适用于非线性端口哈密顿微分代数方程保结构且高效积分的广义标量辅助变量方法
A Generalized Scalar Auxiliary Variable Method for Structure-Preserving and Efficient Integration of Nonlinear port-Hamiltonian DAEs
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中文总结 AI 辅助
本文针对非线性指数1端口哈密顿微分代数方程开发了EOP-GSAV框架，提出的BDF-1/BDF-2格式保结构且高效，经数值实验验证其性能稳健，与隐式中点法、SUNDIALS IDA相比表现具竞争力。
中文摘要 AI 辅助
我们针对非线性指数1端口哈密顿微分代数方程（pH-DAEs）开发了能量最优广义标量辅助变量（EOP-GSAV）框架。利用端口哈密顿结构，我们将非线性做功项、互联项和耗散项与常数隐式核心分离。所得的BDF-1和BDF-2格式每个时间步仅需一次线性求解，且可重复使用分解结果，同时保持离散无源性和对哈密顿量的精确跟踪。我们将这些格式与配备全雅可比、修正雅可比及冻结雅可比牛顿迭代的隐式中点法进行了比较。从强状态依赖非线性应力测试到大规模基准测试的数值实验表明，这些格式表现出稳健且具竞争力的性能，在匹配精度范围内具有显著的效率提升。与SUNDIALS IDA的比较显示，尽管采用非专用的Python/SciPy实现，在相同阶数下二者的工作精度行为相当，而无限制变阶自适应IDA在高精度 regime 中速度更快。
英文摘要
We develop an energy-optimal generalized scalar auxiliary variable (EOP-GSAV) framework for nonlinear index-one port-Hamiltonian differential-algebraic equations (pH-DAEs). Exploiting the port-Hamiltonian structure, we separate the nonlinear effort, interconnection, and dissipation terms from a constant implicit core. The resulting BDF-1 and BDF-2 schemes require one linear solve per time step with a reusable factorization, while retaining discrete passivity and accurate tracking of the Hamiltonian. The schemes are compared with the implicit midpoint method equipped with full, modified, and frozen-Jacobian Newton iterations. Numerical experiments ranging from a strongly state-dependent nonlinear stress test to large-scale benchmarks demonstrate robust and competitive performance, with substantial efficiency gains in matched-accuracy regimes. A comparison with SUNDIALS IDA shows comparable work-precision behavior at equal order despite a non-specialized Python/SciPy implementation, while unrestricted variable-order adaptive IDA is faster in the high-accuracy regime.
发表机构
- University of Wuppertal（伍珀塔尔大学）
- Chemnitz University of Technology（开姆尼茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。
