Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains

Thumbnail image of item number 1 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.
Thumbnail image of item number 2 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.
Thumbnail image of item number 3 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.
Thumbnail image of item number 4 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.
Showing 1-4 of 31 pages in this article.

PDF Version Also Available for Download.

Description

The Reproducing Kernel Particle Method (RKPM) is a discretization technique for partial differential equations that uses the method of weighted residuals, classical reproducing kernel theory and modified kernels to produce either ``mesh-free'' or ``mesh-full'' methods. Although RKPM has many appealing attributes, the method is new, and its numerical performance is just beginning to be quantified. In order to address the numerical performance of RKPM, von Neumann analysis is performed for semi-discretizations of three model one-dimensional PDEs. The von Neumann analyses results are used to examine the global and asymptotic behavior of the semi-discretizations. The model PDEs considered for this analysis ... continued below

Physical Description

29 p.

Creation Information

Voth, T.E. & Christon, M.A. January 10, 2000.

Context

This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this article can be viewed below.

Who

People and organizations associated with either the creation of this article or its content.

Authors

Sponsor

Publisher

  • Sandia National Laboratories
    Publisher Info: Sandia National Labs., Albuquerque, NM, and Livermore, CA (United States)
    Place of Publication: Albuquerque, New Mexico

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

About | Browse this Partner

Contact Us

Corrections Questions

What

Descriptive information to help identify this article. Follow the links below to find similar items on the Digital Library.

Description

The Reproducing Kernel Particle Method (RKPM) is a discretization technique for partial differential equations that uses the method of weighted residuals, classical reproducing kernel theory and modified kernels to produce either ``mesh-free'' or ``mesh-full'' methods. Although RKPM has many appealing attributes, the method is new, and its numerical performance is just beginning to be quantified. In order to address the numerical performance of RKPM, von Neumann analysis is performed for semi-discretizations of three model one-dimensional PDEs. The von Neumann analyses results are used to examine the global and asymptotic behavior of the semi-discretizations. The model PDEs considered for this analysis include the parabolic and hyperbolic (first and second-order wave) equations. Numerical diffusivity for the former and phase speed for the later are presented over the range of discrete wavenumbers and in an asymptotic sense as the particle spacing tends to zero. Group speed is also presented for the hyperbolic problems. Excellent diffusive and dispersive characteristics are observed when a consistent mass matrix formulation is used with the proper choice of refinement parameter. In contrast, the row-sum lumped mass matrix formulation severely degraded performance. The asymptotic analysis indicates that very good rates of convergence are possible when the consistent mass matrix formulation is used with an appropriate choice of refinement parameter.

Physical Description

29 p.

Notes

OSTI as DE00750192

Medium: P; Size: 29 pages

Source

  • Other Information: Submitted to Computer Methods in Applied Mechanics and Engineering

Language

Item Type

Identifier

Unique identifying numbers for this article in the Digital Library or other systems.

  • Report No.: SAND2000-0092J
  • Grant Number: AC04-94AL85000
  • Office of Scientific & Technical Information Report Number: 750192
  • Archival Resource Key: ark:/67531/metadc708497

Collections

This article is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

About | Browse this Collection

What responsibilities do I have when using this article?

Digital Files

When

Dates and time periods associated with this article.

Creation Date

  • January 10, 2000

Added to The UNT Digital Library

  • Sept. 12, 2015, 6:31 a.m.

Description Last Updated

  • April 10, 2017, 7:07 p.m.

Usage Statistics

When was this article last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 2
More Statistics

Interact With This Article

Here are some suggestions for what to do next.

Start Reading

Thumbnail image of item number 1 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.
Thumbnail image of item number 2 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.
Thumbnail image of item number 3 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.
Thumbnail image of item number 4 in: 'Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains'.

PDF Version Also Available for Download.

Citations, Rights, Re-Use

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Voth, T.E. & Christon, M.A. Discretization errors associated with Reproducing Kernel Methods: One-dimensional domains, article, January 10, 2000; Albuquerque, New Mexico. (digital.library.unt.edu/ark:/67531/metadc708497/: accessed July 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.