Communications in Numerical Methods in Engineering - Articles published in this section are of a more general engineering nature and do not necessarily have biomedical applications

On accurate and time efficient solution of primal-mixed finite element equations in multiscale solid mechanics

  1. Iain Duff1,
  2. Dubravka Mijuca2,*

Article first published online: 7 JUL 2009

DOI: 10.1002/cnm.1296

Issue

International Journal for Numerical Methods in Biomedical Engineering

International Journal for Numerical Methods in Biomedical Engineering

Volume 27, Issue 1, pages 95–112, January 2011

Additional Information

How to Cite

Duff, I. and Mijuca, D. (2011), On accurate and time efficient solution of primal-mixed finite element equations in multiscale solid mechanics. Int. J. Numer. Meth. Biomed. Engng., 27: 95–112. doi: 10.1002/cnm.1296

Author Information

  1. 1

    Computational Science and Engineering Department, Rutherford Appleton Laboratory, Didcot, Oxfordshire, OX11 0QX, U.K.

  2. 2

    Faculty of Civil Construction Management, University UNION, Cara Dusana 62-64, 11000 Belgrade, Serbia

*Faculty of Civil Construction Management, University UNION, Cara Dusana 62-64, 11000 Belgrade, Serbia

Publication History

  1. Issue published online: 8 JAN 2010
  2. Article first published online: 7 JUL 2009
  3. Manuscript Accepted: 22 MAY 2009
  4. Manuscript Revised: 3 MAY 2009
  5. Manuscript Received: 10 JAN 2009

Funded by

  • EPSRC. Grant Numbers: EP/E053351/1, EP/F006535/1
  • Ministry of Science of Republic of Serbia. Grant Number: 144007

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Keywords:

  • thermoelasticity;
  • geometrically multiscale;
  • primal-mixed finite element;
  • reliable;
  • sparse;
  • indefinite;
  • time efficient

Abstract

In order to identify the best technique to solve a class of geometrically multiscale model problems in thermoelasticity, we examine a combination of a primal-mixed finite element approach and direct sparse solvers and matrix scaling routines. The criteria for optimality are robustness, accuracy and execution time. It will be shown that the present finite element approach, where displacement and stress variables are simultaneously solved from large-scale indefinite poorly scaled systems of equations using the sparse HSL solver MA57 with the aid of the matrix scaling routines MC64 or MC30 during the factorization process, enables a reliable solution even if hexahedral finite elements in a mesh differ in size up to six orders of magnitude. A number of tests in multiscale elasticity and thermoelasticity are examined to test the accuracy and execution time efficiency of the proposed solution approach on a standard PC computing platform. Copyright © 2009 John Wiley & Sons, Ltd.

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