3 papers
math.OC2024
Second Order Shape Optimization for an Interface Identification Problem constrained by Nonlocal Models
Matthias Schuster, Volker Schulz
Since shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations, we show how shape optimization techniques…
math.NA2024
Schwarz Methods for Nonlocal Problems
Matthias Schuster, Christian Vollmann, Volker Schulz
The first domain decomposition methods for partial differential equations were already developed in 1870 by H. A. Schwarz. Here we consider a nonlocal Dirichlet problem with variab…
math.OC2024
Interface Identification constrained by Local-to-Nonlocal Coupling
Matthias Schuster, Volker Schulz
Models of physical phenomena that use nonlocal operators are better suited for some applications than their classical counterparts that employ partial differential operators. Howev…