  In the study of micro-swimmers, both artificial and biological ones,
many-query problems arise naturally. Even with the use of advanced high
performance computing (HPC), it is not possible to solve this kind of problems
in an acceptable amount of time. Various approximations of the Stokes equation
have been considered in the past to ease such computational efforts but they
introduce non-negligible errors that can easily make the solution of the
problem inaccurate and unreliable. Reduced order modeling solves this issue by
taking advantage of a proper subdivision between a computationally expensive
offline phase and a fast and efficient online stage.
  This work presents the coupling of Boundary Element Method (BEM) and Reduced
Basis (RB) Reduced
  Order Modeling (ROM) in two models of practical interest, obtaining accurate
and reliable solutions to different many-query problems. Comparisons of
standard reduced order modeling approaches in different simulation settings and
a comparison to typical approximations to Stokes equations are also shown.
Different couplings between a solver based on a HPC boundary element method for
micro-motility problems and reduced order models are presented in detail. The
methodology is tested on two different models: a robotic-bacterium-like and an
Eukaryotic-like swimmer, and in each case two resolution strategies for the
swimming problem, the split and monolithic one, are used as starting points for
the ROM. An efficient and accurate reconstruction of the performance of
interest is achieved in both cases proving the effectiveness of our strategy.
