Programming finite element methods with weighted B-splines

We discuss the main components of the recently developed FEMB program package, which implements finite element methods with weighted B-splines for basic linear elliptic boundary value problems in two and three dimensions. A three-dimensional implementation without topological restrictions has not been available before. We describe in particular the mathematical background for the recursive quadrature/cubature over boundary cells and explain how to utilize the regular data structure of uniform B-splines efficiently. Considering the Lamé–Navier equations of linear elasticity as a typical example, we illustrate the performance of the main FEMB routines. The numerical tests confirm that, due to the new integration routines, the weighted B-spline solvers have become considerably more efficient.