In this paper we consider an approach to improve the performance of exponential integrators/Lawson schemes in cases where the solution of a related, but usually much simpler, problem can be computed efficiently. While for implicit methods such an approach is common (e.g. by using preconditioners), for exponential integrators this has proven more challenging. Here we propose to extract a constant coefficient differential operator from advection-diffusion-reaction equations for which we are then able to compute the required matrix functions efficiently. Both a linear stability analysis and numerical experiments show that the resulting schemes can be unconditionally stable. In fact, we find that exponential integrators and Lawson schemes can have better stability properties than similarly constructed implicit-explicit schemes. We also propose new Lawson type integrators that further improve on these stability properties. The effectiveness of the approach is highlighted by a number of numerical examples in two and three space dimensions.

翻译：本文探讨了一种方法，旨在提升指数积分器/劳森格式在相关但通常更简单问题可高效求解时的性能。尽管对于隐式方法，此类做法（如使用预处理器）较为常见，但在指数积分器领域实施起来更具挑战性。我们提出从对流-扩散-反应方程中提取常系数微分算子，进而能够高效计算所需的矩阵函数。线性稳定性分析与数值实验均表明，由此生成的格式可具备无条件稳定性。事实上，我们发现指数积分器与劳森格式的稳定性优于类似构造的隐式-显式格式。此外，我们还提出了新型劳森型积分器，进一步改善了这些稳定性特性。通过若干二维与三维空间数值算例，充分验证了该方法的有效性。