A Finite Element Method of Lines Scheme for Guided-Wave Structures

Abstract

A hybrid scheme that incorporates the method of finite elements, the method of lines, variational techniques, and conformal mapping is proposed for the analysis of guided-wave structures. This technique is devised to analyze complex waveguide structures with irregular composite geometries. High numerical accuracy is maintained by treating key singularities by semianalytical procedures. Compared with the conventional method of lines with finite difference techniques, the proposed scheme is able to solve many complex guided-wave problems with fewer mesh lines without compromise on accuracy. This gain is due to the added variable mesh-directions and the flexibility in the method of finite elements in choosing appropriate functions for fitting the configuration of concern.Index Terms-Guided-wave problems, method of finite elements, method of lines, variational analysis.

Dynamic Analysis of Tall-Pier Aqueduct Using ODE Solver

“…In contrast, with a low computational cost, the nondiscretization and semi-discretization method based on ordinary differential equation (ODE) solver has been proved highly effective in the simplified structural analysis of tall building [8,9]. And the newly developed finite element method of lines, which is another semi-analytical method based on ODE solver, has been already applied in many fields [10,11] owing to its high precision.…”

Efficient hybrid scheme of finite element method of lines for modelling computational electromagnetic problems

“…However, the conventional MOL makes use of a finite difference technique to discretize the problem and turn it into a set of analytically solvable ordinary differential equations (ODEs) with nodal line functions as the basic unknowns. Different from the conventional MOL, our proposed hybrid finite element method of lines FEMOL scheme utilizes a finite element technique in a semi-discrete form [9][10][11][12][13][14]. Partial differential equations (PDEs) defined on some particular domains even though they may be arbitrary are semi-discretized into a system of ODEs defined on discrete mesh lines (straight or curved) via variational principles, and then the resulting ODE system can directly be solved using a standard and robust ODE solver.…”