TY - JOUR
T1 - Reproducing kernel element method. Part II
T2 - Globally conforming Im/Cn hierarchies
AU - Li, Shaofan
AU - Lu, Hongsheng
AU - Han, Weimin
AU - Liu, Wing Kam
AU - Simkins, Daniel C.
N1 - Funding Information:
This work is made possible by the support from NSF under grants CMS-0239130 to University of California (Berkeley), DMI-0115079 to Northwestern University, and DMS-0106781 to University of Iowa, which are greatly appreciated.
PY - 2004/3/26
Y1 - 2004/3/26
N2 - In this part of the work, a minimal degrees of freedom, arbitrary smooth, globally compatible, Im/Cn interpolation hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary multiple dimensional domains. This is the first interpolation hierarchical structure that has been constructed with both minimal degrees of freedom and higher order smoothness or continuity over multi-dimensional domain. The proposed hierarchical structure possesses the generalized Kronecker property, i.e.∂αΨ(β) I/∂xα(xJ)=δ IJδαβ, α,β≤m. This contribution is the latest breakthrough of an outstanding problem-construction of a minimal degrees of freedom, globally conforming, Im/Cn finite element interpolation fields on an arbitrary mesh or subdivision of multiple dimension. The newly constructed globally conforming interpolant is a hybrid of a set of C∞ global partition polynomials with a highly smooth (Cn) compactly supported meshfree partition of unity. Examples of compatible RKEM hierarchical interpolations are illustrated, and they are used in a Galerkin procedure to solve differential equations.
AB - In this part of the work, a minimal degrees of freedom, arbitrary smooth, globally compatible, Im/Cn interpolation hierarchy is constructed in the framework of reproducing kernel element method (RKEM) for arbitrary multiple dimensional domains. This is the first interpolation hierarchical structure that has been constructed with both minimal degrees of freedom and higher order smoothness or continuity over multi-dimensional domain. The proposed hierarchical structure possesses the generalized Kronecker property, i.e.∂αΨ(β) I/∂xα(xJ)=δ IJδαβ, α,β≤m. This contribution is the latest breakthrough of an outstanding problem-construction of a minimal degrees of freedom, globally conforming, Im/Cn finite element interpolation fields on an arbitrary mesh or subdivision of multiple dimension. The newly constructed globally conforming interpolant is a hybrid of a set of C∞ global partition polynomials with a highly smooth (Cn) compactly supported meshfree partition of unity. Examples of compatible RKEM hierarchical interpolations are illustrated, and they are used in a Galerkin procedure to solve differential equations.
KW - Approximation theory
KW - Finite element method
KW - Meshfree method
KW - Reproducing kernel element method
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U2 - 10.1016/j.cma.2003.12.002
DO - 10.1016/j.cma.2003.12.002
M3 - Article
AN - SCOPUS:1842471037
SN - 0374-2830
VL - 193
SP - 953
EP - 987
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
IS - 12-14
ER -