67 citations · 88 across the 20 of their papers we have counts for
22 papers
Accelerating the Computation of Tensor -eigenvalues
Sara Pollock, Rhea Shroff
Efficient solvers for tensor eigenvalue problems are important tools for the analysis of higher-order data sets. Here we introduce, analyze and demonstrate an extrapolation method…
Filtering for Anderson acceleration
Sara Pollock, Leo G. Rebholz
This work introduces, analyzes and demonstrates an efficient and theoretically sound filtering strategy to ensure the condition of the least-squares problem solved at each iteratio…
Newton-Anderson at Singular Points
Matt Dallas, Sara Pollock
In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton's method for nonlinear systems in which the Jacobian is singular at a solut…
Anderson acceleration for a regularized Bingham model
Sara Pollock, Leo G. Rebholz, Duygu Vargun
This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is the…
Extrapolating the Arnoldi Algorithm To Improve Eigenvector Convergence
Sara Pollock, L. Ridgway Scott
We consider extrapolation of the Arnoldi algorithm to accelerate computation of the dominant eigenvalue/eigenvector pair. The basic algorithm uses sequences of Krylov vectors to fo…
A simple extrapolation method for clustered eigenvalues
Nilima Nigam, Sara Pollock
This paper introduces a simple variant of the power method. It is shown analytically and numerically to accelerate convergence to the dominant eigenvalue/eigenvector pair; and, it…
Acceleration of nonlinear solvers for natural convection problems
Sara Pollock, Leo G. Rebholz, Mengying Xiao
This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. Aft…
Fast convergence to higher multiplicity zeros
Sara Pollock
In this paper, the Newton-Anderson method, which results from applying an extrapolation technique known as Anderson acceleration to Newton's method, is shown both analytically and…
Benchmarking results for the Newton-Anderson method
Sara Pollock, Hunter Schwartz
This paper primarily presents numerical results for the Anderson accelerated Newton method on a set of benchmark problems. The results demonstrate superlinear convergence to soluti…
Anderson acceleration for contractive and noncontractive operators
Sara Pollock, Leo Rebholz
A one-step analysis of Anderson acceleration with general algorithmic depths is presented. The resulting residual bounds within both contractive and noncontractive settings reveal…
Online basis construction for goal-oriented adaptivity in the Generalized Multiscale Finite Element Method
Eric T. Chung, Sara Pollock, Sai-Mang Pun
In this research, we develop an online enrichment framework for goal-oriented adaptivity within the generalized multiscale finite element method for flow problems in heterogeneous…
Anderson-accelerated convergence of Picard iterations for incompressible Navier-Stokes equations
Sara Pollock, Leo G. Rebholz, Mengying Xiao
We propose, analyze and test Anderson-accelerated Picard iterations for solving the incompressible Navier-Stokes equations (NSE). Anderson acceleration has recently gained interest…
A proof that Anderson acceleration improves the convergence rate in linearly converging fixed point methods (but not in those converging quadratically)
Claire Evans, Sara Pollock, Leo G. Rebholz +1
This paper provides the first proof that Anderson acceleration (AA) improves the convergence rate of general fixed point iterations. AA has been used for decades to speed up nonlin…
A matrix analysis approach to discrete comparison principles for nonmonotone PDE
Sara Pollock, Yunrong Zhu
We consider a linear algebra approach to establishing a discrete comparison principle for a nonmonotone class of quasilinear elliptic partial differential equations. In the absence…
Discrete comparison principles for quasilinear elliptic PDE
Sara Pollock, Yunrong Zhu
Comparison principles are developed for discrete quasilinear elliptic partial differential equations. We consider the analysis of a class of nonmonotone Leray-Lions problems featur…
Pseudo-time regularization for PDE with solution-dependent diffusion
Sara Pollock
This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence…
Goal-oriented adaptivity for GMsFEM
Eric T. Chung, Wing Tat Leung, Sara Pollock
In this paper we develop two goal-oriented adaptive strategies for a posteriori error estimation within the generalized multiscale finite element framework. In this methodology, on…
Stabilized and inexact adaptive methods for capturing internal layers in quasilinear PDE
Sara Pollock
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution proc…
An improved method for solving quasilinear convection diffusion problems on a coarse mesh
Sara Pollock
A method is developed for solving quasilinear convection diffusion problems starting on a coarse mesh where the data and solution-dependent coefficients are unresolved, the problem…
A regularized Newton-like method for nonlinear PDE
Sara Pollock
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existe…
Convergence of Goal-Oriented Adaptive Finite Element Methods for Semilinear Problems
Michael Holst, Sara Pollock, Yunrong Zhu
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly…
Convergence of Goal-Oriented Adaptive Finite Element Methods for Nonsymmetric Problems
Michael Holst, Sara Pollock
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular…