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Mathematics > Numerical Analysis

arXiv:2201.07955 (math)
[Submitted on 20 Jan 2022]

Title:Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions

Authors:Xiaoxuan Yu, Yan Xu, Qiang Du
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Abstract:We study the propagation of singularities in solutions of linear convection equations with spatially heterogeneous nonlocal interactions. A spatially varying nonlocal horizon parameter is adopted in the model, which measures the range of nonlocal interactions. Via heterogeneous localization, this can lead to the seamless coupling of the local and nonlocal models. We are interested in understanding the impact on singularity propagation due to the heterogeneities of nonlocal horizon and the local and nonlocal transition. We first analytically derive equations to characterize the propagation of different types of singularities for various forms of nonlocal horizon parameters in the nonlocal regime. We then use asymptotically compatible schemes to discretize the equations and carry out numerical simulations to illustrate the propagation patterns in different scenarios.
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
Cite as: arXiv:2201.07955 [math.NA]
  (or arXiv:2201.07955v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2201.07955

Submission history

From: Yan Xu [view email]
[v1] Thu, 20 Jan 2022 02:13:11 UTC (6,420 KB)
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