GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
Solution of elastic scattering problems in linear acoustics using h-p boundary element method
Computer Methods in Applied Mechanics and Engineering - Special issue on reliability in computational mechanics
Finite Elements in Analysis and Design - Special issue: Optimum design in Japan
Analysis of the truncation errors in the fast multipole method for scattering problems
Journal of Computational and Applied Mathematics - Proceedings of the 8th international congress on computational and applied mathematics
A fast direct solver for boundary integral equations in two dimensions
Journal of Computational Physics
The Fast Solution of Boundary Integral Equations (Mathematical and Analytical Techniques with Applications to Engineering)
A fast direct solver for scattering problems involving elongated structures
Journal of Computational Physics
Stabilized boundary element methods for exterior Helmholtz problems
Numerische Mathematik
A Fast Direct Solver for a Class of Elliptic Partial Differential Equations
Journal of Scientific Computing
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This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton---Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.