6 papers · 1 filter
Optimal preconditioning techniques for finite volume approximation of three-dimensional conservative space-fractional diffusion equations
Wei Qu, Siu-Long Lei, Sean Y. Hon +1
A Crank-Nicolson finite volume approximation for three-dimensional conservative space-fractional diffusion equation results in large and dense three-level Toeplitz discrete linear…
An optimal preconditioner for high-order scheme arising from multi-dimensional Riesz space fractional diffusion equations with variable coefficients
Yuan-Yuan Huang, Wei Qu, Sean Y. Hon +1
In this paper, we propose an efficient method for solving multi-dimensional Riesz space fractional diffusion equations with variable coefficients. The Crank-Nicolson (CN) method is…
An optimal diagonalization-based preconditioner for parabolic optimal control problems
Sean Y. Hon, Po Yin Fung, Xue-lei Lin
In this work, we propose a novel diagonalization-based preconditioner for the all-at-once linear system arising from the optimal control problem of parabolic equations. The propose…
Symbol-based multilevel block preconditioners for multilevel block Toeplitz systems: GLT-based analysis and applications
Sean Y. Hon, Congcong Li, Rosita L. Sormani +2
In recent years, there has been a renewed interest in preconditioning for multilevel Toeplitz systems, a research field that has been extensively explored over the past several dec…
Optimal preconditioners for nonsymmetric multilevel Toeplitz systems with application to solving non-local evolutionary partial differential equations
Yuan-Yuan Huang, Sean Y. Hon, Lot-Kei Chou +1
Preconditioning for multilevel Toeplitz systems has long been a focal point of research in numerical linear algebra. In this work, we develop a novel preconditioning method for a c…
A novel fourth-order scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equations and its optimal preconditioned solver
Wei Qu, Yuan-Yuan Huang, Sean Hon +1
A novel fourth-order finite difference formula coupling the Crank-Nicolson explicit linearized method is proposed to solve Riesz space fractional nonlinear reaction-diffusion equat…