2D Linear Elasticity Using an Efficient Mollified Collocation Method with Local P-Adaptivity
Efficient Mollified Collocation Method with Local P-Adaptivity
Keywords:
local p-adaptivity, mollified basis functions, point collocation method, linear elasticityAbstract
Point collocation method becomes popular in engineering design and analysis in which offers a significant advantage by employing discretized strong form, instead of being averaged over the domain as is the case in weak form approach. Mollified basis functions offer several advantages such as ease of constructing, flexible degree and smoothness, and adaptability to arbitrary partitions. These basis functions are formed by convolving local polynomials within a cell with a smooth kernel called mollifier, which is chosen for its compact support, unit volume, and smoothness. Since mollified basis functions have high order and smoothness, it is possible for us to do local refinement like p-adaptivity, where the polynomial order is chosen to be higher at certain region, one of the examples is stress concentration in linear elasticity problem. The mollified collocation method using p-adaptivity is studied in this paper by evaluating convergence error in linear elasticity plate with a hole problem.
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