M. Croci and P. E. Farrell, Complexity bounds on supermesh construction for quasi-uniform meshes, Journal of Computational Physics 414 (2020), pp. 1–7. Article. Preprint.
Projecting fields between different meshes commonly arises in computational physics. This operation may require a supermesh construction and in this case its computational cost is proportional to the number of cells of the supermesh n. Given any two quasi-uniform meshes of nA and nB cells respectively, we show under standard assumptions that n is proportional to nA + nB. This result substantially improves on the best currently available upper bound on n and is fundamental for the analysis of algorithms that use supermeshes.