Sum factorization techniques for tensor-product elements

[termi-official]

Assembly performance of tensor-product elements (we currently just have Lagrange polynomials on RefCube's) can be improved via tensor-product assembly. Thic technique is often called sum-factorization (e.g. [1-2]). Here we rearrange the summation when building the local stiffness matrix. Technically we can also do this on simplices, see e.g. [3].

TODO here is to provide an example and maybe make internal modifications if required. This technique is not too important for low-order basis functions, because it primarily decreases the evaluation complexity.

References

[1] Homolya, M., Kirby, R. C., & Ham, D. A. (2017). Exposing and exploiting structure: optimal code generation for high-order finite element methods. arXiv preprint arXiv:1711.02473.

[2] Kronbichler, M., & Kormann, K. (2012). A generic interface for parallel cell-based finite element operator application. Computers & Fluids, 63, 135-147.

[3] Eibner, T., & Melenk, J. M. (2005). Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison. SFB 393.