  Learning the physical simulation on large-scale meshes with flat Graph Neural
Networks (GNNs) and stacking Message Passings (MPs) is challenging due to the
scaling complexity w.r.t. the number of nodes and over-smoothing. There has
been growing interest in the community to introduce \textit{multi-scale}
structures to GNNs for physical simulation. However, current state-of-the-art
methods are limited by their reliance on the labor-intensive drawing of coarser
meshes or building coarser levels based on spatial proximity, which can
introduce wrong edges across geometry boundaries. Inspired by the bipartite
graph determination, we propose a novel pooling strategy, \textit{bi-stride} to
tackle the aforementioned limitations. Bi-stride pools nodes on every other
frontier of the breadth-first search (BFS), without the need for the manual
drawing of coarser meshes and avoiding the wrong edges by spatial proximity.
Additionally, it enables a one-MP scheme per level and non-parametrized pooling
and unpooling by interpolations, resembling U-Nets, which significantly reduces
computational costs. Experiments show that the proposed framework,
\textit{BSMS-GNN}, significantly outperforms existing methods in terms of both
accuracy and computational efficiency in representative physical simulations.
