7 papers · 1 filter
On the Spectral Clustering in Algebraic Multigrid Methods
Jose Pablo Lucero Lorca, Conor McCoid, Michal Outrata
We introduce a new direct multilevel method for solving arbitrary complex square linear systems that uses a regular smoother and an arbitrary but equal number of pre- and post-smoo…
Towards a Multigrid Preconditioner Interpretation of Hierarchical Poincaré-Steklov Solvers
J. P. Lucero Lorca
We revisit the Hierarchical Poincaré-Steklov (HPS) method in a preconditioned iterative setting for variable-coefficient Helmholtz problems with impedance boundary conditions. HPS…
Towards modular Hierarchical Poincaré-Steklov solvers
Michal Outrata, José Pablo Lucero Lorca
We revisit the Hierarchical Poincaré-Steklov (HPS) method for the Poisson equation using standard Q1 finite elements, building on the original in work on HPS of Martinsson from 201…
On an efficient line smoother for the p-multigrid γ-cycle
José Pablo Lucero Lorca, Duane Rosenberg, Isidora Jankov +2
As part of the development of a Poisson solver for the spectral element discretization used in the GeoFluid Object Workbench (GeoFLOW) code, we propose a solver for the linear syst…
Should multilevel methods for discontinuous Galerkin discretizations use discontinuous interpolation operators?
Jose Pablo Lucero Lorca, Martin Jakob Gander
Multi-level preconditioners for Discontinuous Galerkin (DG) discretizations are widely used to solve elliptic equations, and a main ingredient of such solvers is the interpolation…
Optimization of two-level methods for DG discretizations of reaction-diffusion equations
José Pablo Lucero Lorca, Martin Jakob Gander
We analyze and optimize two-level methods applied to a symmetric interior penalty discontinuous Galerkin finite element discretization of a singularly perturbed reaction-diffusion…