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Vanka-smoothed shifted Laplacian multigrid preconditioners for the Helmholtz equations
Rachel Yovel, Yunhui He, Eran Treister
We present an improved multigrid preconditioner for the acoustic Helmholtz equation with enhanced scalability. Standard multigrid fails to converge for the Helmholtz equation, and…
A generalized alternating NGMRES method for PDE-constrained optimization problems governed by transport equations
Yunhui He, Andreas Mang
In this work, we propose a generalized alternating nonlinear generalized minimal residual method (GA-NGMRES) to accelerate first-order optimization schemes for PDE-constrained opti…
Implicit-Explicit Scheme with Multiscale Vanka Two-Grid Solver for Heterogeneous Unsaturated Poroelasticity
Maria Vasilyeva, Ben S. Southworth, Yunhui He +1
We consider a coupled nonlinear system of equations that describe unsaturated flow in heterogeneous poroelastic media. For the numerical solution, we use a finite element approxima…
A Generalized Alternating Anderson Acceleration Method
Yunhui He, Santolo Leveque
In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of fixed-point iteration steps, interleaved with steps of Anders…
Convergence Analysis of An Alternating Nonlinear GMRES on Linear Systems
Yunhui He
In this work, we develop an alternating nonlinear Generalized Minimum Residual (NGMRES) algorithm with depth and periodicity , denoted by aNGMRES(), applied to linear…
Convergence Properties of Nonlinear GMRES Applied to Linear Systems
Chen Greif, Yunhui He
The Nonlinear GMRES (NGMRES) proposed by Washio and Oosterlee [Electron. Trans. Numer. Anal, 6(271-290), 1997] is an acceleration method for fixed point iterations. It has been dem…
The worst-case root-convergence factor of GMRES(1)
Yunhui He
In this work, we analyze the asymptotic convergence factor of minimal residual iteration (MRI) (or GMRES(1)) for solving linear systems based on vector-dependent nonlinear e…
Convergence Analysis for Nonlinear GMRES
Yunhui He
In this work, we revisit nonlinear generalized minimal residual method (NGMRES) applied to nonlinear problems. NGMRES is used to accelerate the convergence of fixed-point iteration…