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.

多物理过程的数值模拟需要大量的处理器时间，尤其是在解决由于流体动力学问题而产生的条件不佳的线性系统时。本文致力于针对FireStar3D Wildfire建模代码的此类系统开发有效的并行方法。讨论和分析了两种替代方法，分别基于MILU预处理的共轭梯度法和代数多重网格。考虑了使这些方法并行化的主要困难并提出了解决方案：在第一种情况下，使用阶梯式流水线进行嵌套扭曲分解，在第二种情况下，采用了一种多色技术为强各向异性网格提供了一种新的平滑器。提出了一种新颖的准几何插值技术，用于解决多重网格中正对角线矩阵项的问题。该方法的适用性取决于其灵活性，鲁棒性和并行化能力。性能比较表明，新方法优于传统共轭梯度方法的广泛使用的变体。