A framework for studying the rkem representation of discrete point sets

Daniel C. Simkins; Nathan Collier; Mario Juha; Lisa B. Whitenack

doi:10.1007/978-3-540-79994-8_17

A framework for studying the rkem representation of discrete point sets

Daniel C. Simkins, Nathan Collier, Mario Juha, Lisa B. Whitenack

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

The application of engineering analysis to new areas, such as nanomechanics and the life sciences, often involves geometric problem domains defined by discrete point sets as measured from diagnostic equipment. The development of a suitable mesh for finite element analysis can be a tedious task. One approach to simplifying the geometric description is to use a parametrized set of basis functions, and fit the parameters to the data set. In this paper, we discuss the problem of determining suitable parameters for the Reproducing Kernel Element Method representation of discrete point sets, and in particular the solution of the inverse problem of determining pre-image evaluation points in the parametric space that correspond to a given input point. We justify our solution by posing a theoretical framework and an error indicator.

Original language	English
Title of host publication	Meshfree Methods for Partial Differential Equations IV
Pages	301-314
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-540-79994-8_17
State	Published - 2008
Externally published	Yes
Event	4th International Workshop on Meshfree Methods for Partial Differential Equations - Bonn, Germany Duration: Sep 17 2007 → Sep 20 2007

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	65
ISSN (Print)	1439-7358

Conference

Conference	4th International Workshop on Meshfree Methods for Partial Differential Equations
Country/Territory	Germany
City	Bonn
Period	09/17/07 → 09/20/07

Keywords

Discrete point sets
Geometry representation
RKEM

Access to Document

10.1007/978-3-540-79994-8_17

Cite this

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title = "A framework for studying the rkem representation of discrete point sets",

abstract = "The application of engineering analysis to new areas, such as nanomechanics and the life sciences, often involves geometric problem domains defined by discrete point sets as measured from diagnostic equipment. The development of a suitable mesh for finite element analysis can be a tedious task. One approach to simplifying the geometric description is to use a parametrized set of basis functions, and fit the parameters to the data set. In this paper, we discuss the problem of determining suitable parameters for the Reproducing Kernel Element Method representation of discrete point sets, and in particular the solution of the inverse problem of determining pre-image evaluation points in the parametric space that correspond to a given input point. We justify our solution by posing a theoretical framework and an error indicator.",

keywords = "Discrete point sets, Geometry representation, RKEM",

author = "Simkins, {Daniel C.} and Nathan Collier and Mario Juha and Whitenack, {Lisa B.}",

year = "2008",

doi = "10.1007/978-3-540-79994-8_17",

language = "English",

isbn = "9783540799931",

series = "Lecture Notes in Computational Science and Engineering",

pages = "301--314",

booktitle = "Meshfree Methods for Partial Differential Equations IV",

note = "4th International Workshop on Meshfree Methods for Partial Differential Equations ; Conference date: 17-09-2007 Through 20-09-2007",

}

Simkins, DC, Collier, N, Juha, M & Whitenack, LB 2008, A framework for studying the rkem representation of discrete point sets. in Meshfree Methods for Partial Differential Equations IV. Lecture Notes in Computational Science and Engineering, vol. 65, pp. 301-314, 4th International Workshop on Meshfree Methods for Partial Differential Equations, Bonn, Germany, 09/17/07. https://doi.org/10.1007/978-3-540-79994-8_17

A framework for studying the rkem representation of discrete point sets. / Simkins, Daniel C.; Collier, Nathan; Juha, Mario et al.
Meshfree Methods for Partial Differential Equations IV. 2008. p. 301-314 (Lecture Notes in Computational Science and Engineering; Vol. 65).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - A framework for studying the rkem representation of discrete point sets

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AU - Collier, Nathan

AU - Juha, Mario

AU - Whitenack, Lisa B.

PY - 2008

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N2 - The application of engineering analysis to new areas, such as nanomechanics and the life sciences, often involves geometric problem domains defined by discrete point sets as measured from diagnostic equipment. The development of a suitable mesh for finite element analysis can be a tedious task. One approach to simplifying the geometric description is to use a parametrized set of basis functions, and fit the parameters to the data set. In this paper, we discuss the problem of determining suitable parameters for the Reproducing Kernel Element Method representation of discrete point sets, and in particular the solution of the inverse problem of determining pre-image evaluation points in the parametric space that correspond to a given input point. We justify our solution by posing a theoretical framework and an error indicator.

AB - The application of engineering analysis to new areas, such as nanomechanics and the life sciences, often involves geometric problem domains defined by discrete point sets as measured from diagnostic equipment. The development of a suitable mesh for finite element analysis can be a tedious task. One approach to simplifying the geometric description is to use a parametrized set of basis functions, and fit the parameters to the data set. In this paper, we discuss the problem of determining suitable parameters for the Reproducing Kernel Element Method representation of discrete point sets, and in particular the solution of the inverse problem of determining pre-image evaluation points in the parametric space that correspond to a given input point. We justify our solution by posing a theoretical framework and an error indicator.

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T3 - Lecture Notes in Computational Science and Engineering

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BT - Meshfree Methods for Partial Differential Equations IV

T2 - 4th International Workshop on Meshfree Methods for Partial Differential Equations

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A framework for studying the rkem representation of discrete point sets

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Keywords

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