Various techniques and algorithms are being utilized in computer science and mathematics in order to solve problems by using numerical analysis, simulations, and mathematical modeling

Advanced Computational Methods are developed for the analysis and design of materials, structures and constructions. Numerous analytical and numerical tools have been developed, that extend current computational methodologies and boot solver speeds.

Wavelet-based methods have been developed for the rapid solution of PDEs. Speciality B-Spline wavelets have been developed to merge the concept of hierarchical finite element analysis (FEA) into isogeometric analysis (IGA).

The proposed methodology replaces the traditional grid refinement of IGA with custom enrichment functions. The enrichment functions are properly designed B-Spline wavelets tailored to eliminate scale-coupling terms in the stiffness matrix. In this way, the refined solution is synthesized from contributions of smaller independent problems. The proposed approach has two obvious benefits: (1) the calculations performed at each resolution are not discarded when proceeding to a finer one, and (2) it has less computational requirements since the solution is divided into smaller systems. Numerical results on an elasticity problem demonstrate superior performance and accuracy compared to traditional FEA and IGA schemes. Source: Derivative-orthogonal non-uniform B-Spline wavelets.