arXiv subjects

Jessica Bosch

Publications and source records attributed to Jessica Bosch.

5 recordsLinked to original sources

arXiv2026

Preconditioning for Diffuse Interface Tumor Growth Models

Computational models of tumor growth form a contemporary area of study. Diffuse interface models have been proposed as an important tool for cancer modeling. In this work, we consider preconditioners for numerical simulations of two tumor growth models based on diffuse interface models. For numerical efficiency, we propose block preconditioners that rely on using effective Schur-complement approximations. We show that these methods combined with state-of-the-art adaptive finite element discretizations lead to robust simulations in two and three dimensions. In extensive numerical experiments, we show that the proposed methods show robust convergence behavior.

math.NA↗

arXiv2023

Gravitational Wave Signatures of Gauged Baryon and Lepton Number

We demonstrate that novel types of gravitational wave signatures arise in theories with new gauge symmetries broken at high energy scales. For concreteness, we focus on models with gauged baryon number and lepton number, in which neutrino masses are generated via the type I seesaw mechanism, leptogenesis occurs through the decay of a heavy right-handed neutrino, and one of the new baryonic fields is a good dark matter candidate. Depending on the scalar content of the theory, the gravitational wave spectrum consists of contributions from cosmic strings, domain walls, and first order phase transitions. We show that a characteristic double-peaked signal from domain walls or a sharp domain wall peak over a flat cosmic string background may be generated. Those new signatures are within the reach of future experiments, such as Cosmic Explorer, Einstein Telescope, DECIGO, Big Bang Observer, and LISA.

hep-ph↗

arXiv2019

Node Classification for Signed Social Networks Using Diffuse Interface Methods

Signed networks contain both positive and negative kinds of interactions like friendship and enmity. The task of node classification in non-signed graphs has proven to be beneficial in many real world applications, yet extensions to signed networks remain largely unexplored. In this paper we introduce the first analysis of node classification in signed social networks via diffuse interface methods based on the Ginzburg-Landau functional together with different extensions of the graph Laplacian to signed networks. We show that blending the information from both positive and negative interactions leads to performance improvement in real signed social networks, consistently outperforming the current state of the art.

cs.SI↗

arXiv2016

Generalizing diffuse interface methods on graphs: non-smooth potentials and hypergraphs

Diffuse interface methods have recently been introduced for the task of semi-supervised learning. The underlying model is well-known in materials science but was extended to graphs using a Ginzburg--Landau functional and the graph Laplacian. We here generalize the previously proposed model by a non-smooth potential function. Additionally, we show that the diffuse interface method can be used for the segmentation of data coming from hypergraphs. For this we show that the graph Laplacian in almost all cases is derived from hypergraph information. Additionally, we show that the formerly introduced hypergraph Laplacian coming from a relaxed optimization problem is well suited to be used within the diffuse interface method. We present computational experiments for graph and hypergraph Laplacians.

stat.ML↗

arXiv2016

Preconditioning of a coupled Cahn--Hilliard Navier--Stokes system

Recently, Garcke et al.[Garcke, Hinze, Kahle, A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow, Applied Numerical Mathematics 99, pp. 151-171, 2016] developed a consistent discretization scheme for a thermodynamically consistent diffuse interface model for incompressible two-phase flows with different densities. At the heart of this method lies the solution of large and sparse linear systems that arise in a semismooth Newton method. We propose the use of preconditioned Krylov subspace solvers using effective Schur complement approximations. Numerical results illustrate the efficiency of our approach. In particular, our preconditioner is shown to be robust with respect to parameter changes.

math.NA↗