A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

Klar, Manuel; Capodaglio, Giacomo; D'Elia, Marta; Glusa, Christian; Gunzburger, Max; Vollmann, Christian

doi:10.1016/j.camwa.2023.10.019

Title: A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

Journal Article · 24 October 2023 · Computers and Mathematics with Applications (Oxford)

DOI: https://doi.org/10.1016/j.camwa.2023.10.019 · OSTI ID:2336644

Klar, Manuel ^[1]; Capodaglio, Giacomo ^[2]; D'Elia, Marta ^[3]; Glusa, Christian ^[4]; Gunzburger, Max ^[5]; Vollmann, Christian ^[1]

Universität Trier (Germany)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Pasteur Labs, Brooklyn, NY (United States)
Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Univ. of Texas, Austin, TX (United States)

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 applications. Here, we present a domain decomposition solver that is inspired by substructuring methods for classical local equations. In numerical experiments involving finite element discretizations of scalar and vectorial nonlocal equations of integrable and fractional type, we observe improvements in solution time of up to 14.6x compared to commonly used solver strategies.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: NA0003525; SC0021077

OSTI ID:: 2336644

Alternate ID(s):: OSTI ID: 2203772

Report Number(s):: SAND--2024-04269J

Journal Information:: Computers and Mathematics with Applications (Oxford), Journal Name: Computers and Mathematics with Applications (Oxford) Vol. 151; ISSN 0898-1221

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Title: A scalable domain decomposition method for FEM discretizations of nonlocal equations of integrable and fractional type

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