ON OPTIMAL CONVERGENCE RATE OF THE RATIONAL KRYLOV SUBSPACE REDUCTION FOR ELECTROMAGNETIC PROBLEMS IN UNBOUNDED DOMAINS

Knizhnerman L; Druskin V; Zaslavsky M

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ON OPTIMAL CONVERGENCE RATE OF THE RATIONAL KRYLOV SUBSPACE REDUCTION FOR ELECTROMAGNETIC PROBLEMS IN UNBOUNDED DOMAINS

机译：有界域中电磁问题的有理Krylov子空间约简的最优收敛速度

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摘要

We solve an electromagnetic frequency domain induction problem in R-3 for a frequency interval using rational Krylov subspace (RKS) approximation. The RKS is constructed by spanning on the solutions for a certain a priori chosen set of frequencies. We reduce the problem of the optimal choice of these frequencies to the third Zolotaryov problem in the complex plane, having an approximate closed form solution, and determine the best Cauchy-Hadamard convergence rate. The theory is illustrated with numerical examples for Maxwell's equations arising in 3D magnetotelluric geophysical exploration.

机译：我们使用有理Krylov子空间（RKS）逼近来解决R-3中某个频率间隔的电磁频域感应问题。 RKS是通过在解决方案上跨过某些先验选择的频率集而构建的。我们将这些频率的最佳选择问题简化为复杂平面中的第三个Zolotaryov问题，具有近似的封闭形式解，并确定最佳柯西-哈达玛收敛速度。通过在3D大地电磁地球物理勘探中产生的Maxwell方程的数值示例来说明该理论。

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《SIAM Journal on Numerical Analysis》 |2010年第2期|共19页
作者
Knizhnerman L; Druskin V; Zaslavsky M;
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正文语种 eng
中图分类数值分析;
关键词
frequency domain problems; Galerkin method; third Zolotaryov problem in complex plane;

机译：频域问题;Galerkin方法;复平面中的第三个Zolotaryov问题;

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1. ON OPTIMAL CONVERGENCE RATE OF THE RATIONAL KRYLOV SUBSPACE REDUCTION FOR ELECTROMAGNETIC PROBLEMS IN UNBOUNDED DOMAINS [J] . Knizhnerman L, Druskin V, Zaslavsky M SIAM Journal on Numerical Analysis . 2010,第2期

机译：有界域中电磁问题的有理Krylov子空间约简的最优收敛速度
2. The effect of non-optimal bases on the convergence of Krylov subspace methods [J] . Simoncini V, Szyld DB Numerische Mathematik . 2005,第4期

机译：非最优基对Krylov子空间方法收敛性的影响
3. The effect of non-optimal bases on the convergence of Krylov subspace methods [J] . Valeria Simoncini, Daniel B. Szyld Numerische Mathematik . 2005,第4期

机译：非最优基对Krylov子空间方法收敛的影响
4. Efficient computation of electromagnetic wave fields on unbounded domains using stability-corrected wave functions and Krylov subspace projection methods [C] . Druskin V., Remis R.F., Zaslavsky M., International Conference on Electromagnetics in Advanced Applications . 2015

机译：使用稳定校正波函数和Krylov子空间投影方法有效地计算无限域上的电磁波场
5. Electromagnetic characterisation of structures using Krylov subspace model order reduction methods [D] . Maciver, Mark Alasdair. 2003

机译：使用Krylov子空间模型降阶方法对结构进行电磁表征
6. Convergence of Password Guessing to Optimal Success Rates [O] . Hazel Murray, David Malone 2020

机译：密码收敛猜测最佳成功率
7. 4 An Extended Krylov Subspace Model-Order Reduction Technique to Simulate Wave Propagation in Unbounded Domains [O] . Vladimir Druskin, Rob Remis 2016

机译：4扩展Krylov子空间模型降阶技术模拟无界域中的波传播
8. GEOMETRIC OVER CONVERGENCE OF RATIONAL FUNCTIONS IN UNBOUNDED DOMAINS [R] . E. B. SAFF, R. S. VARGA 1976

机译：无界区域中有理函数收敛的几何

ON OPTIMAL CONVERGENCE RATE OF THE RATIONAL KRYLOV SUBSPACE REDUCTION FOR ELECTROMAGNETIC PROBLEMS IN UNBOUNDED DOMAINS

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