Investigation of a two-dimensional spectral element method for Helmholtz’s equation

Mehdizadeh, Omid Z.; Paraschivoiu, Marius

doi:10.1016/s0021-9991(03)00204-3

Cited by 46 publications

(26 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By doing so, it will be possible to address wider frequency ranges, as this three-dimensional FEM is still expensive regarding the computational cost for solving high frequency acoustic fields. A recent two-dimensional study by the authors of this report demonstrate that a significant gain can be achieved, both in terms of the degrees of freedom and CPU time, by undertaking p-extension, which involves increasing the order of the approximation, as opposed to h-extension, which involves reducing the element size [27]. This confirms the predictions by dispersion analysis [1,31].…”

Section: Resultssupporting

confidence: 79%

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

Mehdizadeh

Paraschivoiu

2005

Applied Acoustics

Self Cite

View full text Add to dashboard Cite

A three-dimensional finite element method has been implemented to predict the transmission loss of a packed muffler and a parallel baffle silencer for a given frequency range. Iso-parametric quadratic tetrahedral elements have been chosen due to their flexibility and accuracy in modeling geometries with curved surfaces. For accurate physical representation, perforated plates are modeled with complex acoustic impedance while absorption linings are modeled as a bulk media with a complex speed of sound and mean density. Domain decomposition and parallel processing techniques are applied to address the high computational and memory requirements. The comparison of the computationally predicted and the experimentally measured transmission loss shows a good agreement.

show abstract

Section: Resultssupporting

confidence: 79%

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

Mehdizadeh

Paraschivoiu

2005

Applied Acoustics

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is a known drawback of the FDTD method [13]. To overcome this drawback, subgridding techniques have been introduced in the literature [24][25][26][27][28][29][30][31][32][33]. In such techniques, part of the FDTD grid is replaced with a finer grid, which is called the subgrid [13].…”

Section: Two Dimensionsmentioning

confidence: 99%

On the application of the spectral element method in electromagnetic problems involving domain decomposition

Mahariq¹

2017

Turk J Elec Eng & Comp Sci

View full text Add to dashboard Cite

Abstract:One of the challenges in electromagnetics is to solve electromagnetic fields originated from a radiating source or a scattering object in distances that largely exceed the dimensions of the source or scatterer. In this paper, domain decomposition based on the application reasoning of the perfectly matched layer (PML) is studied by the spectral element method (SEM) for the first time in order to solve near and far electromagnetic fields without requiring substantially computational resources. Scattering from a loss-free dielectric cylinder and radiated fields from a line source are the problems utilized for the purpose of numerical demonstration in two dimensions in order to verify the successful application of SEM and its accuracy under domain decomposition. It is demonstrated that it is possible to accurately solve for near-field and far-field zones where millions of unknowns are encountered by using a typical personal computer.

show abstract

“…in which the tensor  is defined as: The numerical implementation of SEM introduced in [8] is adopted in this paper with Legendre polynomials being the basis functions.…”

Section: Electromagnetic Scattering Problemsmentioning

confidence: 99%

“…Recently, the features of SEM have attracted researchers to utilize this method in electromagnetic problems [6]- [8]. However, the effect of elemental aspect ratio on accuracy has not been investigated in numerical modeling of electromagnetic radiation and/or scattering problems when SEM is utilized.…”

Section: Introductionmentioning

confidence: 99%

On the Accuracy of Spectral Element Method in Electromagnetic Scattering Problems

Mahariq¹,

Tarman²,

Kuzuoğlu³

2014

IJCTE

View full text Add to dashboard Cite

Abstract-Spectral element method (SEM), which is known of its high accuracy, has been recently applied in solving electromagnetic problems governed by Maxwell's equations. This paper investigates the accuracy of SEM in twodimensional, frequency-domain electromagnetic scattering problems where Helmholtz equation acts as the governing partial differential equation (PDE). As experience in meshing a problem in finite element method is important to obtain accurate results, the choice of elements in SEM, on the other hand, is important too. The aspect ratio in this paper is taken into account while studying the accuracy in a single element by utilizing the Green's function. In addition, the scalar field scattered by a circular cylinder placed in front of an incident plane wave is solved after truncating the domain by perfectly matched layer. Numerical results show that one should carefully discretize the problem and keeping the aspect ratio close to unity as much as possible to guarantee accurate results.Index Terms-Aspect ratio, electromagnetic scattering, PML SEM. I. INTRODUCTIONIt is more an art experience than a science to know how to optimally place and size the mesh in finite element method (FEM). In fact, experience taught us to have more elements in the physical domain where functions change rapidly and less elements where low gradient is expected. Mesh generation may take several trials before achieving a good mesh [1]. On the other hand, the complexity in the physical domain itself may add additional limitations to mesh generation.In FEM, ranges of the aspect ratio have been investigated extensively and for wide variety of problems. As an example, but not restricted to, M. Picasso [2] proposed an adaptive algorithm for solving the Strokes problem with finite elements and meshes with high aspect ratio. In that paper, the effect of aspect ratio on the results is discussed in details and some examples were illustrated for a non-acceptable mesh that can deteriorate accuracy. V. Prachittham et al. [3] presented a two-dimensional adaptive method with large aspect ratio finite elements for the numerical simulation of mixed electroosmotic microflows. In their work, the refinement/ coarsening criterion is based on a posteriori error estimates. On the other side, spectral element method (SEM) which is known for its high degree of accuracy and lower CPU time and less memory requirement, when compared Manuscript received December 20, 2013; revised March 20, 2014 with other numerical methods, has the flexibility of using larger elemental aspect ratio without significant deterioration in accuracy. S. Dong et al. [4] proposed a parallel SEM for dynamic three-dimensional nonlinear elasticity problems that provides a tolerant large elemental aspect ratio employing Jacobi polynomial-based shape functions, as an alternative to the typical Legendre polynomial-based shape functions in solid mechanics. D. Rh. Gwynllyw et al. [5] proposed an iterative method for moving SEM applied to the journal bearing problem where they inve...

show abstract

Investigation of a two-dimensional spectral element method for Helmholtz’s equation

Cited by 46 publications

References 19 publications

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

A three-dimensional finite element approach for predicting the transmission loss in mufflers and silencers with no mean flow

On the application of the spectral element method in electromagnetic problems involving domain decomposition

On the Accuracy of Spectral Element Method in Electromagnetic Scattering Problems

Contact Info

Product

Resources

About