Vorlesung + Übung: Selected Topics in Numerics - Details

Vorlesung + Übung: Selected Topics in Numerics - Details

Allgemeine Informationen

Veranstaltungsname Vorlesung + Übung: Selected Topics in Numerics
Untertitel Computational Multiscale Methods for Partial Differential Equations
Veranstaltungsnummer MTH-3660 / MTH-3668
Semester SS 2026
Aktuelle Anzahl der Teilnehmenden 4
Heimateinrichtung Angewandte Analysis/Numerische Mathematik
Veranstaltungstyp Vorlesung + Übung in der Kategorie Lehre
Erster Termin Freitag, 17.04.26, 12:15 - 13:45 Uhr
Voraussetzungen Basic knowledge of numerical analysis (Introduction to Numerical Analysis) is required; familiarity with numerical methods for ordinary and partial differential equations is desirable.
Veranstaltung findet in Präsenz statt / hat Präsenz-Bestandteile Ja
Hauptunterrichtssprache englisch

Räume und Zeiten

Ohne Raum

  • Freitag, 12:15 - 13:45, Wöchentlich (ab dem 17.04.26)
  • Freitag, 14:00 - 15:30, Wöchentlich (ab dem 17.04.26)

Studienbereiche

Modulzuordnungen

Kommentar/Beschreibung

Many physical and engineering systems are governed by partial differential equations (PDEs) whose coefficients or solutions exhibit features across multiple spatial scales. Direct numerical simulation of such problems is often computationally infeasible due to the high resolution required to capture fine-scale effects. Computational multiscale methods address this challenge by incorporating fine-scale information into coarse-scale numerical schemes without explicitly resolving all scales.

This course is centered on numerical homogenization via localized orthogonal decomposition (LOD), which is developed as a concrete and mathematically well-founded approach to multiscale discretization of elliptic PDEs with rough coefficients. The course covers the analytical foundations of numerical homogenization, the decomposition of scales, localization phenomena, and the algorithmic realization of LOD-based methods in detail. Applications of LOD techniques to nonlinear eigenvalue problems are presented to illustrate their practical impact. In addition, selected discussions of learning-based and hybrid classical--quantum algorithmic extensions are included. An optional concluding lecture provides an outlook on variational relaxation and microstructure formation in nonlinear elasticity, which lies beyond the LOD framework.