Publications of the University of Eastern Finland

Time-dependent wave fields are often approximated using wave equations. Due to the oscillatory nature of wave phenomena, numerical approximations of wave equations are challenging. Approximating wave problems with tolerable accuracy requires the use of a relatively dense spatial discretization. For standard numerical techniques, such as the low-order finite difference and finite element methods, 10 grid points per wavelength is considered the rule of thumb. Particularly for short wavelengths, the requirement of a dense mesh can easily lead to problems of intolerable computational complexity. The computational burden can, however, be reduced using more sophisticated numerical methods. Discontinuous Galerkin (DG) methods to address this issue have been extensively studied. In this thesis, the DG method is used for modeling time-dependent wave fields in an inhomogeneous medium. More precisely, the main focus was to develop a feasible DG method for modeling wave fields with complicated geometries with reduced computational complexity. The DG approach was examined for unbounded twoand three-dimensional wave problems. Truncation of a physically unbounded problem into a problem with a bounded domain affects the accuracy of the numerical solution. A perfectly matched layer is used to truncate the computational domain in three-dimensional wave problems. In the numerical experiments, the DG method was studied from a computational point of view. Based on previous theoretical analyses, non-uniform basis orders to increase the accuracy of the numerical solution was the main research topic. The non-uniform basis orders were investigated in twoand three-dimensional problems. In the model problems, non-uniform basis orders were also extended to a case in which wave propagation and scattering were studied in a geometry that comprised a loudspeaker. In this model problem, the numerical solution was compared to actual measurements. The results predicted that a predetermined error level of the solution can be obtained with the correct basis order choices. At the same time, the use of non-uniform basis orders reduces the computational load. AMS Classification: 65M60, 65Z05, 74J05, 74J20, 74S30, 76Q05 Universal Decimal Classification: 519.6, 534-8, 534.2 INSPEC Thesaurus: acoustic waves; acoustics; numerical analysis; time-domain analysis; modelling Yleinen suomalainen asiasanasto: aaltoliike; akustiikka; numeeriset menetelmät; numeerinen analyysi; matemaattiset mallit; mallintaminen