Wideband Fmbem For 3d Acoustic Sensitivity Analysis

The Boundary Element Method (BEM) as a very powerful alternative to the Finite Element Method (FEM) requires only a surface discretization not a discretization of the domain as the FEM. This reduction of the dimensionalities of the problem by one greatly facilitates the data preparation, permits an easy mesh-refinement and leads to a system of algebraic equations much smaller than the one encountered in the FEM. But due to a fully populated, non-symmetrical and sometimes ill-conditioned coefficient matrix produced in the BEM, the conventional BEM (CBEM) has suffered from the high computational complexity and high storage requirements for several decades until the fast algorithms such as the fast multipole algorithm were proposed. Now, in combinations with the iterative solvers and the fast multipole algorithm, the boundary element method can be accelerated to solve many large-scale practical engineering problems even on desktop PCs.This dissertation is focused in the acoustic field prediction and acoustic sensitivity analysis using the BEM, and the three dimensional wideband fast multipole boundary element approaches for solving large-scale acoustic prediction problems and acoustic sensitivity analyses are developed to overcome the high solution cost and high storage requirements associated with the CBEM. As for large-scale acoustic prediction problems, a wideband fast multipole boundary element algorithm is presented for full-space acoustic wave problems first, and then the full-space algorithm is modified and extended to solve half-space acoustic wave problems. As to large-scale acoustic sensitivity analyses, the fast multipole algorithms and the iterative solver GMRES are also employed to accelerate the boundary element acoustic sensitivity analyses based on the direct differentiation method, the discrete adjoint variable method and the continuous adjoint variable method, respectively.The Burton-Miller method which is a linear combination of the conventional and normal derivative boundary integral equations is employed to overcome the fictitious eigenfrequency problem associated with the conventional boundary integral equation method when solving exterior acoustic wave problems. The Burton-Miller boundary integral formulation has strongly singular and hypersingular boundary integrals which are evaluated as Cauchy principal values and Hadamard finite-parts for the constant element discretization in this study. So that, a set of non-singular boundary integral equations for both acoustic state analyses and acoustic sensitivity analyses can be obtained, which make the fast multipole boundary element method easy programming and more efficient to use, especially in the acoustic sensitivity analyses based on the direct differentiation method and the discrete adjoint variable method.Finally, the developed fast algorithms for both three dimensional acoustic field prediction problems and acoustic sensitivity analyses are employed in the shape design and optimization analyses of the traffic noise barriers, so as to develop a set of fast shape optimization methods for the design of noise barriers. The effect of several types of barriers are compared, and the shape of the best one is further studied and optimized to make it more effective. Also, more engineering applications are expected to be solved using the developed algorithms in the future.