arXiv subjects

Minah Oh

Publications and source records attributed to Minah Oh.

3 recordsLinked to original sources

arXiv2020

The Hodge Laplacian on Axisymmetric Domains and its Discretization

We study the mixed formulation of the abstract Hodge Laplacian on axisymmetric domains with general data through Fourer-finite-element-methods in weighted functions spaces. Closed Hilbert complexes and commuting projectors are used through a family of finite element spaces recently introduced for general axisymmetric problems. In order to get stability results and error estimates for the discrete mixed formulation, we construct commuting projectors that can be applied to functions with low regularity.

math.NA↗

arXiv2019

Multigrid in H(div) on Axisymmetric Domains

In this paper, we will construct and analyze a multigrid algorithm that can be applied to weighted H(div)-problems on a two-dimensional domain. These problems arise after performing a dimension reduction to a three-dimensional axisymmetric H(div)-problem. We will use recently developed Fourier finite element spaces that can be applied to axisymmetric H(div)-problems with general data. We prove that if the axisymmetric domain is convex, then the multigrid V-cycle with modern smoothers will converge uniformly with respect to the meshsize.

math.NA↗

arXiv2013

Integer invariants of an incidence matrix related to Rota's basis conjecture

We compute the spectrum and Smith normal form of the incidence matrix of disjoint transversals, a combinatorial object closely related to the n-dimensional case of Rota's basis conjecture.

math.CO↗