Improved multimodal formulation of the wave propagation in a 3D waveguide with varying cross-section and curvature

Abstract

An efficient method is proposed to solve the multimodal wave propagation within a three-dimensional waveguide bounded by a hard wall with varying cross section and curvature. This is achieved by first turning the original problem, in a complex-shaped waveguide, into a cylindrical waveguide with unit radius, by means of an adapted and flexible geometrical transformation. Then supplementary modes are defined to enrich the standard modal basis that is usually considered in such methods and to help restore the right boundary condition. It is shown through various numerical applications that the introduction of these supplementary modes, whatever the complexity of the waveguide geometry, significantly enhances the multimodal method, notably by increasing its convergence rate, whether one's aim is to solve the wavefield or the scattering problem.

A Fault-Tolerant Structure for Nano-Power Communication Based on the Multidimensional Crossbar Switch Network

“…In order to solve the yield problem of 3D chips, TSV fault tolerance research has gradually been reported in recent years, arousing the attention of researchers at home and abroad. Guennoc, T. et al first proposed a circuit model for vertical channels and then proposed a fault-tolerant technology for TSV redundancy, which improved the yield from 66% to 98% [4]. Xiao, Y. et al proposed a fault-tolerant approach based on multichannel, which can improve reliability and throughput at the same time [5].…”

Transmission line coefficients for viscothermal acoustics in conical tubes

“…Since equation (17) involves no derivative in the longitudinal direction, it can be considered on each cross-section Ω independently. To highlight the fact that the overall shape of ψ depends only on α, the problem is brought back to a reference domain Ω, which is planar for straight tubes, or a section of a sphere for cones.…”

“…Function F (α) fully describes how the shape of the cross-section affects viscothermal losses. This shape function F (α) must be calculated for each considered cross-sectional shape, by solving equation (17). Analytical expressions are given below for cylinders and for circular cones (see (35) and ( 52)).…”

“…Several techniques are available to obtain better predictions in wide tubes or in horns with abrupt section variation [2, §7.6.3.5] including 3D finite elements [15], multi-modal propagation [16,17], and ad hoc methods [18]. The use of a horn equation with a modified effective radius profile has also shown improved results [6,19,20].…”

Efficient 3D Acoustic Simulation of the Vocal Tract by Combining the Multimodal Method and Finite Elements

“…Following earlier works on the multimodal formulation in complex-shaped waveguides (2D [39] or 3D with circular cross-section [30]), we define a geometrical transformation from the Cartesian coordinates (X, Y, Z) in which the segments are curved with a varying cross-sectional area (see Fig. 2a), to the coordinates (x, y, z) in which they are straight with a constant cross-sectional area, as illustrated in Fig.…”