32 citations · 51 across the 21 of their papers we have counts for
21 papers
Broken-space Additive Schwarz Mass Inverse Approximations and (Block) Preconditioning
Oliver A. Krzysik, Ben S. Southworth, Golo A. Wimmer
Finite-element mass matrix solves and approximate inverses arise often in explicit time integration as well as Schur-complement-based block preconditioning. A diagonal approximatio…
A black-box, multilevel algebraic preconditioning framework for conforming finite elements
O. A. Krzysik, B. S. Southworth, G. A. Wimmer
Recently we introduced the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) method as a multilevel, algebraic preconditioner for sparse symmetric positive definit…
Two-level convergence of Algebraic Multigrid with Overlapping Smoothers and Spectral Coarse Grids
O. A. Krzysik, B. S. Southworth, H. Al Daas
We recently developed the least-squares algebraic-multigrid domain-decomposition (LS-AMG-DD) solver as an algebraic multilevel method for sparse symmetric positive definite matrice…
Parallel-in-iteration optimization using multigrid reduction-in-time
G. H. M. Araújo, O. A. Krzysik, H. De Sterck
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowl…
Optimal transfer operators in algebraic two-level methods for nonsymmetric and indefinite problems
Oliver A. Krzysik, Ben S. Southworth, Golo A. Wimmer +3
Consider an algebraic two-level method applied to the -dimensional linear system using fine-space preconditioner (i.e., ``relaxation'' or ``smoother'…
Generalized Optimal AMG Convergence Theory for Stokes Equations Using Smooth Aggregation and Vanka Relaxation Strategies
Ahsan Ali, James J. Brannick, Karsten Kahl +4
This paper discusses our recent generalized optimal algebraic multigrid (AMG) convergence theory applied to the steady-state Stokes equations discretized using Taylor-Hood elements…
Overlapping Schwarz methods are not anisotropy-robust multigrid smoothers
Oliver A. Krzysik, Ben S. Southworth, Bobby Philip
We analyze overlapping multiplicative Schwarz methods as smoothers in the geometric multigrid solution of two-dimensional anisotropic diffusion problems. For diffusion equations, i…
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…
First-order PDES for Graph Neural Networks: Advection And Burgers Equation Models
Yifan Qu, Oliver Krzysik, Hans De Sterck +1
Graph Neural Networks (GNNs) have established themselves as the preferred methodology in a multitude of domains, ranging from computer vision to computational biology, especially i…
Generalized Optimal AMG Convergence Theory for Nonsymmetric and Indefinite Problems
Ahsan Ali, James Brannick, Karsten Kahl +3
Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is wel…
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…
Asymptotic convergence of restarted Anderson acceleration for certain normal linear systems
Oliver A. Krzysik, Hans De Sterck, Adam Smith
Anderson acceleration (AA) is widely used for accelerating the convergence of an underlying fixed-point iteration , , with $\…
Constrained Local Approximate Ideal Restriction for Advection-Diffusion Problems
Ahsan Ali, James Brannick, Karsten Kahl +3
This paper focuses on developing a reduction-based algebraic multigrid method that is suitable for solving general (non)symmetric linear systems and is naturally robust from pure a…
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 convergence for advection problems: A Fourier analysis perspective
H. De Sterck, S. Friedhoff, O. A. Krzysik +1
A long-standing issue in the parallel-in-time community is the poor convergence of standard iterative parallel-in-time methods for hyperbolic partial differential equations (PDEs),…
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…
Anderson Acceleration as a Krylov Method with Application to Asymptotic Convergence Analysis
Hans De Sterck, Yunhui He, Oliver A. Krzysik
Anderson acceleration (AA) is widely used for accelerating the convergence of nonlinear fixed-point methods , , but little is known about ho…
Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part II: nonlinearities and DAEs
Ben S. Southworth, Oliver Krzysik, Will Pazner
Fully implicit Runge-Kutta (IRK) methods have many desirable accuracy and stability properties as time integration schemes, but high-order IRK methods are not commonly used in prac…
Fast solution of fully implicit Runge-Kutta and discontinuous Galerkin in time for numerical PDEs, Part I: the linear setting
Ben S. Southworth, Oliver Krzysik, Will Pazner +1
Fully implicit Runge-Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly…
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…
On selecting coarse-grid operators for Parareal and MGRIT applied to linear advection
Oliver A. Krzysik, Hans De Sterck, Scott P. MacLachlan +1
We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a b…