Parallel modeling of wildfires using efficient solvers for ill-conditioned linear systems

Abstract

Numerical simulation of multi-physical processes requires a lot of processor time, especially when solving ill-conditional linear systems arising in fluid dynamics problems. This paper is devoted to the development of efficient parallel methods for such systems for FireStar3D wildfire modeling code. Two alternative approaches are discussed and analyzed, based on the MILU-preconditioned conjugate gradient method and on the algebraic multigrid, respectively. The main difficulties of parallelizing these methods are considered and solutions are presented: in the first case, nested twisted factorization with a staircase pipelining, and in the second, a multicolor technique for a new smoother for strongly anisotropic grids. A novel quasi-geometric interpolation technique is presented for solving the problem of positive off-diagonal matrix entries in the multigrid. The limits of applicability of the methods are determined depending on their flexibility, robustness and parallelization capabilities. The performance comparison demonstrates the superiority of the new methods over the widely used variants of the traditional conjugate gradient method.