Efficient generation of Gaussian random fields on metric graphs via domain decomposition and mass matrix lumping

Mihály Kovács; Gyula Molnár; Máté András Száraz

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arXiv · 2605.02670

Efficient generation of Gaussian random fields on metric graphs via domain decomposition and mass matrix lumping

Mihály Kovács·Gyula Molnár·Máté András Száraz

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Abstract

We consider Gaussian Random Fields on metric graphs defined implicitly as the stationary solution to a fractional SPDE driven by Gaussian white noise. Sampling from the finite element approximation requires the Cholesky factorization of the mass matrix, causing non-linear execution time explosions and massive memory fill-in on large graphs. Hence, we combine Neumann-Neumann graph decomposition with mass matrix lumping and demonstrate empirically, that our approach preserves exact theoretical convergence rates established in [8] while achieving multi-order speedups and massive memory reductions.

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Mihály Kovács, Gyula Molnár, Máté András Száraz. 2026-05-04. Efficient generation of Gaussian random fields on metric graphs via domain decomposition and mass matrix lumping. https://arxiv.org/abs/2605.02670

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