Perpustakaan Digital ITB

Point collocation method becomes popular in engineering design and analysis. It offers a significant advantage by employing a discretized strong form, where the governing Partial Differential Equations (PDE) and boundary conditions of the problem are enforced at discrete collocation points instead of being averaged over the domain, as is the case in a weak form approach. Generating mollified basis functions offers several advantages in terms of their ease of construction, flexibility in degrees and smoothness, and ability to handle arbitrary partitions. These basis functions are constructed through the convolution of piecewise polynomials defined within cells and a selected smooth kernel or mollifier. The mollifier is chosen to be smooth, have compact support, and possess a unit volume. The resulting properties of the basis functions are governed by the smoothness of the mollifier and the local polynomial approximation order. Since mollified basis functions have arbitrary high order, smoothness, and available to set arbitrary polynomial order in each cells, The local refinement becomes one way to improve the efficiency of mollified collocation method, two of them are p-adaptivity which can be analyzed by setting different polynomial order in one simulation and h-refinement. The h-refinement study begins with the regularisation of Voronoi diagram using Lloyds algorithm. Also, the effect of p-adaptivity will be analyzed by evaluating the convergence error in simulating linear elasticity plate with hole problem.