Application of a Hierarchical Chromosome Based Genetic Algorithm to the Problem of Finding Optimal Initial Meshes for the Self-Adaptive hp-FEM

The paper presents an algorithm for finding the optimal initial mesh for the self-adaptive hp Finite Element Method (hp-FEM) calculations. We propose the application of the hierarchical chromosome based genetic algorithm for optimal selection of the initial mesh. 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 a result of some stochastic algorithm and it is not possible to design optimal initial mesh by hand. The algorithm has been tested on the non-stationary mass transport problem modeling phase transition phenomenon

A New Divergence Method for Heat Transfer with Neumann Boundary Condition

New Divergence Theorem is a new formulation for the simplest case of heat transfer problem involving Neumann Boundary Condition which combines two different numerical techniques which are Finite Element Method (FEM) and Finite Volume Method (FVM). The use of numerical techniques to solve such problems is therefore considered essentials since the powerful Finite Element Method (FEM) is capable in solving heat transfer analysis by giving a piecewise approximation of the domain. This study aims to evaluate the hypothesis of combining FEM with the FVM and to develop a new formulation of heat transfer problem involving Neumann Boundary Condition. Finite Volume Method (FVM), which uses the concept of Green Divergence Theorem, where a surface integral can be transformed to line integral has less accuracy since it develops the assumption of constant flux