13 papers
A Metric Space of Spatial Graphs: Two-Sample Testing, Data Depth, and Application to Cardiac Fibrosis
Anna Calissano, Arstanbek Okenov, Katja Zeppenfeld +1
Cardiac fibrosis reduces electrical conductivity and is a leading cause of arrhythmia. Arrhythmic waves typically rotate around non-conducting fibrotic patches, so the geometry and…
A priori error analysis of a mass-lumped midpoint finite element method with a structure-preserving solver for the Landau--Lifshitz--Gilbert equation with Dzyaloshinskii--Moriya interaction
Agus L. Soenjaya
The Landau--Lifshitz--Gilbert (LLG) equation is a fundamental model in micromagnetics for the magnetisation dynamics of ferromagnets at temperatures well below the Curie temperatur…
Error analysis of a divergence-preserving mixed finite element scheme for the incompressible Hall--magnetohydrodynamic equations
Beniamin Goldys, Agus L. Soenjaya, Thanh Tran
The incompressible Hall-magnetohydrodynamics (Hall--MHD) system presents substantial analytical and computational challenges due to its stiff, highly nonlinear Hall term and the st…
The Landau--Lifshitz--Bloch equation with spin diffusion: Global strong solution and finite element approximation
Agus L. Soenjaya
The spin-diffusion Landau--Lifshitz--Bloch (SDLLB) system is a nonlinearly coupled system of quasilinear vector-valued PDEs which models the interaction between spin-polarised curr…
Error analysis of scalar auxiliary variable finite element methods for the Landau--Lifshitz--Bloch equation
Agus L. Soenjaya
The Landau--Lifshitz--Bloch (LLB) equation is a well-established micromagnetic model for describing magnetisation dynamics in ferromagnets at elevated temperatures. In this paper,…
Strong convergence of finite element schemes for the stochastic Landau--Lifshitz--Bloch equation
Agus L. Soenjaya
The dynamics of magnetisation in a bounded ferromagnet in () at high temperatures can be described by the stochastic Landau--Lifshitz--Bloch (sLLB) equation,…