UNIVERSITY OF WESTERN AUSTRALIA

The scaled boundary finite element method involves solution of a quadratic eigenproblem, the computational expense of which increases rapidly as the number of degrees of freedom increases. It is desirable to obtain solutions at a specified level of accuracy while using the minimum number of degrees of freedom necessary. In previous work, h adaptivity and p adaptivity have been considered. This stimulates the investigation to advance the individual adaptive schemes to develop hphierarchical adaptivity approach based on a conventional energy norm. This project is suitable for either undergraduate or master student. 2. p adaptive procedure in 3D for the scaled boundary finite element method (Suitability Undergraduate, Master Degree) Abstract: The scaled boundary finite element method is a novel semi-analytical technique, whose versatility, accuracy and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. In previous works, it was shown that higher rates of convergence can be obtained using p-refinement instead of h-refinement. This stimulated the development of various p-hierarchical adaptive strategies. Numerical studies were performed on various bounded domain and unbounded domain 2D problems. The results indicate these strategies works efficiently. This project extends the past study to examine performance of one proposed p-adaptive technique towards 3D problems. The phierarchical adaptivity approach based on a conventional energy norm will be considered. This project is suitable for either undergraduate or master student. The scaled boundary finite element method is a novel semi-analytical technique, whose versatility, accuracy and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. In previous works, it was shown that higher rates of convergence can be obtained using p-refinement instead of h-refinement. This stimulated the development of various p-hierarchical adaptive strategies. Numerical studies were performed on various bounded domain and unbounded domain 2D problems. The results indicate these strategies works efficiently. This project extends the past study to examine performance of one proposed p-adaptive technique towards 3D problems. The phierarchical adaptivity approach based on a conventional energy norm will be considered. This project is suitable for either undergraduate or master student.