Wavelet-based numerical and semianalytical methods of computational local structural analysis

Numerical or semianalytical solution of problems of structural mechanics of high dimensionality is computationally costly process in many cases. However, structural engineer does not normally face the task of obtaining a solution of the problem with high accuracy at all points of the considered domain occupied by the structure. As a rule, all subdomains that are potentially dangerous in terms of structural strength are well known in advance. Operational and variational formulations of boundary problems of structural mechanics with the use of method of extended domain are presented. After corresponding (finite element or finite difference) discretization and passage to governing equations considering problems are transformed to a multilevel space with the use of multilevel wavelet transform (discrete Haar basis is used). Special algorithms of averaging are presented.