The mixed-cell-complex partition-of-unity method

DOI10.1016/j.cma.2008.04.026zbMath1157.65492OpenAlexW2074817897MaRDI QIDQ1008925

Carsten Riker, Stefan M. Holzer

Publication date: 30 March 2009

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.2008.04.026

zbMATH Keywords

Galerkin method\(p\)-versionmeshless methodsfinite element method (FEM)generalized finite element method (GFEM)\(h\)-versionmixed cell complexpartition of unity method (PUM)

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (12)

Augmented numerical manifold method with implementation of flat-top partition of unity ⋮ Meshless method based on Shepard function and partition of unity for two-dimensional crack problems ⋮ Improved numerical manifold method (iNMM) -- an extra-DOF free and interpolating NMM with continuous nodal stress ⋮ Dynamic high order numerical manifold method based on weighted residual method ⋮ Generalizations of the finite element method ⋮ Prediction of rank deficiency in partition of unity-based methods with plane triangular or quadrilateral meshes ⋮ A new partition of unity finite element free from the linear dependence problem and possessing the delta property ⋮ Proof of linear independence of flat-top PU-based high-order approximation ⋮ Maximum-entropy meshfree method for compressible and near-incompressible elasticity ⋮ A new way to treat material discontinuities in the numerical manifold method ⋮ Investigation of linear dependence problem of three-dimensional partition of unity-based finite element methods ⋮ Multilevel particle-partition of unity method

Uses Software

• LAPACK

Cites Work

• Imposing essential boundary conditions in mesh-free methods
• Deformable smooth surface design
• Meshfree, probabilistic determination of point sets and support regions for meshless computing
• Meshless methods: An overview and recent developments
• \(hp\)-meshless cloud method
• Automatic generation of octree-based three-dimensional discretizations for partition of unity methods
• Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind. (On a variational principle for solving Dirichlet problems less boundary conditions using subspaces)
• A Particle-Partition of Unity Method--Part II: Efficient Cover Construction and Reliable Integration
• LAPACK Users' Guide
• A quadtree data structure for the coupled finite-element/element-free Galerkin method
• A Particle-Partition of Unity Method for the Solution of Elliptic, Parabolic, and Hyperbolic PDEs
• A Particle-Partition of Unity Method--Part III: A Multilevel Solver
• A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation
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