Zobrazeno 1 - 10
of 31
pro vyhledávání: '"Vollmann, Christian"'
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 variable coefficients, where a nonlocal diffusion operator is used. We find
Externí odkaz:
http://arxiv.org/abs/2405.01905
Autor:
Klar, Manuel, Capodaglio, Giacomo, D'Elia, Marta, Glusa, Christian, Gunzburger, Max, Vollmann, Christian
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 main concerns for the use of nonlocal models in real world engineering ap
Externí odkaz:
http://arxiv.org/abs/2306.00094
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 measurable, nonnegative kernels, whose solutions require less regularity a
Externí odkaz:
http://arxiv.org/abs/2208.04561
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 demonstrate the code on a nonlocal diffusion model in various configura
Externí odkaz:
http://arxiv.org/abs/2207.03921
Autor:
Capodaglio, Giacomo, D'Elia, Marta, Gunzburger, Max, Bochev, Pavel, Klar, Manuel, Vollmann, Christian
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a tradition
Externí odkaz:
http://arxiv.org/abs/2008.11780
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) setting. For example, one has to deal with weak forms involving double
Externí odkaz:
http://arxiv.org/abs/2005.10775
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 problems constrained by nonlocal equations which involve interface-depe
Externí odkaz:
http://arxiv.org/abs/1909.08884
Autor:
Vollmann, Christian, Schulz, Volker
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 integral operator characterized by a certain kernel function. We assum
Externí odkaz:
http://arxiv.org/abs/1708.02526
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