Application of Hierarchical Chromosome Based Genetic Algorithm to the problem of finding optimal initial three dimensional meshes for the self adaptive hp-Finite Element Method
Procedia Computer Science
The paper presents an algorithm for finding the optimal initial three dimensional mesh for the self-adaptive hp Finite Element Method (hp-FEM) calculations. In our previous work we have proposed a method of selection of optimal initial two dimensional mesh. The problem of finding the optimal mesh was solved by means of hierarchical chromosome based genetic algorithm (HCBGA). In this paper the extension of the HCBGA to three dimensional problems is presented. The selection of the optimal initial
... mesh will optimize the convergence rate of the numerical error of the solution over the sequence of meshes generated by the self-adaptive hp-FEM. This is especially true in the case when material data are selected as result of some stochastic algorithm and it is not possible to design optimal initial mesh by hand. The hierarchical genetic algorithm is tested on the numerical simulations of three dimensional Step-and-Flash Imprint Lithography (SFIL). The SFIL is a modern patterning process utilizing the photopolymerization to replicate the topology of the substrate onto the template. The SFIL is modeled as linear elasticity with thermal expansion coefficient. It is shown that the convergence rate of the self-adaptive hp-FEM depends on the quality of the initial mesh provided by the genetic algorithm.