The use of pseudo-inertia in asymptotic modelling of constraints in boundary value problems
| Autor: | Leon Henderson, S Ilanko |
|---|---|
| Rok vydání: | 2010 |
| Předmět: |
Mathematical optimization
Partial differential equation Applied Mathematics media_common.quotation_subject Biomedical Engineering Function (mathematics) Inertia symbols.namesake Computational Theory and Mathematics Modeling and Simulation Lagrange multiplier Free boundary problem symbols Applied mathematics Penalty method Boundary value problem Molecular Biology Software Eigenvalues and eigenvectors media_common Mathematics |
| Zdroj: | International Journal for Numerical Methods in Biomedical Engineering. 27:59-68 |
| ISSN: | 2040-7939 |
| DOI: | 10.1002/cnm.1287 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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