Review Of Finite Element Methods Research Articles

A Review of Finite Element Methods for Room Acoustics

Accurate predictions of the wave-dominated region of an acoustic field in a room can be generated using wave-based computational methods. One such method is the finite element method (FEM). With presently available computing power and advanced numerical techniques, it is possible to obtain FEM predictions of sound fields in rooms with complicated geometries and complex boundary conditions in realistic time frames. The FEM has been continuously developed since its inception and attempts to provide solutions in real time using finite element-based methods are beginning to appear in the literature; these developments are especially interesting for auralization and virtual acoustics applications. To support these efforts, and provide a resource for neophytes, the use of the FEM for room acoustics is reviewed in this article. A history is presented alongside examples of the method’s derivation, implementation, and solutions. The current challenges and state-of-the-art are also presented, and it is found that the most recent contributions to the field make use of one or a mixture of the following: the finite element-based discontinuous Galerkin method, extended reaction boundary conditions written in the frequency domain but solved in the time domain, and the solution of large-scale models using parallel processing and graphics processing units.

Finite Element Methods for Arc Discharge Simulation

The numerical simulation of industrial arc discharge processes, such as plasma spraying, cutting, and welding, faces severe challenges that include resolution of multiscale features, multiphysics coupling, and robustness in the presence of large gradients. A review of Finite Element Methods (FEMs), particularly the Variational Multiscale (VMS) method, applied to arc discharge simulation is presented. The plasma is modeled as a compressible electromagnetic fluid in chemical equilibrium and thermodynamic nonequilibrium (NLTE). The effectiveness of the NLTE model and the VMS‐FEM is demonstrated with the simulation of canonical and industrially relevant arc discharges, namely the plasma flow in transferred and non‐transferred arc plasma torches and the free‐burning arc.

Finite element applications in acoustics

A review of finite element methods in acoustics is presented. General concepts of FEM such as weighted residual and variational formulations, element types and interpolation within elements, the assembly of elements, continuity of the solution at element boundaries, requirements placed on FEM meshes by high frequencies, the imposition of boundary conditions on rigid, flexible, and absorbing surfaces, the representation of sources, and the approximation of far-field radiation conditions are discussed. The application of FEM to several types of problems in acoustics is demonstrated by reference to published results. Specific examples include: (1) interior problems such as resonant frequencies and forced response in enclosures such as car bodies, aircraft cabins, auditoria, and combustors; (2) sound propagation in moving media in ducts and propagation and radiation in and around aircraft turbofan engines; (3) structure and acoustic interatction such as transmission of sound through aircraft fuselages; (4) acoustic radiation problems which are related to (2) and (3). Emphasis is placed on the physical content of the various problems, mesh generation, the choice of elements, solution procedures, accuracy, and computer resource requirements.

Finite element analysis of waveguides and cavities-a review

A review of finite-element methods (FEMs) of analyzing uniform waveguides used in microwaves and optics, with emphasis on the latter, is given. The main concern is with modal analysis of the waveguides, such as finding the few dominant modes of any prescribed waveguide structure. Spurious modes are considered, with two recent schemes for their avoidance. Attention is also given to the commonly ignored complex modes. Modal analysis of the same optical waveguides, but including nonlinear material, is considered. Z-stepping algorithms are referred to for their importance in dealing with nonlinear waveguides, and with slowly varying, long, guiding structures. >

Optimum design of internal upset geometry of drill pipe for longer fatigue life: Tsukano, Y., Miyoshi, H., Sogo, Y., Nishi, S. and Takeuchi, E. Nippon Steel Technical Report Jan. 1990 (44), 37–42

The paper gives a bibliographical review of finite element methods(FEMs) applied for the analysis of pressure vessel structures/components and piping from the theoretical as well as practical points of view. This bibliography is a new addendum to the Finite elements in the analysis of pressure vessels and piping—a bibliography [1], [2], [3]. The listings at the end of the paper contain 856 references to papers and conference proceedings on the subject that were published in 2001–2004. These are classified in the following categories: linear and nonlinear, static and dynamic, stress and deflection analyses; stability problems; thermal problems; fracture mechanics problems; contact problems; fluid–structure interaction problems; manufacturing of pipes and tubes; welded pipes and pressure vessel components; development of special finite elements for pressure vessels and pipes; finite element software; and other topics.

Review of finite element methods for microwave and optical waveguides

The authors review the application of the finite element method to analysis of waveguide problems. They discuss the significance of different variational formulations, the modeling of the infinite domain of open-boundary waveguides, techniques to avoid spurious solutions, and matrix solution techniques. They briefly refer to the application of these techniques to waveguides containing nonlinear materials and to three-dimensional problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>