221 citations · 1.4k across the 88 of their papers we have counts for
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A Direct Parallel-in-Time Quasi-Boundary Value Method for Inverse Space-Dependent Source Problems
Yi Jiang, Jun Liu, Xiang-Sheng Wang
Inverse source problems arise often in real-world applications, such as localizing unknown groundwater contaminant sources. Being different from Tikhonov regularization, the quasi-…
A well-conditioned direct PinT algorithm for first-and second-order evolutionary equations
Jun Liu, Xiang-Sheng Wang, Shu-Lin Wu +1
In this paper, we propose a direct parallel-in-time (PinT) algorithm for time-dependent problems with first- or second-order derivative. We use a second-order boundary value method…
Parallel-in-time preconditioners for the Sinc-Nyström method
Jun Liu, Shu-Lin Wu
The Sinc-Nyström method is a high-order numerical method based on Sinc basis functions for discretizing evolutionary differential equations in time. But in this method we have to s…
Fast Parallel-in-Time Quasi-Boundary Value Methods for Backward Heat Conduction Problems
Jun Liu
In this paper we proposed two new quasi-boundary value methods for regularizing the ill-posed backward heat conduction problems. With a standard finite difference discretization in…
Convergence rate for a Gauss collocation method applied to constrained optimal control
William W. Hager, Jun Liu, Subhashree Mohapatra +2
A local convergence rate is established for a Gauss orthogonal collocation method applied to optimal control problems with control constraints. If the Hamiltonian possesses a stron…