Complexity bounds on supermesh construction for quasi-uniform meshes

TL;DR

This paper establishes that the supermesh construction cost for projecting fields between quasi-uniform meshes scales linearly with the sum of the individual mesh sizes, improving previous bounds and aiding algorithm analysis.

Contribution

The paper proves a new complexity bound showing supermesh size is proportional to the sum of the mesh sizes, under standard assumptions, enhancing understanding of computational costs.

Findings

Supermesh size n is proportional to n_A + n_B.

Improves upon previous upper bounds for supermesh complexity.

Fundamental for analyzing algorithms involving supermeshes.

Abstract

Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two quasi-uniform meshes of $n_A$ and $n_B$ cells respectively, we show under standard assumptions that n is proportional to $n_A + n_B$. This result substantially improves on the best currently available upper bound on $n$ and is fundamental for the analysis of algorithms that use supermeshes.