论文标题
具有结构性正交化的Arnoldi算法
Arnoldi algorithms with structured orthogonalization
论文作者
论文摘要
我们研究了在大规模递送网络（PDN）的时域模拟中，用于基质指数的稳定性保留的Arnoldi算法，该算法被称为半明确的差分代数方程（DAES）。该解决方案可以分解为两个预测的总和，一个在系统操作员的范围内，另一个在其空空间中。范围投影可以使用一个移位和插入Krylov子空间方法计算。可以使用代数方程计算另一个投影。与普通的Arnoldi方法不同，Krylov子空间中的正交性被阳性半限定系统操作员诱导的半成分产品取代。通过适当的调整，Krylov操作员的数值范围位于右半平面，我们在计算PHI功能中的修改后的Arnoldi算法获得了理论收敛分析。最后，证明了RLC网络上的模拟，以验证具有结构性正交化的Arnoldi算法的有效性。
We study a stability preserved Arnoldi algorithm for matrix exponential in the time domain simulation of large-scale power delivery networks (PDN), which are formulated as semi-explicit differential algebraic equations (DAEs). The solution can be decomposed to a sum of two projections, one in the range of the system operator and the other in its null space. The range projection can be computed with one shift-and -invert Krylov subspace method. The other projection can be computed with the algebraic equations. Differing from the ordinary Arnoldi method, the orthogonality in the Krylov subspace is replaced with the semi-inner product induced by the positive semi-definite system operator. With proper adjustment, numerical ranges of the Krylov operator lie in the right half plane, and we obtain theoretical convergence analysis for the modified Arnoldi algorithm in computing phi-functions. Lastly, simulations on RLC networks are demonstrated to validate the effectiveness of the Arnoldi algorithm with structured-orthogonalization.
