Algorithms for construction of elimination tree for multi-frontal solver of isogeometric finite element method
dr hab. inż. Maciej Paszyński
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We need an optimal strategy
There are two existing strategies
Both of them are using T-Splines
Computational complexity of isogeometric FEM with T-splines and B-splines over 2D h-refined grids
The 1st Strategy
Utilizes h refinements and T-spline basis functions
For the point singularity the supports of T-spline basis functions from all the levels of the mesh overlap, which results in O(N^3) computational complexity of the solution
The 2nd Strategy
additional h refinements to the first one, so that T-spline basis functions do not overlap and therefore the computational complexity is reduced to O(N)
N for the second strategy is larger than for the first one
The 3rd Strategy
No global C1 continuity of the solution anymore
The third adaptive strategy uses h refinements with B-spline basis functions [1 and C0 separators (recursively repeated knots).
We show that the computational cost of the third strategy is also linear, but we no longer preserve C1 global continuity of the solution
