论文标题
最小$ \ ell^2 $ norm norm iNDIPLIER方法
Minimal $\ell^2$ Norm Discrete Multiplier Method
论文作者
论文摘要
我们对离散的乘数方法（DMM）介绍了一个扩展，称为最小$ \ ell_2 $ norm norm norm norm norm Indiple乘数方法（MN-DMM），其中为具有多个保守数量的动力学系统的保守有限差差方案在程序上是按程序构建的，而不是在分析上如原始DMM中的分析构建。对于具有多个保守量的大型动力学系统，MN-DMM减轻了原始DMM在构建满足离散乘数条件的保守方案时可能引起的困难。特别是，MN-DMM利用离散乘数矩阵的右Moore-Penrose Pseudoinverse来解决与离散乘数条件相关的不确定的最小平方问题。我们证明了MN-DMM方案的一致性和保守性。我们还使用单数值分解引入了两个变体 - 混合Mn -DMM和Mn -DMM-并在实践中讨论它们的用法。此外，与原始DMM相比，有关数学科学引起的各种问题的数值示例及其相对易于实现，证明了MN-DMM的广泛适用性。
We introduce an extension to the Discrete Multiplier Method (DMM), called Minimal $\ell_2$ Norm Discrete Multiplier Method (MN-DMM), where conservative finite difference schemes for dynamical systems with multiple conserved quantities are constructed procedurally, instead of analytically as in the original DMM. For large dynamical systems with multiple conserved quantities, MN-DMM alleviates difficulties that can arise with the original DMM at constructing conservative schemes which satisfies the discrete multiplier conditions. In particular, MN-DMM utilizes the right Moore-Penrose pseudoinverse of the discrete multiplier matrix to solve an underdetermined least-square problem associated with the discrete multiplier conditions. We prove consistency and conservative properties of the MN-DMM schemes. We also introduce two variants - Mixed MN-DMM and MN-DMM using Singular Value Decomposition - and discuss their usage in practice. Moreover, numerical examples on various problems arising from the mathematical sciences are shown to demonstrate the wide applicability of MN-DMM and its relative ease of implementation compared to the original DMM.
