Perpustakaan Digital ITB

This study introduces a framework for solving thermo-mechanical problems by using Mollified Collocation Method (MCM), that is, method that employs Mollified Basis Functions in the Point Collocation Method (PCM). By directly evaluating Partial Differential Equations (PDEs) in their strong form, offering a more straightforward and computationally efficient alternative to weak form approach. The strong form evaluation enables precise enforcement of boundary and governing equations, making the method particularly interesting for steep gradient problem solutions. A key feature of MCM is the flexibility of its basis functions, which possess arbitrary smoothness and polynomial degrees. This characteristic allows for seamless implementation of local refinement strategies, including p- (locally increasing polynomial degree), h-refinement (locally reducing element size) and hp-refinement (combining both strategies). These refinements allow for control over accuracy and resolution of the solution, focusing computational effort in regions with complex physical phenomena, such as high-temperature gradients. The proposed framework demonstrates significant potential for addressing thermoelasticity problem with locally steep gradients by combining mathematical rigor with practical efficiency. This study numerically investigates the effects of local refinements on solving high-gradient thermo and coupled thermoelasticity problems, aiming to balance solution accuracy and computational cost. Results indicate that local refinement strategies significantly enhance convergence rates and reduce errors, as measured by relative error discretisation in terms of L2 -norm and H1 -seminorm error.