11 citations · 15 across the 7 of their papers we have counts for
9 papers
Mixed precision solvers for the all-at-once Runge--Kutta discretization of the heat equation
Santolo Leveque, Luca Bergamaschi, Ángeles Martínez +1
We study the effect of mixed precision on the numerical integration of the heat equation discretized with a Runge--Kutta method in time. A full space-time discretization is applied…
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…
An Augmented Lagrangian Preconditioner for Navier--Stokes Equations with Runge--Kutta in Time
Santolo Leveque, Yunhui He, Maxim Olshanskii
We consider a Runge--Kutta method for the numerical time integration of the nonstationary incompressible Navier--Stokes equations. This yields a sequence of nonlinear problems to b…
Automatic Differentiation for All-at-once Systems Arising in Certain PDE-Constrained Optimization Problems
Santolo Leveque, James R. Maddison, John W. Pearson
An automated framework is presented for the numerical solution of optimal control problems with PDEs as constraints, in both the stationary and instationary settings. The associate…
An augmented Lagrangian preconditioner for the control of the Navier--Stokes equations
Santolo Leveque, Michele Benzi, Patrick E. Farrell
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality con…
Parallel-in-Time Solver for the All-at-Once Runge--Kutta Discretization
Santolo Leveque, Luca Bergamaschi, Ángeles Martínez +1
In this article, we derive fast and robust parallel-in-time preconditioned iterative methods for the all-at-once linear systems arising upon discretization of time-dependent PDEs.…
Parameter-Robust Preconditioning for Oseen Iteration Applied to Stationary and Instationary Navier--Stokes Control
Santolo Leveque, John W. Pearson
We derive novel, fast, and parameter-robust preconditioned iterative methods for steady and time-dependent Navier--Stokes control problems. Our approach may be applied to time-depe…
Fast Iterative Solver for the Optimal Control of Time-Dependent PDEs with Crank-Nicolson Discretization in Time
Santolo Leveque, John W. Pearson
In this article, we derive a new, fast, and robust preconditioned iterative solution strategy for the all-at-once solution of optimal control problems with time-dependent PDEs as c…
Fast Solution Methods for Convex Quadratic Optimization of Fractional Differential Equations
Spyridon Pougkakiotis, John W. Pearson, Santolo Leveque +1
In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on…