6 papers
Spectral analysis of a class of IRK stage preconditioners for linear wave equations
Michal Outrata, Aman Rani
We lay out the analysis of the ``Kronecker preconditioners'' adopted in [24] for the linear wave equations. Importantly, we deliver the analysis justifying the claims in~[24, Secti…
Domain Decomposition for Mean Curvature Flow of Surface Polygonal Meshes
Lenka Ptackova, Michal Outrata
We examine the use of domain decomposition for potentially more efficient mean curvature flow of surface meshes, whose faces are arbitrary simple polygons. We first test traditiona…
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 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 the recent advances of spectral analysis for systems arising from fully-implicit RK methods
Michal Outrata
This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equation…
Multiprecision computations with Schwarz methods
Michal Outrata, Daniel B. Szyld
Schwarz methods and preconditioners, where the approximate solution of the local problems is performed at a lower precision, i.e., with fewer digits of accuracy than in the underly…