Efficient quadrature rules for finite element discretizations of nonlocal equations
- Texas Tech Univ., Lubbock, TX (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Bologna (Italy)
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
In this paper we design efficient quadrature rules for finite element 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 showthat 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 finite element assembly.
- Research Organization:
- Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC04-94AL85000; NA0003525
- OSTI ID:
- 1763180
- Report Number(s):
- SAND--2021-0672R; 693539
- Country of Publication:
- United States
- Language:
- English
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