Numerical Solution Of Wave Propagation Problems Based On Zero-moment Scaling Function And Enriched Finite Element

In wavelet finite element, wavelet analysis is introduced into the conventional finiteelement, using scaling function as interpolation function to approximation solving. Usingwavelet multi-resolution features, it can be achieved to improve the resolution withoutchanging the grid subdivision, so the amount of calculation can be significantly reduced.Conventional finite element has some problems for solving the problem of wavepropagation, such as low accuracy, large amount of calculation, and so on, especially forthe wave propagation problem of big wave numbers. So, in this work, we introducedwavelet finite element into the solution of wave propagation problem. Because of Zeromoment scaling function has the vanishing moments of both wavelet function and scalingfunction, the algorithm of translated moments is predigested to make relative calculations,such as translated moments, connection coefficient and so on, more convenient andprecise, so, in this work, we introduce Coiflet wavelet finite element into the solution ofwave propagation equations, then to search more effective methods.First, we construct the scaling function of two-dimensional Coiflet wavelet, andcalculate its values, then we construct two-dimensional Coiflet wavelet finite element.Then we use the method to solve two-dimensional Helmholtz equation and transient wavepropagation problems; at the same time, we introduce one-dimensional Coiflet waveletfinite element into the solution of one-dimensional Helmholtz equation, the results allshow a good solution accuracy.Then, we also construct the enriched finite element method in this work. The essenceof the method is using the special functions to enrich the traditional finite element basisfunctions, introducing additional degrees of freedom on the same node, thereby toimprove the solution accuracy of traditional finite element. In this work, we also use thismethod to solve one-dimensional, two-dimensional Helmholtz equation and transientwave propagation problems, and the results all demonstrate that enriched finite elementmethod has higher solution accuracy than traditional finite element, especially for thewave propagation problem of big wave numbers.