Grammatical evolution (GE), which is a kind of evolutionary algorithms, is designed to find a function, an executable program or program fragment that will achieve a good fitness value for the given objective function to be minimized. In this study, GE is applied for the coefficient identification problem of the stiffness matrix in the two-dimensional elastic problem. Finite element analysis of the plate with a circular hole is performed for determining the set of the stress and the strain components. Grammatical evolution determines the coefficient matrix of the relationship between the stress and strain components. The coefficient matrix is compared with Hooke's law in order to confirm the validity of the algorithm. After that, three algorithms are shown for improving the convergence speed of the original GE algorithm.


Keywords: grammatical evolution, Backus-Naur form (BNF), coefficient matrix, plane strain state.

This paper presents the out-of-core solver for three-dimensional multiphysics problems. In particular, our study focuses on the three-dimensional simulations of the linear elasticity coupled with acoustics. The out-of-core solver is designed with three principles in mind. First, to store the dense matrices associated with the nodes of the elimination tree with blocks related to nodes of the mesh, where many degrees of freedom may be located in the case of multiphysics computations with high order polynomials. The second principle is to minimize the memory usage. This is obtained by dumping out all local systems from the entire elimination tree to the disk during the elimination stage. The local systems are reutilized later during the backward substitution stage. The third principle is that the communication in the parallel version of the out-of-core solver occurs through the parallel file system. The memory usage of the solver is compared against the state-of-the-art MUMPS solver.


Keywords: multi-frontal direct solver, finite element method, out-of-core, parallel simulations, multiphysics.

We present a layered architecture for iterative solvers of linear equations, designed to allow for easy integration with existing hp-adaptive FEM codes. We discuss interfaces between a solver and an external FEM code and requirements for the FEM code that must be met in order to work with the solver. Our solution is suited to work effectively with stationary as well as time-dependent problems. In this article, we provide an overview of the layered solver's structure and modules of each layer. In subsequent articles, we will present specific implementations of particular layers.


Keywords: solver, FEM, higher-order.

Mesh smoothing improves mesh quality by node relocation without altering mesh topology. Such methods play a vital role in finite element mesh improvement with a direct consequence on the quality of the discretized solution. In this work, an improved version of the recently proposed geometric element transformation method (GETMe) for mesh smoothing is presented. Key feature is the introduction of adaptive concepts, which improve the resulting mesh quality, reduce the number of parameters, and enhance the parallelization capabilities. Implementational aspects are discussed and results of a more efficient version are presented, which demonstrate that GETMe adaptive smoothing yields high quality meshes, is particularly fast, and has a comparably low memory profile. Furthermore, results are compared to those of other state-of-the-art smoothing methods.


Keywords: mesh smoothing, GETMe adaptive, parallel smoothing, finite element mesh, mesh quality, mesh generation.

We proposed a method to analyze the galloping, a vibration by wind force, of transmission conductors. The Cosserat rod model was introduced to describe the motion of the conductor line. The deformation was tracked using the intrinsic framework of material coordinates which are able to handle the large motion in galloping phenomena. The Cosserat model provided a theory framework to simulate the non-linear coupling of the torsional motion and the translational motion. Such non-linear coupling was reported as one of the main causes for the galloping phenomena.


Keywords: galloping, numerical simulation, conductor, Cosserat rod.