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Efficient Solutions for Nonlocal Diffusion Problems Via Boundary-Adapted Spectral Methods
- Source :
- Journal of Peridynamics and Nonlocal Modeling; 20240101, Issue: Preprints p1-26, 26p
- Publication Year :
- 2024
-
Abstract
- We introduce an efficient boundary-adapted spectral method for peridynamic transient diffusion problems with arbitrary boundary conditions. The spectral approach transforms the convolution integral in the peridynamic formulation into a multiplication in the Fourier space, resulting in computations that scale as O(Nlog N). The limitation of regular spectral methods to periodic problems is eliminated using the volume penalization method. We show that arbitrary boundary conditions or volume constraints can be enforced in this way to achieve high levels of accuracy. To test the performance of our approach we compare the computational results with analytical solutions of the nonlocal problem. The performance is tested with convergence studies in terms of nodal discretization and the size of the penalization parameter in problems with Dirichlet and Neumann boundary conditions.
Details
- Language :
- English
- ISSN :
- 2522896X and 25228978
- Issue :
- Preprints
- Database :
- Supplemental Index
- Journal :
- Journal of Peridynamics and Nonlocal Modeling
- Publication Type :
- Periodical
- Accession number :
- ejs52261343
- Full Text :
- https://doi.org/10.1007/s42102-019-00026-6