A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

Ricardo Costa; Gaspar J. Machado; Stéphane Clain

International Journal of Applied Mathematics and Computer Science (2015)

  • Volume: 25, Issue: 3, page 529-537
  • ISSN: 1641-876X

Abstract

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A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

How to cite

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Ricardo Costa, Gaspar J. Machado, and Stéphane Clain. "A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation." International Journal of Applied Mathematics and Computer Science 25.3 (2015): 529-537. <http://eudml.org/doc/271772>.

@article{RicardoCosta2015,
abstract = {A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.},
author = {Ricardo Costa, Gaspar J. Machado, Stéphane Clain},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {finite volume method; polynomial reconstruction operator; harmonic operator; biharmonic operator; high-order method},
language = {eng},
number = {3},
pages = {529-537},
title = {A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation},
url = {http://eudml.org/doc/271772},
volume = {25},
year = {2015},
}

TY - JOUR
AU - Ricardo Costa
AU - Gaspar J. Machado
AU - Stéphane Clain
TI - A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation
JO - International Journal of Applied Mathematics and Computer Science
PY - 2015
VL - 25
IS - 3
SP - 529
EP - 537
AB - A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.
LA - eng
KW - finite volume method; polynomial reconstruction operator; harmonic operator; biharmonic operator; high-order method
UR - http://eudml.org/doc/271772
ER -

References

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