On completeness of RFM solution structures

SUMMARYIn this paper, an overview of the construction of meshfree basis functions is presented, with particular emphasis on moving least-squares approximants, natural neighbour-based polygonal interpolants, and entropy approximants. The use of information-theoretic variational principles to derive approximation schemes is a recent development. In this setting, data approximation is viewed as an inductive inference problem, with the basis functions being synonymous with a discrete probability distribution and the polynomial reproducing conditions acting as the linear constraints. The maximization (minimization) of the Shannon-Jaynes entropy functional (relative entropy functional) is used to unify the construction of globally and locally supported convex approximation schemes. A JAVA applet is used to visualize the meshfree basis functions, and comparisons and links between different meshfree approximation schemes are presented.

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“…• As alternative compactly supported priors, R-functions [71,72] or implicit (level set) functions that are defined on a graph are also suitable.…”

Section: N Sukumar and R W Wrightmentioning

confidence: 99%

Overview and construction of meshfree basis functions: from moving least squares to entropy approximants

Sukumar

Wright

2006

Numerical Meth Engineering

101

128

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“…At the core of the meshfree method of analysis with distances field is representation of a physical field by the Taylor series expansion, originally proposed by Kantorovich [6] and developed by Rvachev [12] and [13].…”

Section: Meshfree Methods With Distance Fieldmentioning

confidence: 99%

Meshfree Method for Prediction of Thermal Properties of Porous Ceramic Materials

Zahedi¹

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“…At the core of the meshfree method of analysis with distance fields is the representation of a physical field by the Taylor series expansion, originally proposed by Kantorovich [25] and developed by Rvachev [26,27]:…”

Section: Meshfree Finite Element Methods With Distance Fieldsmentioning

confidence: 99%

“…The remainder term ω k+1 Φ assures completeness of the Taylor series [27], and it can be used to satisfy additional constraints imposed on u, which are usually formulated in the form of differential equations, integral equations, or variational principles. To find a function u that satisfies both boundary conditions and additional constraints one needs to determine the function Φ.…”

Section: Meshfree Finite Element Methods With Distance Fieldsmentioning

confidence: 99%

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

Mudrich¹

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which has become a cornerstone of my graduate career. He has always encouraged me to take on new tasks of which I had no experience and provided limitless support through their completion, resulting in continuous learning and growth. In the presented thesis work, the meshfree method with distance fields was coupled with the lattice Boltzmann method to obtain solutions of fluid-structure interaction problems. The thesis work involved development and implementation of numerical algorithms, data structure, and software. Numerical and computational properties of the coupling algorithm combining the meshfree method with distance fields and the lattice Boltzmann method were investigated. Convergence and accuracy of the methodology was validated by analytical solutions.The research was focused on fluid-structure interaction solutions in complex, meshresistant domains as both the lattice Boltzmann method and the meshfree method with distance fields are particularly adept in these situations. Furthermore, the fluid solution provided by the lattice Boltzmann method is massively scalable, allowing extensive use of cutting edge parallel computing resources to accelerate this phase of the solution process. The meshfree method with distance fields allows for exact satisfaction of boundary conditions making it possible to exactly capture the effects of the fluid field on the solid structure.

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On completeness of RFM solution structures

Cited by 87 publications

References 30 publications

Overview and construction of meshfree basis functions: from moving least squares to entropy approximants

Overview and construction of meshfree basis functions: from moving least squares to entropy approximants

Meshfree Method for Prediction of Thermal Properties of Porous Ceramic Materials

Development of a Coupling Model for Fluid-Structure Interaction using the Mesh-free Finite Element Method and the Lattice Boltzmann Method

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