TY - JOUR
T1 - Efficient quadrature rules for finite element discretizations of nonlocal equations
AU - Aulisa, Eugenio
AU - Capodaglio, Giacomo
AU - Chierici, Andrea
AU - D'Elia, Marta
N1 - Funding Information:
This work was supported by the National Science Foundation (NSF) Division of Mathematical Sciences (DMS) program, project 1912902, by Sandia National Laboratories (SNL) Laboratory‐directed Research and Development (LDRD) program, project 218318 and by the U.S. Department of Energy, Office of Advanced Scientific Computing Research under the Collaboratory on Mathematics and Physics‐Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project. Funding information
Funding Information:
Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration contract number DE‐NA0003525. This paper, SAND2021‐0672, describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
Funding Information:
information This work was supported by the National Science Foundation (NSF) Division of Mathematical Sciences (DMS) program, project 1912902, by Sandia National Laboratories (SNL) Laboratory-directed Research and Development (LDRD) program, project 218318 and by the U.S. Department of Energy, Office of Advanced Scientific Computing Research under the Collaboratory on Mathematics and Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PhILMs) project.Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration contract number DE-NA0003525. This paper, SAND2021-0672, describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
Publisher Copyright:
© 2021 Wiley Periodicals LLC.
PY - 2022/11
Y1 - 2022/11
N2 - In this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.
AB - In this paper, we design efficient quadrature rules for finite element (FE) discretizations of nonlocal diffusion problems with compactly supported kernel functions. Two of the main challenges in nonlocal modeling and simulations are the prohibitive computational cost and the nontrivial implementation of discretization schemes, especially in three-dimensional settings. In this work, we circumvent both challenges by introducing a parametrized mollifying function that improves the regularity of the integrand, utilizing an adaptive integration technique, and exploiting parallelization. We first show that the “mollified” solution converges to the exact one as the mollifying parameter vanishes, then we illustrate the consistency and accuracy of the proposed method on several two- and three-dimensional test cases. Furthermore, we demonstrate the good scaling properties of the parallel implementation of the adaptive algorithm and we compare the proposed method with recently developed techniques for efficient FE assembly.
KW - asymptotic behavior of solutions
KW - finite element discretizations
KW - nonlocal models
KW - numerical quadrature
UR - http://www.scopus.com/inward/record.url?scp=85111209676&partnerID=8YFLogxK
U2 - 10.1002/num.22833
DO - 10.1002/num.22833
M3 - Article
AN - SCOPUS:85111209676
VL - 38
SP - 1767
EP - 1793
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
SN - 0749-159X
IS - 6
ER -