Reproducing polynomial (singularity) particle methods and adaptive meshless methods for two-dimensional elliptic boundary value problems

DOI10.1016/j.cma.2008.11.005zbMath1229.65227OpenAlexW2085119833MaRDI QIDQ658199

Jae Woo Jeong, Hae-Soo Oh

Publication date: 11 January 2012

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2008.11.005

zbMATH Keywords

partition of unity function with flat-topadaptive RPPMpatch-wise uniformly spaced particlesreproducing polynomial particle (RPP) shape functionsreproducing singularity particle (RSP) shape functionsthe jump boundary data singularity

Mathematics Subject Classification ID

Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs (65N75)

Related Items

Enriched meshfree method for an accurate numerical solution of the Motz problem ⋮ Meshfree particle methods in the framework of boundary element methods for the Helmholtz equation ⋮ The direct method of lines for elliptic problems in star-shaped domains ⋮ Reproducing polynomial particle methods for boundary integral equations ⋮ Meshfree particle methods for thin plates ⋮ A new partition of unity finite element free from the linear dependence problem and possessing the delta property ⋮ Mapping techniques for isogeometric analysis of elliptic boundary value problems containing singularities ⋮ Almost everywhere partition of unity to deal with essential boundary conditions in meshless methods

Cites Work

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• Reproducing kernel element method. II: Globally conforming \(I^m/C^n\) hierarchies
• The piecewise polynomial partition of unity functions for the generalized finite element methods
• The smooth piecewise polynomial particle shape functions corresponding to patch-wise non-uniformly spaced particles for meshfree particle methods
• The reproducing singularity particle shape functions for problems containing singularities
• The closed form reproducing polynomial particle shape functions for meshfree particle methods
• The method of auxiliary mapping for the finite element solutions of elliptic problems containing singularities
• An \(h\)-\(p\) adaptive method using clouds
• The partition of unity finite element method: basic theory and applications
• Filters, reproducing kernel, and adaptive meshfree method
• Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids.
• On the approximability and the selection of particle shape functions
• The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities
• Meshfree Particle Methods
• Boundary Methods for Solving Elliptic Problems with Singularities and Interfaces
• Survey of meshless and generalized finite element methods: A unified approach
• Convergence of Adaptive Finite Element Methods
• Reproducing kernel particle methods for structural dynamics
• Reproducing kernel particle methods
• Adaptivity for structured meshfree particle methods in 2D and 3D
• The p‐version of the finite element method for domains with corners and for infinite domains
• The generalized finite element method
• The numerical methods for oscillating singularities in elliptic boundary value problems
• Error analysis of the reproducing kernel particle method