dc.contributor.author Ilanko, Sinniah dc.contributor.author Henderson, L. dc.date.accessioned 2010-06-17T23:22:50Z dc.date.available 2010-06-17T23:22:50Z dc.date.issued 2009 dc.identifier.citation Ilanko, S. & Henderson, L. (2009). The use of pseudo-inertia in asymptotic modelling of constraints in boundary value problems. International Journal of Numerical Methods in Biomedical Engineering, published online: 12 June 2009. en_NZ dc.identifier.uri https://hdl.handle.net/10289/4012 dc.description.abstract In recent publications, the validity of using positive and negative inertial penalty parameters and the advantage of this approach over the conventional positive penalty function approach have been established for linear eigenvalue problems. This paper shows how this method may be applied to solve a boundary value problem. A steady-state 2-D heat transfer problem is used to demonstrate the method. First, the governing partial differential equation is modified by adding a pseudo-inertial term that results in an equation, which is mathematically identical to the equation governing the free vibration of a membrane. The essential boundary conditions of zero temperature along a specified line are imposed using inertial penalty parameters. The characteristic vibration modes found in this way are used to generate the complementary function to the heat transfer problem. This solution satisfies all natural boundary conditions (adiabatic) and zero temperature conditions using the inertial penalty parameter. To satisfy any additional temperature distribution imposed on the system, two sets of corrector terms are superimposed resulting in the final solution. The results are compared with constrained solutions obtained using the Lagrangian multiplier method and the ordinary penalty method. en_NZ dc.format.mimetype application/pdf dc.language.iso en dc.publisher John Wiley & Sons Ltd en_NZ dc.rights This is an author’s submitted version of an article published in the International Journal of Numerical Methods in Biomedical Engineering. Copyright © 2010 John Wiley & Sons, Ltd. dc.subject pseudo-inertia en_NZ dc.subject penalty method en_NZ dc.subject asymptotic modelling en_NZ dc.subject constraints en_NZ dc.title The use of pseudo-inertia in asymptotic modelling of constraints in boundary value problems en_NZ dc.type Journal Article en_NZ dc.identifier.doi 10.1002/cnm.1287 en_NZ dc.relation.isPartOf International Journal for Numerical Methods in Biomedical Engineering en_NZ pubs.begin-page 59 en_NZ pubs.elements-id 35271 pubs.end-page 68 en_NZ pubs.issue 1 en_NZ pubs.volume 27 en_NZ
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