Efficient Multilevel Preconditioners for Three-Dimensional Plane Wave Helmholtz Systems with Large Wave Numbers

2017 ◽  
Vol 15 (3) ◽  
pp. 1242-1266 ◽  
Author(s):  
Qiya Hu ◽  
Xuan Li
Keyword(s):  
Plane Wave ◽  
Three Dimensional ◽  
Large Wave ◽  
Multilevel Preconditioners ◽  
Dimensional Plane ◽  
Wave Numbers

scholarly journals Adaptive-multilevel BDDC algorithm for three-dimensional plane wave Helmholtz systems

2021 ◽  
Vol 381 ◽  
pp. 113011
Author(s):  
Jie Peng ◽  
Shi Shu ◽  
Junxian Wang ◽  
Liuqiang Zhong
Keyword(s):  
Plane Wave ◽  
Three Dimensional ◽  
Dimensional Plane

scholarly journals EXACT DUALITY AND NILPOTENT GAUGING

1994 ◽  
Vol 09 (10) ◽  
pp. 925-933 ◽  
Author(s):  
ALOK KUMAR ◽  
SWAPNA MAHAPATRA
Keyword(s):  
Plane Wave ◽  
Three Dimensional ◽  
Inverse Transformation ◽  
Duality Transformations ◽  
Dimensional Plane

We obtain new duality transformations, relating some exact string backgrounds, by defining the nilpotent duality. We show that the ungauged SL (2, ℝ) WZW model transforms by its action into the three-dimensional plane wave geometry. We also give the inverse transformation from the plane wave to the SL (2, ℝ) model and discuss the implications of the results.

scholarly journals Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Daniel Omondi Onyango ◽  
Robert Kinyua ◽  
Abel Nyakundi Mayaka
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Plane Wave ◽  
Acoustic Pressure ◽  
Three Dimensional ◽  
The Other ◽  
Expansion Chamber ◽  
Central Tube ◽  
Simple Expansion ◽  
Plane Wave Propagation

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

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