Guaranteed two-sided bounds on all eigenvalues of preconditioned diffusion and elasticity problems solved by the finite element method

针对具有弱奇异核的非局部演化方程线性系统的单侧全预条件

A single-sided all-at-once preconditioning for linear system from a non-local evolutionary equation with weakly singular kernels

本文将非局部演化方程的双侧预条件合并为单侧预条件，通过快速可对角化矩阵近似空间矩阵，理论上证明单侧预条件GMRES方法收敛速率不劣于双侧，且总计算时间更少。

时间离散采用θ-方法的一类演化偏微分方程的高效预条件子

An efficient preconditioner for evolutionary partial differential equations with $θ$-method in time discretization

本文针对θ-方法时间离散的演化偏微分方程，提出一种可时间并行实现的高效单侧预条件子，并通过双侧预条件系统的条件数一致有界性证明保证GMRES收敛，数值实验验证了其有效性与鲁棒性。

预条件迭代法用于时空分数阶对流-扩散方程

Preconditioned iterative methods for space-time fractional advection-diffusion equations

本文提出了解决时空分数阶对流-扩散方程初值边界问题的数值方法，采用隐式方法和预条件GMRES、CGNR方法，利用快速傅里叶变换提高计算效率，通过数值实验验证了预条件器的有效性。

A parallel-in-time two-sided preconditioning for all-at-once system from a non-local evolutionary equation with weakly singular kernel

In this paper, we study a parallel-in-time (PinT) algorithm for all-at-once system from a non-local evolutionary equation with weakly singular kernel where the temporal term involves a non-local convolution with a weakly singular kernel and the spatial term is the usual Laplacian operator with variable coefficients. We propose to use a two-sided preconditioning technique for the all-at-once discretization of the equation. Our preconditioner is constructed by replacing the variable diffusion coefficients with a constant coefficient to obtain a constant-coefficient all-at-once matrix. We split a…

一种用于对称特征值问题的混合精度预条件雅可比方法

A mixed precision preconditioned Jacobi method for the symmetric eigenvalue problem

针对对称特征值问题，提出混合精度预条件雅可比方法，结合低精度特征分解与高精度正交化生成初始猜测，完成误差分析并拓展至奇异值问题，实验验证其效率优于原始雅可比方法。

随机伽辽金方法中参数依赖近不可压缩线性弹性方程的鲁棒预处理

Robust preconditioning for stochastic Galerkin formulations of parameter-dependent nearly incompressible linear elasticity equations

本文研究了具有不确定空间变化杨氏模量的近不可压缩线性弹性问题，提出了一种新的三场混合变分公式，并利用随机伽辽金混合有限元技术进行近似，同时引入了适用于最小残差法（MINRES）的新型预处理器，证明了预处理后的系统特征值界与离散参数和泊松比无关。