12 citations · 15 across the 7 of their papers we have counts for
8 papers
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…
A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type
Manuel Klar, Giacomo Capodaglio, Marta D'Elia +3
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the mai…
The nonlocal Neumann problem
Leonhard Frerick, Christian Vollmann, Michael Vu
The classical local Neumann problem is well studied and solutions of this problem lie, in general, in a Sobolev space. In this work, we focus on nonlocal Neumann problems with meas…
nlfem: A flexible 2d Fem Code for Nonlocal Convection-Diffusion and Mechanics
Manuel Klar, Christian Vollmann, Volker Schulz
In this work we present the mathematical foundation of an assembly code for finite element approximations of nonlocal models with compactly supported, weakly singular kernels. We d…
A general framework for substructuring-based domain decomposition methods for models having nonlocal interactions
Giacomo Capodaglio, Marta D'Elia, Max Gunzburger +3
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a…
A cookbook for finite element methods for nonlocal problems, including quadrature rules and approximate Euclidean balls
Marta D'Elia, Max Gunzburger, Christian Vollmann
The implementation of finite element methods (FEMs) for nonlocal models with a finite range of interaction poses challenges not faced in the partial differential equations (PDEs) s…
Shape optimization for interface identification in nonlocal models
Volker Schulz, Matthias Schuster, Christian Vollmann
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization p…
Exploiting multilevel Toeplitz structures in high dimensional nonlocal diffusion
Christian Vollmann, Volker Schulz
We present a finite element implementation for the steady-state nonlocal Dirichlet problem with homogeneous volume constraints. Here, the nonlocal diffusion operator is defined as…