Conforming window functions for meshfree methods
Abstract
Window functions provide a base for the construction of approximation functions in many meshfree methods. They control the smoothness and extent of the approximation functions and are commonly defined using Euclidean distances which helps eliminate the need for a meshed discretization, simplifying model development for some classes of problems. However, for problems with complicated geometries such as nonconvex or multi-body domains, poor solution accuracy and convergence can occur unless the extents of the window functions, and thus approximation functions, are carefully controlled, often a time consuming or intractable task. Here in this paper, we present a method to provide more control in window function design, allowing efficient and systematic handling of complex geometries. “Conforming” window functions are constructed using Bernstein–Bézier splines defined on local triangulations with constraints imposed to control smoothness. Graph distances are used in conjunction with Euclidean metrics to provide adequate information for shaping the window functions. The conforming window functions are demonstrated using the Reproducing Kernel Particle Method showing improved accuracy and convergence rates for problems with challenging geometries. Conforming window functions are also demonstrated as a means to simplify the imposition of essential boundary conditions.
- Authors:
-
[1];
[2]
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Engineering Sciences Center; Univ. of California, San Diego, CA (United States). Dept. of Structural Engineering
- Univ. of California, San Diego, CA (United States). Dept. of Structural Engineering
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1492348
- Alternate Identifier(s):
- OSTI ID: 1642279
- Report Number(s):
- SAND-2019-0310J
Journal ID: ISSN 0045-7825; 671475
- Grant/Contract Number:
- AC04-94AL85000; 1655264
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 347; Journal Issue: C; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; meshfree methods; , rapid design-to-analysis; conforming window functions
Citation Formats
Koester, Jacob J., and Chen, Jiun-Shyan. Conforming window functions for meshfree methods. United States: N. p., 2019.
Web. doi:10.1016/j.cma.2018.12.042.
Koester, Jacob J., & Chen, Jiun-Shyan. Conforming window functions for meshfree methods. United States. https://doi.org/10.1016/j.cma.2018.12.042
Koester, Jacob J., and Chen, Jiun-Shyan. Wed .
"Conforming window functions for meshfree methods". United States. https://doi.org/10.1016/j.cma.2018.12.042. https://www.osti.gov/servlets/purl/1492348.
@article{osti_1492348,
title = {Conforming window functions for meshfree methods},
author = {Koester, Jacob J. and Chen, Jiun-Shyan},
abstractNote = {Window functions provide a base for the construction of approximation functions in many meshfree methods. They control the smoothness and extent of the approximation functions and are commonly defined using Euclidean distances which helps eliminate the need for a meshed discretization, simplifying model development for some classes of problems. However, for problems with complicated geometries such as nonconvex or multi-body domains, poor solution accuracy and convergence can occur unless the extents of the window functions, and thus approximation functions, are carefully controlled, often a time consuming or intractable task. Here in this paper, we present a method to provide more control in window function design, allowing efficient and systematic handling of complex geometries. “Conforming” window functions are constructed using Bernstein–Bézier splines defined on local triangulations with constraints imposed to control smoothness. Graph distances are used in conjunction with Euclidean metrics to provide adequate information for shaping the window functions. The conforming window functions are demonstrated using the Reproducing Kernel Particle Method showing improved accuracy and convergence rates for problems with challenging geometries. Conforming window functions are also demonstrated as a means to simplify the imposition of essential boundary conditions.},
doi = {10.1016/j.cma.2018.12.042},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 347,
place = {United States},
year = {Wed Jan 09 00:00:00 EST 2019},
month = {Wed Jan 09 00:00:00 EST 2019}
}
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Works referencing / citing this record:
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