Implementation of Karhunen–Loeve expansion for simulation using a wavelet-Galerkin scheme

Huang, 2001, Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes, Int J Num Meth Engng, 52, 1029, 10.1002/nme.255 Huang, 2000, Digital simulation of non-Gaussian stationary processes using Karhunen–Loeve expansion, 8th ASCE Specialty Conf Probab Mech Struct Reliab, July, 1 Phoon, 2002, Simulation of second-order processes using Karhunen–Loeve expansion, Comput Struct (special issue on probabilistic mechanics and structural reliability) Ghanem, 1991 Zhang, 1994, Orthogonal series expansions of random processes in reliability analysis, J Engng Mech, ASCE, 120, 2660, 10.1061/(ASCE)0733-9399(1994)120:12(2660) Schenk, C.A., Schueller, G.I. On the analysis of cylindrical shells with random imperfections. 4th International Colloquium on Computation of Shell and Spatial Structures, June 2000, Chania-Crete, Greece. Baker, 1977 Agrawal, 1998, Application of wavelets in modeling stochastic dynamic systems, J Sound Vibrat, 120, 763 Alpert, 1993, A class of bases in L2 for the sparse representation of integral operators, J Math Anal, SIAM, 24, 246, 10.1137/0524016 Alpert, 1993, Wavelet-like bases for the fast solution of the second kind integral equations, J Sci Comput, SIAM, 14, 159, 10.1137/0914010 Beylkin, 1991, Fast wavelet transforms and numerical algorithm I, Commun Pure Appl Math, 44, 141, 10.1002/cpa.3160440202 Greenshields, 1992, Spectral decomposition by wavelet approximation to the Karhunen–Loeve transform, Ophthal Technol II, SPIE, 1644, 282, 10.1117/12.137432 Mallat, 1989, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans Pattern Anal Mach Intell, 11, 674, 10.1109/34.192463 Daubechies, 1988, Orthonormal bases of compactly supported wavelets, Commun Pure Appl Math, 41, 909, 10.1002/cpa.3160410705 Zeldin, 1996, Random field simulation using wavelet bases, J Appl Mech, ASME, 63, 946, 10.1115/1.2787251 Gurley, 1997, Analysis and simulation tools for wind engineering, Prob Engng Mech, 12, 9, 10.1016/S0266-8920(96)00010-0 Gurley, 1999, Applications of wavelet transforms in wind, earthquake and ocean engineering, Engng Struct, 21, 149 Micchelli, 1997, Wavelet Galerkin methods for second-kind integral equations, J Comput Appl Math, 86, 251, 10.1016/S0377-0427(97)00160-X Greenshields, 1998, A fast wavelet-based Karhunen–Loeve transform, Patten Recogn, 31, 839, 10.1016/S0031-3203(97)00109-X Chen, 1996, The computational of wavelet-Galerkin approximation on a bounded interval, Int J Num Meth Engng, 39, 2921, 10.1002/(SICI)1097-0207(19960915)39:17<2921::AID-NME983>3.0.CO;2-D Wang, 1997, Application of wavelet on the interval to numerical analysis of integral equation in electromagnetic scattering problems, Int J Num Meth Engrg, 40, 1, 10.1002/(SICI)1097-0207(19970115)40:1<1::AID-NME44>3.0.CO;2-V Daubechies, 1992 Newland, 1993 Meyer, 1993 Franklin, 1928, A set of continous orthogonal functions, Math Ann, 100, 522, 10.1007/BF01448860 Chui, 1992 Nag foundation toolbox for use with MATLAB. The Math Works Inc., 1995. Nievergelt, 1999 Wagner, 1995, A study of wavelets for the solution of Electromagnetic integral equations, IEEE Trans Antennas Propag, 43, 802, 10.1109/8.402199