The development of the method of fundamental solutions (MFS) and related methods for the numerical solution of scattering and radiation problems in fluids and solids is described and reviewed A brief review of the developments and applications in all areas of the MFS over the last five years is also given Future possible areas of applications in fields related to scattering and radiation problems are identified

https://inside.mines.edu/~pamartin/ref-paps/R080_EABEw.pdf

The method of fundamental solutions for scattering and radiation problems

The Green's function for three-dimensional transient heat conduction (diffusion equation) for functionally graded materials (FGMs) is derived. The thermal conductivity and heat capacitance both vary exponentially in one coordinate. In the process of solving this diffusion problem numerically, a Laplace transform (LT) approach is used to eliminate the dependence on time. The fundamental solution in Laplace space is derived and the boundary integral equation formulation for the Laplace Transform boundary element method (LTBEM) is obtained. The numerical implementation is performed using a Galerkin approximation, and the time-dependence is restored by numerical inversion of the LT. Two numerical inversion techniques have been investigated: a Fourier series method and Stehfest's algorithm, the latter being preferred. A number of test problems have been examined, and the results are in excellent agreement with available analytical solutions.

Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method

Up to now, work on topological design optimization of vibrating structures against noise radiation has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, and minimization of the dynamic compliance subject to harmonic loading on the structure. In this paper, we deal with topology optimization problems formulated directly with the design objective of minimizing the sound power radiated from the structural surface(s) into a surrounding acoustic medium. Bi-material elastic continuum structures without material damping are considered. The structural vibrations are excited by time-harmonic external mechanical loading with prescribed frequency and amplitude. It is assumed that air is the acoustic medium and that a feedback coupling to the structure can be neglected. Certain conditions are assumed that imply that the sound power emission from the structural surface can be obtained in a simpler way than by solving Helmholz’ integral equation. Hereby, the computational cost of the structural-acoustical analysis is substantially reduced. Several numerical results are presented and discussed for plate- and pipe-like structures with different sets of boundary and loading conditions.

Minimization of sound radiation from vibrating bi-material structures using topology optimization

Simulating sounds produced by realistic vibrating objects is challenging because sound radiation involves complex diffraction and interreflection effects that are very perceptible and important. These wave phenomena are well understood, but have been largely ignored in computer graphics due to the high cost and complexity of computing them at audio rates.We describe a new algorithm for real-time synthesis of realistic sound radiation from rigid objects. We start by precomputing the linear vibration modes of an object, and then relate each mode to its sound pressure field, or acoustic transfer function, using standard methods from numerical acoustics. Each transfer function is then approximated to a specified accuracy using low-order multi-pole sources placed near the object. We provide a low-memory, multilevel, randomized algorithm for optimized source placement that is suitable for complex geometries. At runtime, we can simulate new interaction sounds by quickly summing contributions from each mode's equivalent multipole sources. We can efficiently simulate global effects such as interreflection and changes in sound due to listener location. The simulation costs can be dynamically traded-off for sound quality. We present several examples of sound generation from physically based animations.

Precomputed acoustic transfer: output-sensitive, accurate sound generation for geometrically complex vibration sources

Acoustic attenuation performance of circular expansion chambers with extended inlet/outlet

Fundamentals of Linear Acoustics The Helmholtz Integral Equation Two-Dimensional Problems Three-Dimensional Problems The Normal-Derivative Integral Equation Indirect Variational Boundary Element Method in Acoustics Acoustic Eigenvalue Analysis by Boundary Element Methods Time Domain Three-Dimensional Analysis Extended Kirchhoff Integral Formulations.

Boundary Element Acoustics Fundamentals and Computer Codes

Boundary Element Analysis of Mufflers with AN Improved Method for Deriving the Four-Pole Parameters

A multidomain boundary element solution for silencer and muffler performance prediction

A direct boundary integral formulation for acoustic radiation in a subsonic uniform flow

Bulk-reacting sound absorbing materials are often used in packed silencers to reduce broadband noise. A bulk-reacting material is characterized by a complex mean density and a complex speed of sound. These two material properties can be measured by the two-cavity method or calculated by empirical formulas. Modeling the entire silencer domain with a bulk-reacting lining will involve two different acoustic media, air and the bulk-reacting material. Traditionally, the interior silencer domain is divided into different zones and a multi-domain boundary element method (BEM) may be applied to solve the problem. However, defining different zones and matching the elements along each interface is tedious, especially when the zones are intricately connected. In this paper, a direct mixed-body boundary element method is used to model a packed silencer without subdividing it into different zones. This is achieved by summing up all the integral equations in different zones and then adding the hypersingular integral equations at interfaces. Several test cases, including a packed expansion chamber with and without an absorbing center bullet, and a parallel baffle silencer, are studied. Numerical results for the prediction of transmission loss (TL) are compared to experimental data.

T.W. Wu

Papers

Boundary Element Acoustics Fundamentals and Computer Codes

Boundary Element Analysis of Mufflers with AN Improved Method for Deriving the Four-Pole Parameters

A multidomain boundary element solution for silencer and muffler performance prediction

A direct boundary integral formulation for acoustic radiation in a subsonic uniform flow

A direct mixed-body boundary element method for packed silencers