9 papers
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…
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…
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…
Sum-of-norms regularized Nonnegative Matrix Factorization
Andersen Ang, Waqas Bin Hamed, Hans De Sterck
When applying nonnegative matrix factorization (NMF), the rank parameter is generally unknown. This rank, called the nonnegative rank, is usually estimated heuristically since comp…
Fast Multipole Attention: A Scalable Multilevel Attention Mechanism for Text and Images
Yanming Kang, Giang Tran, Hans De Sterck
While Transformer networks benefit from a global receptive field, their quadratic cost relative to sequence length restricts their application to long sequences and high-resolution…