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Wavelet‐based adaptive grid method for the resolution of nonlinear PDEs
Author(s) -
Cruz Paulo,
Mendes Adélio,
Magalhães Fernão D.
Publication year - 2002
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690480412
Subject(s) - partial differential equation , collocation (remote sensing) , grid , wavelet , context (archaeology) , domain (mathematical analysis) , nonlinear system , computer science , resolution (logic) , collocation method , multiresolution analysis , partial derivative , algorithm , mathematics , mathematical optimization , computational science , ordinary differential equation , differential equation , wavelet transform , mathematical analysis , artificial intelligence , geometry , discrete wavelet transform , physics , geology , machine learning , paleontology , quantum mechanics
Theoretical modeling of dynamic processes in chemical engineering often implies the numeric solution of one or more partial differential equations. The complexity of such problems is increased when the solutions exhibit sharp moving fronts. A new numerical method is established, based on interpolating wavelets, that dynamically adapts the collocation grid so that higher resolution is automatically attributed to domain regions where sharp features are present. The effectiveness of the method is demonstrated with some relevant examples in a chemical engineering context.