The Partition of Unity Method

Keywords

Partition of unity, Finite element method, Helmholtz equation, Mathematics, Mixed finite element method

References

• Table of Integrals, Series, and ProductsI. S. Gradshteyn, I.M. RYZHIK, D. F. Hays — 1966
• A three‐dimensional acoustic infinite element based on a prolate spheroidal multipole expansionDavid S. Burnett — 1994
• Surfaces generated by moving least squares methodsPeter Lancaster, K. Šalkauskas — 1981
• Efficient preconditioning for the p -version finite element method in two dimensionsIvo Babuška, Alan W. Craig, Jan Mandel — 1991
• A Generalized Finite Element Method for solving the Helmholtz equation in two dimensions with minimal pollutionIvo Babuška, Frank Ihlenburg, Ellen T. Paik — 1995
• Reproducing kernel particle methods for structural dynamicsWing Kam Liu, Sukky Jun, Shaofan Li — 1995
• n-Widths in Approximation TheoryKlaus Höllig, Allan Pinkus — 1985
• A survey of I. N. Vekua's theory of elliptic partial differential equations with analytic coefficientsPeter Henrici — 1957
• The finite difference method at arbitrary irregular grids and its application in applied mechanicsTadeusz Liszka, Janusz Orkisz — 1980
• A feedback element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimatorIvo Babuška, Anthony D. Miller — 1987
• Fracture and crack growth by element free Galerkin methodsTed Belytschko, Linxia Gu, Ye Lu — 1994
• ON THE USE OF VARIABLE ORDER INFINITE WAVE ENVELOPE ELEMENTS FOR ACOUSTIC RADIATION AND SCATTERINGLuc Cremers, K.R. Fyfe — 1995
• An introduction to SPHJ. J. Monaghan — 1987
• Information-based numerical practiceIvo Babuška — 1987
• The p -version of the finite element method for the elliptic boundary value problems with interfacesHae‐Soo Oh, Ivo Babuška — 1992
• The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularitiesHae‐Soo Oh, Ivo Babu⩽ska — 1993
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear SystemsRoland W. Freund — 1993
• Generalizing the finite element method: Diffuse approximation and diffuse elementsBernard Nayroles, Gilbert Touzot, Pierre Villon — 1992
• Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimatesE.J. Kansa — 1990
• Physical stabilization of the 4-node shell element with one point quadratureTed Belytschko, Itai Leviathan — 1994

Cited by

• Etude d'une méthodologie multiéchelles appliquée à différents problèmes en milieu continu et discretLaetitia Carballal Perdiz — 2010
• Propagation numérique de zones critiques dans un pneumatique par approches multi-modèlesOlivier Jamond — 2011
• Analysis of Materials with Strain-Gradient Effects: A Meshless Local Petrov-Galerkin(MLPG) Approach, with Nodal Displacements onlyZhenyuan Tang, Shih-Yu Shen, Satya N. Atluri — 2003
• Applications of the MLPG Method in Engineering &Sciences: A ReviewJ. Sládek, P. Staňák, Z-D. Han — 2013
• The Reproducing Kernel DMS-FEM: 3D Shape Functions and Applications to Linear Solid MechanicsN. Sunilkumar, Debasish Roy — 2010
• Numerical modelling of sound transmission in lightweight structuresJordi Poblet Puig — 2008
• Micromechanical Study of Rock Fracture and Fragmentation under Dynamic Loads using Discrete Element MethodT. Kazerani — 2011
• Modelización constitutiva y computacional del daño y la fractura de materiales compuestosPere Maimí Vert — 2007
• Contribution à la résolution numérique des problèmes de Helmholtz.Magdalena Grigoroscuta-Strugaru — 2009
• Étude de l'apparition des contraintes résiduelles dans le procédé d'empilement par soudage et consolidation en continu de composites thermoplastiquesFrançois Lemarchand — 2008
• Modélisation avec la méthode X-FEM de la propagation dynamique et de l'arrêt de fissure de clivage dans un acier de cuve REPBenoit Prabel — 2007
• Moving Meshless Methods (I): Moving Element Free Petrov-Galerkin Viscous MethodAli Reza Soheili, Mehrzad Ghorbany — 2003
• Application of the Generalized Finite Difference Method to improve the approximated solution of pdesJuan José Benito, Francisco Ureña, L. Gavete — 2008
• Arbitrary Placement of Secondary Nodes, and Error Control, in the Meshless Local Petrov-Galerkin (MLPG) MethodH.-G. Kim, Satya N. Atluri — 2000
• A novel augmented finite element method for modeling arbitrary cracking in solidsSeyedreza Mohammadizadeh — 2013
• The development of a generalized meshfree approximation for solid and fracture analysisChung-Kyu Park — 2009
• A NURBS-based Parametric Method Bridging Mesh-free and Finite Element FormulationsAmit Shaw, B. Banerjee, Debasish Roy — 2008
• Immersed Finite Element Particle-In-Cell Simulations of Ion PropulsionRaed Kafafy — 2005
• Approximation with harmonic and generalized harmonic polynomials in the partition of unity methodJens Markus Melenk, Ivo Babuška — 1997
• Finite Element Simulation of Bone MicrostructuresTobias Preußer, Martin Rumpf, Lars Ole Schwen — 2007

Related papers

• Finite element analysis: theory and practiceMaurice J. Fagan — 1992
• A Review of the Extended Finite Element Method and its ApplicationsGang Chen — 2011
• Comparative Analysis of the Adaptive Generalized Finite Element Method and the Finite Element Method for Free Vibration of BarsMarcos Arndt, Roberto Dalledone Machado, A. Scremin — 2010
• Moving particle finite element method with global smoothnessSu Hao, Wing Kam Liu, Ted Belytschko — 2004
• The partition of unity finite element methodMelenk, Jens M., Babuška, Ivo — 1996
• Generalizations of the Finite Element MethodMarc Alexander Schweitzer — 2012
• Researching Progress of Generalized Finite Element MethodMoe Key — 2009
• A partition‐of‐unity‐based finite element method for level setsStéphane Valance, René de Borst, Julien Réthoré — 2008
• Stability of incompressible formulations enriched with X-FEMGrégory Legrain, Nicolas Moës, Antonio Huerta — 2008
• CHARACTERISTIC METHOD FOR TWO PHASE DISPLACEMENT IN POROUS MEDIA AND ITS CONVERGENCE ANALYSIS BASING ON THE POSTPROGRESSING OF FINITE ELEMENT METHOD FOR PRESSUREWei Zhao — 2000