**6. Numerical results for capsule dynamics**

The algorithm is applied to a problem of a deformable capsule flowing into a square-based microchannel (typical for microfluidic channels created by soft lithography) with a mean inflow velocity *V* [1, 2]. Related works and variant ROM approaches on this topic can be found in [14, 16]. The capsule dynamics is simulated by the full-order fluid–structure interaction solver Cite [1]. The fluid solver is based on the solution of the Stokes equations and a nonlinear Neo-Hookean law is used for the membrane. The initial capsule is spherical, corresponding to the shape at rest. The sphere is discretized with a finite element mesh made of *I* ¼ 2562 vertices.
