Penalty functions in constrained variational principles for element free Galerkin method |
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| Institution: | 1. Department of Chemistry, University of Helsinki, P.O. Box 55, FIN-00014, HU, Finland;2. Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland;1. Laboratory of Materials Innovation, Department of Materials and Metallurgical Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Keputih Sukolilo 60111, Surabaya, East Java, Indonesia;2. Laboratory of Materials Physics, Department of Materials and Metallurgical Engineering, Institut Teknologi Sepuluh Nopember, Kampus ITS Keputih Sukolilo 60111, Surabaya, East Java, Indonesia |
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| Abstract: | An improved formulation of the Element Free Galerkin (EFG) method is presented in this paper. In the Element Free Galerkin method, enforcement of essential boundary conditions is awkward as the approximations do not satisfy the Kronecker delta condition. A method of generating admissible approximations to the essential boundary conditions is given, using a constrained variational principle with a penalty function. Several examples of Laplace equation are solved and compared with analytical solutions and flux Lagrange multipliers, to demonstrate the performance of the method. A parametric study comparing three different weight functions is made. A guide on the EFG/penalisation method is given, considering the possibility of using irregular grids with a variable domain of influence for each point. |
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