32 citations · 57 across the 16 of their papers we have counts for
11 papers · 1 filter
Stable Mesh-Free Variational Radial Basis Function Approximation for Elliptic PDEs and Obstacle Problems
Tan Phuong Dong Le, Giang Tran, Hans De Sterck
We present a comprehensive study of radial basis function (RBF) approximations for elliptic and obstacle-type boundary value problems under a variational formulation. Our focus is…
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…
Multilevel Monte Carlo methods for stochastic convection-diffusion eigenvalue problems
Tiangang Cui, Hans De Sterck, Alexander D. Gilbert +2
We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection-diffusion operator with random coefficients.…
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…
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…