Analysis of Open Waveguides Using the Finite-Element Method and Boundary Integral Equations

2008 ◽  
Vol 44 (7) ◽  
pp. 676-679 ◽  
Author(s):  
Hyoungsuk Yoo ◽  
Y. Boubendir ◽  
A. Gopinath
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
The Finite Element Method ◽  
Open Waveguides ◽  
Element Method

Fundamentals and Applications of the Finite-Element Method in Analyzing Structural and Nonstructural Marine Problems

1982 ◽  
Vol 19 (03) ◽  
pp. 272-292
Author(s):  
Donald Liu ◽  
Yung-Kuang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Static And Dynamic Analysis ◽  
Marine Industry ◽  
Wide Range ◽  
Element Method

The finite-element method has become a popular and effective tool not only for structural analysis, but also for a wide range of physical problems which are of particular interest to the marine industry. A brief review of the finite-element formulation for structural and nonstructural problems is presented. Applications to marine structures, including static and dynamic analysis and fracture mechanics, are given. Nonstructural applications to heat transfer and ship hydrodynamic problems are also demonstrated. Recent developments in the coupled fluid-structural interaction problem using the boundary integral method, which is considered as an extension of the finite-element method, are also described.

Coupling of finite element method and integral formulation for vector Helmholtz equation

2018 ◽  
Vol 37 (4) ◽  
pp. 1405-1417
Author(s):  
Sebastian Grabmaier ◽  
Matthias Jüttner ◽  
Wolfgang Rucker
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Helmholtz Equation ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Formulation ◽  
The Finite Element Method ◽  
Content Type ◽  
Wide Range ◽  
Element Method

Purpose Considering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral formulation. It is demonstrated that the method is well-suited for many realistic three-dimensional problems in high-frequency engineering. Design/methodology/approach The formulation is based on partial solutions fulfilling the global boundary conditions and the iterative interaction between them. In comparison to other coupling formulation, this approach avoids the typical singularity in the integral kernels. The approach applies ideas from domain decomposition techniques and is implemented for a parallel calculation. Findings Using confirming elements for the trace space and default techniques to realize the infinite domain, no additional loss in accuracy is introduced compared to a monolithic finite element method approach. Furthermore, the degree of coupling between the finite element method and the integral formulation is reduced. The accuracy and convergence rate are demonstrated on a three-dimensional antenna model. Research limitations/implications This approach introduces additional degrees of freedom compared to the classical coupling approach. The benefit is a noticeable reduction in the number of iterations when the arising linear equation systems are solved separately. Practical implications This paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications. Originality/value The novelty of the paper is the proposed formulation for the coupling of both methods.

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