A model-integrated localized collocation meshless method (MIMS)

Abstract

A model integrated meshless solver (MIMS) tailored to solve practical large-scale industrial problems is based on robust meshless methods strategies that integrate a native model-based point generation procedures. The MIMS approach fully exploits strengths of meshless methods to achieve automation, stability, and accuracy by blending meshless solution strategies based on a variety of shape functions to achieve stable and accurate iteration process that is integrated with a newly developed, highly adaptive model generation employing quaternary triangular surface discretization for the boundary, a binary-subdivision discretization for the interior, and a unique shadow layer discretization for near-boundary regions. Together, these discretization techniques provide directionally independent, automatic refinement of the underlying native problem model to generate accurate adaptive solutions without need for intermediate user intervention. By coupling the model generation with the solution process, MIMS addresses issues posed by ill-constructed geometric input and pathologies often generated from solid models in the course of CAD design.