ITERATIVE SOLUTION OF SPATIAL NETWORK MODELS BY SUBSPACE DECOMPOSITION
Journal article, 2024

. We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be applied to a wide range of models, fulfilling a set of abstract assumptions. The proposed method builds on a classical subspace decomposition into a coarse subspace, realized as the restriction of a finite element space to the nodes of the spatial network, and localized subspaces with support on mesh stars. The main contribution of this work is the convergence analysis of the proposed method. The analysis translates results from finite element theory, including interpolation bounds, to the spatial network setting. A convergence rate of the PCG algorithm, only depending on global bounds of the operator and homogeneity, connectivity and locality constants of the network, is established. The theoretical results are confirmed by several numerical experiments.

& nbsp

isoparametric dimension

conjugate gradient

Algebraic connectivity

iterative network

Author

Morgan Görtz

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Fredrik Hellman

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Axel Målqvist

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mathematics of Computation

0025-5718 (ISSN) 1088-6842 (eISSN)

Vol. 93 345 233-258

Subject Categories

Telecommunications

DOI

10.1090/mcom/3861

More information

Latest update

7/5/2024 1