论文标题
线性隐式天才计划
Linearly implicit GARK schemes
论文作者
论文摘要
由多个物理过程驱动的系统对于许多科学和工程领域都是核心。多物理系统的时间离散化是具有挑战性的，因为不同的过程具有不同级别的刚度和特征时间尺度。多方法方法通过适当的数值方法离散每个物理过程。这些方法是适当耦合的，因此总体解决方案具有所需的准确性和稳定性。作者开发了通用结构添加剂runge-kutta（Gark）框架，该框架构建了基于runge-kutta方案的多方法。 本文构建了基于线性隐含的Rosenbrock/Rosenbrock-W方案的多途径的新的Gark-Ros/Gark-Row家族。对于普通的微分方程模型，我们使用精确或近似的雅各布人开发了具有任何数量分区的线性隐式方法的通用条件理论。我们将顺序条件理论推广到双向划分的指数-1差分 - 代数方程。该框架的应用程序包括线性隐式，线性隐式/显式和线性隐式/隐式方法。最多构建了最多四个秩序的实用高地摩尔斯和天才行李计划。
Systems driven by multiple physical processes are central to many areas of science and engineering. Time discretization of multiphysics systems is challenging, since different processes have different levels of stiffness and characteristic time scales. The multimethod approach discretizes each physical process with an appropriate numerical method; the methods are coupled appropriately such that the overall solution has the desired accuracy and stability properties. The authors developed the general-structure additive Runge-Kutta (GARK) framework, which constructs multimethods based on Runge-Kutta schemes. This paper constructs the new GARK-ROS/GARK-ROW families of multimethods based on linearly implicit Rosenbrock/Rosenbrock-W schemes. For ordinary differential equation models, we develop a general order condition theory for linearly implicit methods with any number of partitions, using exact or approximate Jacobians. We generalize the order condition theory to two-way partitioned index-1 differential-algebraic equations. Applications of the framework include decoupled linearly implicit, linearly implicit/explicit, and linearly implicit/implicit methods. Practical GARK-ROS and GARK-ROW schemes of order up to four are constructed.
