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.

中文翻译：

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线性隐式 GARK 方案

由多个物理过程驱动的系统是许多科学和工程领域的核心。多物理场系统的时间离散化具有挑战性，因为不同的过程具有不同程度的刚度和特征时间尺度。多方法方法用适当的数值方法离散每个物理过程；这些方法被适当地耦合，使得整体解决方案具有所需的精度和稳定性特性。作者开发了通用结构加性 Runge-Kutta (GARK) 框架，该框架构建了基于 Runge-Kutta 方案的多方法。本文基于线性隐式 Rosenbrock/Rosenbrock-W 方案构建了新的 GARK-ROS/GARK-ROW 系列多方法。对于常微分方程模型，我们为具有任意数量分区的线性隐式方法开发了一般顺序条件理论，使用精确或近似雅可比行列式。我们将阶条件理论推广到双向分区索引 1 微分代数方程。该框架的应用包括解耦线性隐式、线性隐式/显式和线性隐式/隐式方法。构建了最多四阶的实用 GARK-ROS 和 GARK-ROW 方案。