Semi-convergence analysis of preconditioned deteriorated PSS iteration method for singular saddle point problems

In this paper, we propose a two-parameter preconditioned variant of the deteriorated PSS iteration method (J. Comput. Appl. Math., 273, 41–60 (2015)) for solving singular saddle point problems. Semi-convergence analysis shows that the new iteration method is convergent unconditionally. The new iteration method can also be regarded as a preconditioner to accelerate the convergence of Krylov subspace methods. Eigenvalue distribution of the corresponding preconditioned matrix is presented, which is instructive for the Krylov subspace acceleration. Note that, when the leading block of the saddle point matrix is symmetric, the new iteration method will reduce to the preconditioned accelerated HSS iteration method (Numer. Algor., 63 (3), 521–535 2013), the semi-convergence conditions of which can be simplified by the results in this paper. To further improve the effectiveness of the new iteration method, a relaxed variant is given, which has much better convergence and spectral properties. Numerical experiments are presented to investigate the performance of the new iteration methods for solving singular saddle point problems.     

Fast solver of optimal control problems constrained by Ohta-Kawasaki equations

Numerical Algorithms - This paper is concerned with fast solver of distributed optimal control problems constrained by a nonlocal Cahn-Hilliard equation. By eliminating the control variable, a...     

A generalized variant of two-sweep modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems

Numerical Algorithms - Based on the two-sweep modulus-based matrix splitting iteration (TMMS) method for linear complementarity problems developed by Wu and Li (Comput. Appl. Math. 302:...     

On SSOR iteration method for a class of block two-by-two linear systems

In this paper, the optimal iteration parameters of the symmetric successive overrelaxation (SSOR) method for a class of block two-by-two linear systems are obtained, which result in optimal convergence factor. An accelerated variant of the SSOR (ASSOR) method is presented, which significantly improves the convergence rate of the SSOR method. Furthermore, a more practical way to choose iteration parameters for the ASSOR method has also been proposed. Numerical experiments demonstrate the efficiency of the SSOR and ASSOR methods for solving a class of block two-by-two linear systems with the optimal parameters.     

极低温散粒噪声测试系统及隧道结噪声测量

介观体系输运过程中载流子的离散性导致了散粒噪声.通过测量散粒噪声可以得到传统的基于时间平均值的电导测量无法得到的随时间涨落信息,因而作为一种重要手段在极低温量子输运研究中得到了一定的应用.极低温环境下的噪声测量是一种难度很大的极端条件下的微弱信号测量,通常需要在低温端安装前置放大器并且尽量靠近待测器件以提高测量信噪比和带宽,因此对放大器的噪声水平和功耗都有严格的要求.提出了在稀释制冷机内搭建的散粒噪声测量系统,以及利用此套系统得到了在mK温区超导隧道结散粒噪声的测量结果.自行研制的高电子迁移率晶体管低温前置放大器采用整体封装,便于安装在商用干式稀释制冷机的4 K温区,本底电压噪声为0.25 nV/√Hz,功耗仅为0.754 mW.通过对隧道结进行散粒噪声测量,得到的Fano因子和理论计算吻合.     

A robust structured preconditioner for time-harmonic parabolic optimal control problems

We consider the iterative solution of optimal control problems constrained by the time-harmonic parabolic equations. Due to the time-harmonic property of the control equations, a suitable discretization of the corresponding optimality systems leads to a large complex linear system with special two-by-two block matrix of saddle point form. For this algebraic system, an efficient preconditioner is constructed, which results in a fast Krylov subspace solver, that is robust with respect to the mesh size, frequency, and regularization parameters. Furthermore, the implementation is straightforward and the computational complexity is of optimal order, linear in the number of degrees of freedom. We show that the eigenvalue distribution of the corresponding preconditioned matrix leads to a condition number bounded above by 2. Numerical experiments confirming the theoretical derivations are presented, including comparisons with some other existing preconditioners.     

Robust additive block triangular preconditioners for block two-by-two linear systems

Numerical Algorithms - In this paper, a class of additive block triangular preconditioners are constructed for solving block two-by-two linear systems with symmetric positive (semi-)definite...     

新型三唑硫酮席夫碱的微波合成与结构表征

微波辐射条件下,以氨基均三唑硫醇与查尔酮为原料,通过亲核取代反应,制备了3-（4-氨基-5-巯基-3-对甲苯基均三唑-1-氮代）-1,3-二苯-1-丙酮（3）,（3）与系列芳香醛经缩合反应,合成了4种三唑硫酮席夫碱（4a-4d）.探讨了各实验因素对收率的影响,得到了优化的工艺条件：n（芳香醛）∶n（氨基三唑硫酮）=1∶1.1微波功率500W,催化剂冰醋酸2mL,反应时间4-7min,溶剂DMF,收率为65％-77％.利用IR、MS、1H NMR对目标产物进行了结构表征.     

A class of block alternating splitting implicit iteration methods for double saddle point linear systems

In the framework of a special block alternating splitting implicit (BASI) iteration scheme for generalized saddle point problems, we establish some new iteration methods for solving double saddle point problems by means of a suitable partitioning strategy. Convergence analysis of the corresponding BASI iteration methods indicates that they are convergent unconditionally under certain weak requirements for the related matrix splittings, which are satisfied directly for our specific application to double saddle point problems. Numerical examples for liquid crystal director and time-harmonic eddy current models are presented to demonstrate the efficiency of the proposed BASI preconditioners to accelerate the GMRES method.