Algorithms for construction of Element Partition Trees for Direct Solver executed over h refined grids with B-splines and C0 separators

We propose a way of performing isogeometric finite element method (IGA-FEM) computations over h refined grids with B-spline basis functions. Namely, we propose to use the B-spline basis functions defined over patches of elements with C0 separators between the refinement levels. Our definition of the B-splines and C0 separators allows introduction of arbitrary order B-splines over 2D grids refined towards singularities. We also present an algorithm for construction of element partition trees (EPT) over h refined grids with modified B-splines. The EPT allows generating an ordering which gives a linear computational cost of the multi-frontal solver over 2D grids refined towards a point or an edge singularity. We present the algorithm for transforming the EPT into an ordering. We also verify the linear computational cost of the proposed method on grids with point and edge singularity. We compare our method to h-adaptive finite element method (h-FEM) computations with Lagrange polynomials.