A damping preconditioner for time-harmonic wave equations in fluid and elastic material

A physical damping is considered as a preconditioning technique for acoustic and elastic wave scattering. The earlier preconditioners for the Helmholtz equation are generalized for elastic materials and three-dimensional domains. An algebraic multigrid method is used in approximating the inverse of damped operators. Several numerical experiments demonstrate the behavior of the method in complicated two-dimensional and three-dimensional domains. peerReviewed

An algebraic multigrid based shifted-Laplacian preconditioner for the Helmholtz equation

A preconditioner defined by an algebraic multigrid cycle for a damped Helmholtz operator is proposed for the Helmholtz equation. This approach is well suited for acoustic scattering problems in complicated computational domains and with varying material properties. The spectral properties of the preconditioned systems and the convergence of the GMRES method are studied with linear, quadratic, and cubic finite element discretizations. Numerical experiments are performed with two-dimensional problems describing acoustic scattering in a cross-section of a car cabin and in a layered medium. Asymptotically the number of iterations grows linearly with respect to the frequency while for lower freq…

Numerical methods for acoustics and noise control

Artikkeliväitöskirja. Sisältää yhteenveto-osan ja viisi artikkelia. Article dissertation. Contains an introduction part and five articles. This dissertation considers numerical methods for wave propagation modelling and noise control. The first part of the dissertation discusses an efficient method for solving time-harmonic wave equations in acoustic (the Helmholtz equation) and elastic domains (the Navier equation). The solver is based on preconditioning a Krylov subspace method, such as GMRES, with approximations of damped variants of the corresponding wave equations. An algebraic multigrid method is used in approximating the inverse of damped operators. The method can be used in complex …

Numeerista virtauslaskentaa hila-Boltzmann-simulointimenetelmällä

Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics

Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz pro…

Multiobjective muffler shape optimization with hybrid acoustics modelling

Shape optimization of a duct system with respect to sound transmission loss is considered. The objective of optimization is to maximize the sound transmission loss at multiple frequency ranges simultaneously by adjusting the shape of a reactive muffler component. The noise reduction problem is formulated as a multiobjective optimization problem. The sound attenuation for each considered frequency is determined by a hybrid method, which requires solving Helmholtz equation numerically by finite element method. The optimization is performed using non-dominated sorting genetic algorithm, NSGA-II, which is a multi-objective genetic algorithm. The hybrid numerical method is flexible with respect …

LOCAL CONTROL OF SOUND IN STOCHASTIC DOMAINS BASED ON FINITE ELEMENT MODELS

A numerical method for optimizing the local control of sound in a stochastic domain is developed. A three-dimensional enclosed acoustic space, for example, a cabin with acoustic actuators in given locations is modeled using the finite element method in the frequency domain. The optimal local noise control signals minimizing the least square of the pressure field in the silent region are given by the solution of a quadratic optimization problem. The developed method computes a robust local noise control in the presence of randomly varying parameters such as variations in the acoustic space. Numerical examples consider the noise experienced by a vehicle driver with a varying posture. In a mod…

Äänenvaimentimien mallinnuspohjainen monitavotteinen muodonoptimointi

Multi-objective actuator placement optimization for local sound control evaluated in a stochastic domain

A method to find optimal locations and properties of anti-noise actuators in local noise control system is considered. The local noise control performance is approximated by a finite element method based approach, that attempts to estimate the average performance of optimal active noise control (ANC) system. The local noise control uses a fixed number of circular actuators that are located on the boundary of a three-dimensional enclosed acoustic space. Actuator signals are used to minimize the known harmonic noise at specified locations. The average noise reduction is maximized at two frequency ranges by adjusting the anti-noise actuator configuration, which is a non-linear multi-objective …

Multiobjective muffler shape optimization with hybrid acoustics modelling

This paper considers the combined use of a hybrid numerical method for the modeling of acoustic mufflers and a genetic algorithm for multiobjective optimization. The hybrid numerical method provides accurate modeling of sound propagation in uniform waveguides with non-uniform obstructions. It is based on coupling a wave based modal solution in the uniform sections of the waveguide to a finite element solution in the non-uniform component. Finite element method provides flexible modeling of complicated geometries, varying material parameters, and boundary conditions, while the wave based solution leads to accurate treatment of non-reflecting boundaries and straightforward computation of the …

Prospectives to tractor cabin design with computational acoustics tools

Computational acoustical models allow automated optimization of tractor design with respect to acoustic properties, which could speed up significantly the design process of tractor cabin prototypes. This article gives insightful prospectives to the tractor design process by considering modern computational acoustics technology. Mathematical formulation for a system consisting of vibrating elastic tractor structure and airfilled acoustic enclosure are given and a related numerical solution technique with finite element method (FEM) is presented. Simulation results produced with commercially available software are reviewed. nonPeerReviewed

Quadratic least-squares formulation for a local active noise control with stochastic domain and noise source

A local active noise control method that uses stochastic numerical acoustical modeling is introduced. The frequency domain acoustical simulations are performed by a sequence solutions to Helmholtz equations approximated by FEM. The proposed ANC method maps microphone measurements linearly to the output signals of antinoise actuators. The matrix defining the linear mapping is optimized for each frequency to minimize expected value of the noise. The paper concentrates on defining the quadratic least-squares optimization problem for the minimization of the sound pressure field in the silet region. The formulation leads to a robust and accurate noise control in stochastic domains that has a sto…

An optimal local active noise control method based on stochastic finite element models

A new method is presented to obtain a local active noise control that is optimal in stochastic environment. The method uses numerical acoustical modeling that is performed in the frequency domain by using a sequence of finite element discretizations of the Helmholtz equation. The stochasticity of domain geometry and primary noise source is considered. Reference signals from an array of microphones are mapped to secondary loudspeakers, by an off-line optimized linear mapping. The frequency dependent linear mapping is optimized to minimize the expected value of error in a quiet zone, which is approximated by the numerical model and can be interpreted as a stochastic virtual microphone. A leas…