We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages special splitting and interpolation schemes, providing iterative algorithm with a large degree of parallelization possibilities. We combine that algorithm with the finite element method to solve obtained one-dimensional problems, but in fact, it can be combined also with other discretization methods, like finite volume or finite difference methods.

翻译：本文提出一种求解二维非定常与定常对流-扩散-反应边值问题的方法，其核心思想是将原问题转化为一系列对应的一维问题进行求解。该方法利用特殊的分裂格式与插值格式，构建出具有高度并行化潜力的迭代算法。我们将该算法与有限元方法相结合以求解所得的一维问题，但实际上该方法亦可与其他离散化方法（如有限体积法或有限差分法）结合使用。