Narrow Results

The convergence behavior of the Krylov subspace iterative solvers towards the systems with the 3D acoustical BEM is investigated through numerical experiments. The fast multipole BEM, which is an efficient BEM based on the fast multipole method, is used for solving problems with up to about 100,000 DOF. It is verified that the convergence behavior of solvers is much affected by the formulation of the BEM (singular, hypersingular, and Burton-Miller formulation), the complexity of the shape of the problem, and the sound absorption property of the boundaries. In BiCG-like solvers, GPBiCG and BiCGStab2 have more stable convergence than others, and these solvers are useful when solving interior problems in basic singular formulation. When solving exterior problems with greatly complex shape in Burton-Miller formulation, all solvers hardly converge without preconditioning, whereas the convergence behavior is much improved with ILU-type preconditioning. In these cases GMRes is the fastest, whereas CGS is one of the good choices, when taken into account the difficulty of determining the timing of restart for GMRes. As for calculation for rigid thin objects in hypersingular formulation, much more rapid convergence is observed than ordinary interior/exterior problems, especially using BiCG-like solvers.

Krylov subspace iterative solvers are applied to large-scale finite element sound-field analyses of architectural rooms. First, convergence behaviors are compared among four iterative solvers. Results show that the Conjugate Orthogonal Conjugate Gradient (COCG) method offers the best characteristics for finite-element (FE) analysis from the viewpoint of robustness of convergence and computation time. Two investigations to reduce the computation time of the COCG method were carried out. Results show the following. (1) The mean residual of sound pressure levels between COCG method and direct method is less than 0.1 dB if the convergence criterion is set to 10^-4 and the maximum residual of those between COCG method and direct method is less than 0.2 dB if the convergence criterion is set to 10^-6. (2) The computation time of the COCG method with diagonal preconditioning is about 30% shorter than that of COCG method without preconditioning. Finally, sound pressure level distributions obtained using the authors' FEM are compared to those obtained using fast multipole BEM (FMBEM) and measurements.

The present study involves numerical assessment of two types of boundary elements, namely constant and discontinuous quadratic elements based on a hypersingular Burton and Miller boundary integral formulation to tackle spurious frequencies manifesting in exterior problems. Convergence trends of the two types of boundary element with/without the inclusion of hypersingular formulation were studied for various combinations of boundary conditions and over a wide range of frequencies. The results indicate that discontinuous quadratic elements and constant elements give comparable results, with the quadratic elements being computationally more efficient as they take lesser computational time. Nevertheless, the constant element formulation is easier to implement, and it may be used for solving exterior wave propagation problems.