Preconditioning of complex symmetric linear systems with applications in optical tomography
Preconditioning of complex symmetric linear systems with applications in optical tomography
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DOI：
10.1016/j.apnum.2013.06.008
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发表时间：
2013-12
影响因子：
2.8
通讯作者：
S. Arridge;H. Egger;M. Schlottbom
中科院分区：
文献类型：
--
作者：
S. Arridge;H. Egger;M. Schlottbom
我们考虑形式为（A+ i κ B） x= y的线性系统的数值解，它在许多应用中出现，例如，在时谐声学，电磁学或辐射传输中。我们提出并分析了一类导致复杂对称迭代算子的预条件，并研究了相应的预条件迭代方法的收敛性。在对算子A和B的温和假设下，我们建立了与参数和维数无关的收敛性。然后将所提出的方法应用于求解时调和辐射传输的偶宇称公式。对于这个应用程序，我们验证了收敛分析所需的所有假设。通过数值试验验证了预条件迭代的性能。
We consider the numerical solution of linear systems of the form (A+ i κ B) x= y, which arise in many applications, eg, in time-harmonic acoustics, electromagnetics, or radiative transfer. We propose and analyze a class of preconditioners leading to complex symmetric iteration operators and investigate convergence of corresponding preconditioned iterative methods. Under mild assumptions on the operators A and B, we establish parameter and dimension independent convergence. The proposed methods are then applied to the solution of even-parity formulations of time-harmonic radiative transfer. For this application, we verify all assumptions required for our convergence analysis. The performance of the preconditioned iterations is then demonstrated by numerical tests supporting the theoretical results.