论文标题
在逐件总和运营商的特征值属性上
On an eigenvalue property of Summation-By-Parts operators
论文作者
论文摘要
逐个组合（SBP）方法提供了一种系统的方法来构建可证明的稳定数值方案。但是，许多收敛和准确性的证据都取决于SBP操作员具有特定特征值属性的假设。在本说明中，证明了与此属性有关的三个结果。首先，特征值属性不适合所有一致的NullSpace一致的SBP操作员。其次，可以通过向SBP操作员添加一个专门设计的，任意的扰动项来解决此问题而不会影响方法的准确性。第三，所有伪谱方法都满足特征值属性。
Summation-By-Parts (SBP) methods provide a systematic way of constructing provably stable numerical schemes. However, many proofs of convergence and accuracy rely on the assumption that the SBP operator possesses a particular eigenvalue property. In this note, three results pertaining to this property are proven. Firstly, the eigenvalue property does not hold for all nullspace consistent SBP operators. Secondly, this issue can be addressed without affecting the accuracy of the method by adding a specially designed, arbitrarily small perturbation term to the SBP operator. Thirdly, all pseudospectral methods satisfy the eigenvalue property.
