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Title: The dual reciprocity boundary element method for linear and non-linear problems.
Author: Toutip, Wattana.
ISNI:       0000 0001 3535 6187
Awarding Body: University of Herfordshire
Current Institution: University of Hertfordshire
Date of Award: 2001
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A problem encountered in the boundary element method is the difficulty caused by corners and/or discontinuous boundary conditions. An existing code using standard linear continuous elements is modified to overcome such problems using the multiple node method with an auxiliary boundary collocation approach. Another code is implemented applying the gradient approach as an alternative to handle such problems. Laplace problems posed on variety of domain shapes have been introduced to test the programs. For Poisson problems the programs have been developed using a transformation to a Laplace problem. This method cannot be applied to solve Poissontype equations. The dual reciprocity boundary element method (DRM) which is a generalised way to avoid domain integrals is introduced to solve such equations. The gradient approach to handle corner problems is co-opted in the program using DRM. The program is modified to solve non-linear problems using an iterative method. Newton's method is applied in the program to enhance the accuracy of the results and reduce the number of iterations. The program is further developed to solve coupled Poisson-type equations and such a formulation is considered for the biharmonic problems. A coupled pair of non-linear equations describing the ohmic heating problem is also investigated. Where appropriate results are compared with those from reference solutions or exact solutions. v
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Corners; Continuous; Discontinuous conditions