Conforming window functions for meshfree methods

Koester, Jacob J.; Chen, Jiun-Shyan

doi:10.1016/j.cma.2018.12.042

Conforming window functions for meshfree methods

Journal Article · Tue Jan 08 23:00:00 EST 2019 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2018.12.042· OSTI ID:1492348

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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

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.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1492348

Alternate ID(s):: OSTI ID: 1642279

Report Number(s):: SAND--2019-0310J; 671475

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: C Vol. 347; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Treatment of near-incompressibility in meshfree and immersed-particle methods Moutsanidis, Georgios; Koester, Jacob J.; Tupek, Michael R. Computational Particle Mechanics, Vol. 7, Issue 2 https://doi.org/10.1007/s40571-019-00238-z	journal	April 2019
A kinematic comparison of meshfree and mesh-based Lagrangian approximations using manufactured extreme deformation fields Bishop, Joseph Computational Particle Mechanics, Vol. 7, Issue 2 https://doi.org/10.1007/s40571-019-00256-x	journal	June 2019

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