  The computational cost of the boundary-condition-enforced immersed boundary
method (IBM) increases in the order of $\mathcal{O}(N^2)$ as the number of
Lagrangian points, $N$, increases. This is due to the time-consuming
calculation of the correction operator in the diffuse-interface IBM to enforce
the no-slip boundary condition. In this study, a computationally efficient IBM
algorithm for an extruded wall geometry is developed, and the correction
operator calculation is significantly simplified while maintaining the accuracy
of the solution. This method takes advantage of the geometrical symmetricity to
apply several matrix simplifications, which result in a huge increase in the
computational efficiency and an improved scalability of $\mathcal{O}(max(N,
N^2/r^2))$ ($r$: the number of grid points towards the extruded direction). The
boundary-condition-enforced IBM for an extruded wall geometry is applicable to
the numerical simulations of the flow around a wall surface that satisfies both
(a) an extruded wall geometry that retains the same cross-section geometry and
(b) an Eulerian grid that is either uniform or whose stretch rate towards the
extruded direction is constant. As this type of geometry is commonly studied to
investigate the fundamental behavior of the fluid, the presented algorithm has
wide applications. Several calculations are conducted to demonstrate the higher
computational efficiency of the presented algorithm compared with that of the
original algorithm. The results show improvements in computational efficiency
of up to 2,800 times for the correction operator calculation and 160 times for
the overall IBM calculations compared with the original algorithm while
retaining the computational accuracy.
