19 citations · 19 across the 5 of their papers we have counts for
3 papers · 1 filter
Multilevel Adaptive-Rank Methods for Linear and Nonlinear Systems in the Hierarchical Tucker Format
William A. Sands, Pierson T. Guthrey, Nathan V. Roberts
We develop multilevel adaptive-rank iterative methods for the solution of linear and nonlinear systems arising from high-dimensional partial differential equations. Our contributio…
An ultraweak DPG method for viscoelastic fluids
Brendan Keith, Philipp Knechtges, Nathan V. Roberts +3
We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1,2]. In our…
A Geometric Multigrid Preconditioning Strategy for DPG System Matrices
Nathan V. Roberts, Jesse Chan
The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan [15,17] guarantees the optimality of the solution in an energy norm, and provides several featur…