Z razvojem računalništva je numerično reševanje fizikalnih problemov postalo enostavnejše. Omogočilo nam je obravnavo kompleksnejših problemov, hkrati pa so se povečale tudi zahteve po natančnosti rezultatov. Osnovni pristop k reševanju je zato pogosto časovno zelo potraten. Z uporabo dodatnih metod je možno čas računanja pri numerični analizi znatno zmanjšati ter pri tem ohraniti natančne rezultate. V okviru te magistrske naloge je predstavljena numerična analiza problema širjenja akustičnega valovanja z uporabo metode končnih elementov. Izpeljani numerični model in implementacijo z lastno programsko kodo smo validirali z različnimi primeri. Ker bistveno dogajanje obravnavanega problema poteka na lokalnem območju, je predstavljena metoda za adaptivno izpopolnjevanje mreže z razdelitvijo elementov. Poleg tega smo predstavili tudi lastno metodo za pohitritev izračunov, ki izhaja iz aktivacije končnih elementov. Obe metodi smo skupaj z osnovnim pristopom uporabili za numerično analizo enodimenzijskega in dvodimenzijskega problema ter izvedli primerjavo z vidika časov računanja. With the development of computer science, numerical solving of physical problems has become easier. It has allowed us to tackle more complex problems, but has also increased the demands on the accuracy of the results. The basic approach to solving is therefore often very time-consuming. By using additional methods, the computation time for numerical analysis can be significantly reduced while maintaining accurate results. This master thesis presents a numerical analysis of the acoustic wave propagation problem using the finite element method. We validated the derived numerical model and the implementation with our own programming code using different examples. Since the essential action of the considered problem takes place in the local area, a method for adaptive mesh refinement with element subdivision is presented. In addition, we have presented our own method to speed up calculations, which is based on finite element activation. Both methods, together with the basic approach, were used to numerically analyse the one-dimensional and two-dimensional problems and to make a comparison in terms of computation times.
