilevel

In our study we solve 2D equations that model the mathematical phenomenon of steady state heat diffusion. The discretization of the equations is performed with the smoothed particle hydrodynamics (SPH) method and the resolution of the associated system of linear equations is determined with a modified solver that we call the Gauss–Seidel–Silva (G–S–S). The single level parallel G–S–S solver is compared to the algebraic multilevel (AML) with serial G–S–S smoother which has the ability to smooth the error of the numerical solutions and accelerate convergence due to its iterative formulation. The AML with serial G–S–S smoother is responsible for determining speed-ups of 4084 times for uniform and 5136 times for non-uniform particle discretization. We estimate a speed-up of 41082 times for the AML with parallel G–S–S smoother.