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Continuous Solution of Partial Differential Equations on Non-Rectangular and Non-Continuous Geometry

[+] Author Affiliations
P. Venkataraman

Rochester Institute of Technology, Rochester, NY

Paper No. DETC2014-35148, pp. V01AT02A009; 10 pages
doi:10.1115/DETC2014-35148
From:
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1A: 34th Computers and Information in Engineering Conference
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4628-5
  • Copyright © 2014 by ASME

abstract

A high order continuous solution is obtained for partial differential equations on non-rectangular and non-continuous domain using Bézier functions. This is a mesh free alternative to finite element or finite difference methods that are normally used to solve such problems. The problem is handled without any transformation and the setup is direct, simple, and involves minimizing the error in the residuals of the differential equations along with the error in the boundary conditions over the domain. The solution can be expressed in polynomial form. The effort is same for linear and nonlinear partial differential equations. The procedure is developed as a combination of symbolic and numeric calculation. The solution is obtained through the application of standard unconstrained optimization. A constrained approach is also developed for nonlinear partial differential equations. Examples include linear and nonlinear partial differential equations. The solution for linear partial differential equations is compared to finite element solutions from COMSOL.

Copyright © 2014 by ASME

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