arXiv subjects

Michal Outrata

Publications and source records attributed to Michal Outrata.

5 recordsLinked to original sources

arXiv2026

Domain Decomposition for Mean Curvature Flow of Surface Polygonal Meshes

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 traditional domain decomposition methods with and without overlap of deconstructed domains. And we present adapted Robin transmission conditions of optimized Schwarz method. We then analyze the resulting smoothing from the point of view of shape quality and texture deformation. By decomposing the initial mesh into two sub-meshes, we solve two smaller boundary value problems instead of one big problem, and we can process these two tasks almost entirely in parallel.

math.NA↗

arXiv2025

On the Spectral Clustering in Algebraic Multigrid Methods

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-smoothings. Through careful analysis of the error propagation operator, we cluster the spectrum of this operator. This allows us to write a direct K-cycle version of the method.

math.NA↗

arXiv2025

Towards modular Hierarchical Poincar\'{e}-Steklov solvers

We revisit the Hierarchical Poincar\'{e}-Steklov (HPS) method for the Poisson equation using standard Q1 finite elements, building on the original in work on HPS of Martinsson from 2013. While corner degrees of freedom were implicitly handled in that work, subsequent spectral-element implementations have typically avoided them. In Q1-FEM, however, corner coupling cannot be factored out, and we show how the HPS merge procedure naturally accommodates it when corners are enclosed by elements. This clarification bridges a conceptual gap between algebraic Schur-complement methods and operator-based formulations, providing a consistent path for the FEM community to adopt HPS to retain the Poincar\'{e}-Steklov interpretation at both continuous and discrete levels.

math.NA↗

arXiv2025

On the recent advances of spectral analysis for systems arising from fully-implicit RK methods

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 equations. These were applied for different formulations of the same problem and used different tools to arrive at results that do not immediately coincide. We show the equivalence of the results as well as the equivalence of the approaches, unifying the two directions.

math.NA↗

arXiv2025

Multiprecision computations with Schwarz methods

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 underlying (double precision) computation. Conditions for the appropriate round-off criteria for the lower precision are presented. It is found experimentally that for the model problems about 5 digits of accuracy are sufficient to achieve the theoretical restrictions, and thus, single precision suffices for the local solves. Several numerical experiments illustrate the obtained results.

math.NA↗