Study of compression techniques for partial differential equation solvers
Tutor / directorHernández Ortega, Joaquín Alberto
Document typeBachelor thesis
Rights accessOpen Access
Partial Differential Equations (PDEs) are widely applied in many branches of science, and solving them efficiently, from a computational point of view, is one of the cornerstones of modern computational science. The finite element (FE) method is a popular numerical technique for calculating approximate solutions to PDEs. A not necessarily complex finite element analysis containing substructures can easily gen-erate enormous quantities of elements that hinder and slow down simulations. Therefore, compression methods are required to decrease the amount of computational effort while retaining the significant dynamics of the problem. In this study, it was decided to apply a purely algebraic approach. Various methods will be included and discussed, ranging from research-level techniques to other apparently unrelated fields like image compression, via the discrete Fourier transform (DFT) and the Wavelet transform or the Singular Value Decomposition (SVD).
SubjectsDerivatives (Mathematics), Finite element method, Fourier transformations, Derivades (Matemàtica), Elements finits, Mètode dels, Fourier, Transformacions de
DegreeGRAU EN ENGINYERIA EN TECNOLOGIES AEROESPACIALS (Pla 2010)