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• W1620960189 abstract "The Reproducing Kernel Element Method (RKEM) is a hybrid between finite elements and meshfree methods that provides shape functions of arbitrary order and continuity yet retains the Kronecker-δ property. To achieve these properties, the underlying mesh must meet certain regularity constraints, unique to RKEM. The aim of this dissertation is to develop a precise definition of these constraints, and a general algorithm for assessing a mesh is developed. This check is a critical step in the use of RKEM in any application. The general checking algorithm is made more specific to apply to two-dimensional triangular meshes with circular supports and to three-dimensional tetrahedral meshes with spherical supports. The checking algorithm features the output of the uncovered regions that are used to develop a mesh-mending technique for fixing offending meshes. The specific check is used in conjunction with standard quality meshing techniques to produce meshes suitable for use with RKEM. The RKEM quasi-uniformity definitions enable the use of RKEM in solving Galerkin weak forms as well as in general interpolation applications, such as the representation of geometries. A procedure for determining a RKEM representation of discrete" @default.
• W1620960189 created "2016-06-24" @default.
• W1620960189 creator A5011118627 @default.
• W1620960189 date "2009-01-01" @default.
• W1620960189 modified "2023-09-27" @default.
• W1620960189 title "The Quasi-Uniformity Condition and Three-Dimensional Geometry Representation as it Applies to the Reproducing Kernel Element Method" @default.
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• W1620960189 hasPublicationYear "2009" @default.
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