25 citations · 36 across the 9 of their papers we have counts for
9 papers
Cascading Smoothers for Multigrid
Robert I. Saye
Multigrid methods are among the most effective frameworks for solving large-scale sparse systems. However, achieving their hallmark linear scaling and rapid convergence crucially d…
On efficient multigrid solvers for mixed-degree local discontinuous Galerkin multiphase Stokes problems
Robert I. Saye
We design and investigate efficient multigrid solvers for multiphase Stokes problems discretised via mixed-degree local discontinuous Galerkin methods. Using the template of a stan…
A comparative study of efficient multigrid solvers for high-order local discontinuous Galerkin methods: Poisson, elliptic interface, and multiphase Stokes problems
Robert I. Saye
We design and investigate a variety of multigrid solvers for high-order local discontinuous Galerkin methods applied to elliptic interface and multiphase Stokes problems. Using the…
A Connected Component Labeling Algorithm for Implicitly-Defined Domains
Robert I. Saye
A connected component labeling algorithm is developed for implicitly-defined domains specified by multivariate polynomials. The algorithm operates by recursively subdividing the co…
On two conjectures concerning the ternary digits of powers of two
Robert I. Saye
Erdős conjectured that 1, 4, and 256 are the only powers of two whose ternary representations consist solely of 0s and 1s. Sloane conjectured that, except for $\{2^0,2^1,2^2,2^3,2^…
Modelling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
Vincenzo Gulizzi, Robert Saye
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-bo…
High-Order Quadrature on Multi-Component Domains Implicitly Defined by Multivariate Polynomials
Robert I. Saye
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) mult…
Fast multigrid solution of high-order accurate multi-phase Stokes problems
Robert Saye
A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple…
Efficient operator-coarsening multigrid schemes for local discontinuous Galerkin methods
Daniel Fortunato, Chris H. Rycroft, Robert Saye
An efficient -multigrid scheme is presented for local discontinuous Galerkin (LDG) discretizations of elliptic problems, formulated around the idea of separately coarsening the…