Journal of Computational Acoustics

A promising new fast (of order N log₂N)method for finding the numerical solution of broad classes of partial differential equations is introduced. This method is referred to as the Iterative Dual Domain Method (IDDM), since its iterations occur in both transformed and untransformed domains. The specific example used is the Helmholtz equation for both homogeneous and almost arbitrarily inhomogeneous media. Preliminary indications of the algorithm’s performance are illustrated by examples of: wave focusing through a thick lens, scattering from an inclusion, and guided waves in layered media.

Many computer algorithms contain an operation that accounts for a substantial portion of the total execution cost in a frequently executed loop. The use of a parallel computer to execute that operation may represent an alternative to a sheer increase in processor speed. The signal processing technique known as matched-field processing (MFP) involves performing identical and independent operations on a potentially huge set of vectors. To investigate a massively parallel approach to MFP and clustered nearest neighbors MFP, algorithms were implemented on a DECmpp 12000 massively parallel computer (from Digital Equipment and MasPar Corporation) with 8192 processors. The execution time for the MFP technique on the MasPar machine was compared with that of MFP on a serial VAX9000–210 equipped with a vector processor. The results showed that the MasPar achieved a speedup factor of at least 17 relative to the VAX9000. The speedup was 3.5 times higher than the ratio of the peak ratings of 600 MFLOPS for the MasPar versus 125 MFLOPS for the VAX9000 with vector processor. The execution speed on the parallel machine represented 64% of its peak rating. This is much better than what is commonly assumed for a parallel machine and was obtained with modest programming effort. An initial implementation of a massively parallel approach to clustered MFP on the MasPar showed a further order of magnitude increase in speed, for an overall speedup factor of 35.

It is well known that Euler equations support small amplitude acoustic, vorticity and entropy waves. To perform high quality direct numerical simulations of flow generated noise problems, acoustic radiation boundary conditions are required along inflow boundaries. Along boundaries where the mean flow leaves the computation domain, outflow boundary conditions are needed to allow the acoustic, vorticity and entropy disturbances to exit the computation domain without significant reflection. A set of radiation and outflow boundary conditions for problems with nonuniform mean flows are developed in this work. Flow generated acoustic disturbances are usually many orders of magnitude smaller than that of the mean flow. To capture weak acoustic waves by direct computation (without first separating out the mean flow), the intensity of numerical noise generated by the numerical algorithm and the radiation and outflow boundary conditions (and the computer) must be extremely low. It is demonstrated by a test problem involving sound generation by an oscillatory source that weak acoustic waves with maximum velocity fluctuation of the order of 10⁻⁹ of the mean flow velocity can be computed accurately using the proposed radiation boundary conditions. The intensity of such acoustic waves is much smaller than the numerical error of the mean flow solution.

Color is commonly used in representing scientific data, especially as color output devices have become widely available. The misuse of color can lead to confusing or even misleading representations of data. The purpose of this paper is to provide a review of guidelines for using color effectively, specifically aimed at the computational acoustics community. The question of whether or not to use color at all is initially raised, and gray-scale is suggested for appropriate cases. Human color deficiencies in technical audiences are then described, and the consequential choices of equally-accessible color schemes are discussed. The topics of human color perception models, hypsometric tints, contoured plots, and histogram equalization are introduced. Color palettes specifically suited for acoustical phenomena, such as linear and dB magnitudes, scales for positive and negative data, circular palettes for phase, and methods for illustrating different classes of phenomena (e.g., wave types) on a single plot, are discussed in detail. Color examples and Mathematica code are provided, and final recommendations are made for choosing effective color schemes.

This paper describes the development of high-order Kirchhoff algorithms and confirms that high-order accuracy can be achieved with the Kirchhoff approach when high-order integration and interpolation are properly implemented. This paper also establishes guidelines for enhancing accuracy of a given order property when the Kirchhoff formula is applied to results obtained from a computational fluid dynamics (CFD) solution. Accuracy is shown to increase when the Kirchhoff surface size is minimized. Reduction of the Kirchhoff surface size also enhances efficiency of the calculation because the size of the relatively expensive CFD computation is reduced. The accuracy of the Kirchhoff approach is also enhanced by increasing the density of information along the Kirchhoff surface. This increase in information is necessary because evaluation of the Kirchhoff integrand at the retarded time demands higher spatial resolution than the integration of the time-dependent nonlinear equations of the CFD calculation. A procedure has been developed that addresses the Kirchhoff resolution requirements without sacrificing efficiency. The error reduction realized with this procedure matches that realized with CFD mesh refinement, with almost no increase in cost.