43 citations · 97 across the 20 of their papers we have counts for
18 papers · 1 filter
Convergence Analysis of Block Newton Methods for 1D Shallow Neural Network Approximation
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper analyzes local convergence of the block Newton (BN) method introduced in [5, 6] for one-dimensional shallow neural network approximation to functions and diffusion-react…
Nodal Coarsening and Approximate Ideal Interpolation for H(curl) in Algebraic Multigrid
Taoli Shen, James Brannick, Robert Falgout +2
We propose an approximate interpolation construction and a practical coarsening algorithm for algebraic multigrid (AMG) method when applied to H(curl) problems. Building on the gen…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
Nodal AMG Coarsening and Interpolation for PDE Systems
James Brannick, Robert Falgout, Karsten Kahl +2
We present an approach to constructing a practical coarsening algorithm and interpolation operator for the algebraic multigrid (AMG) method, tailored towards systems of partial dif…
Parallel-in-time solution of hyperbolic PDE systems via characteristic-variable block preconditioning
O. A. Krzysik, H. De Sterck, R. D. Falgout +1
We consider the parallel-in-time solution of hyperbolic partial differential equation (PDE) systems in one spatial dimension, both linear and nonlinear. In the nonlinear setting, t…
Efficient Shallow Ritz Method For 1D Diffusion-Reaction Problems
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper studies the shallow Ritz method for solving one-dimensional diffusion-reaction problems. The method is capable of improving the order of approximation for non-smooth pro…
Efficient Shallow Ritz Method For 1D Diffusion Problems
Zhiqiang Cai, Anastassia Doktorova, Robert D. Falgout +1
This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatica…
Parallel-in-time solution of scalar nonlinear conservation laws
O. A. Krzysik, H. De Sterck, R. D. Falgout +1
We consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume m…
Efficient multigrid reduction-in-time for method-of-lines discretizations of linear advection
H. De Sterck, R. D. Falgout, O. A. Krzysik +1
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems.…
Multigrid Reduction in Time for Chaotic Dynamical Systems
David A. Vargas, Robert D. Falgout, Stefanie Günther +1
As CPU clock speeds have stagnated and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architect…
A New Semi-Structured Algebraic Multigrid Method
Victor A. Paludetto Magri, Robert D. Falgout, Ulrike M. Yang
Multigrid methods are well suited to large massively parallel computer architectures because they are mathematically optimal and display excellent parallelization properties. Since…
Fast multigrid reduction-in-time for advection via modified semi-Lagrangian coarse-grid operators
H. De Sterck, R. D. Falgout, O. A. Krzysik
Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs), but are inefficient or even diverge…
Toward Parallel in Time for Chaotic Dynamical Systems
David A. Vargas, Robert D. Falgout, Stefanie Günther +1
As CPU clock speeds have stagnated, and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architec…
Optimizing multigrid reduction-in-time (MGRIT) and Parareal coarse-grid operators for linear advection
Hans De Sterck, Robert D. Falgout, Stephanie Friedhoff +2
Parallel-in-time methods, such as multigrid reduction-in-time (MGRIT) and Parareal, provide an attractive option for increasing concurrency when simulating time-dependent PDEs in m…
Multilevel convergence analysis of multigrid-reduction-in-time
Andreas Hessenthaler, Ben S. Southworth, David Nordsletten +3
This paper presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori u…
Optimal interpolation and Compatible Relaxation in Classical Algebraic Multigrid
James Brannick, Fei Cao, Karsten Kahl +2
In this paper, we consider a classical form of optimal algebraic multigrid (AMG) interpolation that directly minimizes the two-grid convergence rate and compare it with the so-call…
Robust A Posteriori Error Estimation for Finite Element Approximation to H(curl) Problem
Zhiqiang Cai, Shuhao Cao, Rob Falgout
In this paper, we introduce a novel a posteriori error estimator for the conforming finite element approximation to the H(curl) problem with inhomogeneous media and with the right-…
Div First-Order System LL* (FOSLL*) for Second-Order Elliptic Partial Differential Equations
Zhiqiang Cai, Rob Falgout, Shun Zhang
The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [10], in order to retain the full efficie…