Large-Scale Noise Simulation in Urban Environments Using a Preconditioned Helmholtz Solver

Sammanfattning

This thesis studies the finite element solution of the time-harmonic Helmholtz equationfor acoustic wave propagation in urban environments. The discretized Helmholtzequation gives rise to large, complex-valued, indefinite linear systems, for whichstandard iterative methods may converge very slowly. The aim of this work is toimplement and evaluate a preconditioned GMRES solver for such systems, withfocus on solver performance, parameter choices, and practical memory limitations.The solver uses a two-level restricted additive Schwarz preconditioner with aspectral coarse space, following the RAS/MS-GFEM approach of Ma, Alber, Scheichl,and Zhang. The implementation is first verified on an exact plane-wave problem,then tested on a controlled rectangular box domain, and finally applied torealistic city-domain meshes representing part of Gothenburg. The experimentsinvestigate how mesh resolution, frequency, and the choice of coarse space affectconvergence and computational cost.The results show that the two-level coarse correction considerably improves GMRESconvergence compared with a one-level method and with plain GMRES withoutpreconditioning. On the box domain, the method gives stable algebraic convergenceup to 30 Hz, although the acoustic field is not fully mesh-converged at the higherfrequencies. On the city geometry, the 5 Hz case gives the clearest mesh-refinementbehaviour, while the 10 Hz, 20 Hz, and 30 Hz cases become increasingly demanding.The largest city runs show that explicit storage of the coarse basis can becomememory-limiting. The study therefore shows that the two-level spectral Schwarz preconditioneris promising for large Helmholtz problems in urban acoustics, but thathigher-frequency simulations require careful choices of mesh resolution, coarse-spacesize, and memory-efficient implementation.Keywords: