15 citations · 28 across the 7 of their papers we have counts for
7 papers
A nearly optimal explicitly-sparse representation for oscillatory kernels with curvelet-like functions
Yanchuang Cao, Jun Liu, Dawei Chen
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are co…
Smoothing analysis of two robust multigrid methods for elliptic optimal control problems
Yunhui He, Jun Liu
In this paper we study and compare two multigrid relaxation schemes with coarsening by two, three, and four for solving elliptic sparse optimal control problems with control constr…
A ROM-accelerated parallel-in-time preconditioner for solving all-at-once systems from evolutionary PDEs
Jun Liu, Zhu Wang
In this paper we propose to use model reduction techniques for speeding up the diagonalization-based parallel-in-time (ParaDIAG) preconditioner, for iteratively solving all-at-once…
Non-commutative Discretize-then-Optimize Algorithms for Elliptic PDE-Constrained Optimal Control Problems
Jun Liu, Zhu Wang
In this paper, we analyze the convergence of several discretize-then-optimize algorithms, based on either a second-order or a fourth-order finite difference discretization, for sol…
Efficient Time Domain Decomposition Algorithms for Parabolic PDE-Constrained Optimization Problems
Jun Liu, Zhu Wang
Optimization with time-dependent partial differential equations (PDEs) as constraints {appears} in many science and engineering applications. The associated first-order necessary o…
A multigrid scheme for 3D Monge-Ampère equations
Jun Liu, Brittany D. Froese, Adam M. Oberman +1
The elliptic Monge-Ampère equation is a fully nonlinear partial differential equation which has been the focus of increasing attention from the scientific computing community. Fast…
Rank-one Characterization of Joint Spectral Radius of Finite Matrix Family
Jun Liu, Mingqing Xiao
In this paper we study the joint/generalized spectral radius of a finite set of matrices in terms of its rank-one approximation by singular value decomposition. In the first part o…