Reproducibility repository for Coupling-Aware Vanka Smoothing for Multigrid Preconditioning of the Implicit Immersed Boundary Equations

This repository contains the MATLAB code needed to reproduce the numerical results in the accompanying paper by Cole Gruninger and Boyce E. Griffith.

Requirements

• MATLAB R2025a

Optional MEX acceleration

The experiments run without compiled extensions. To build the faster CAV smoother after configuring a supported C++ compiler with mex -setup C++, run:

run('scripts/build_cav_smoother_mex.m')

Running the experiments

Start MATLAB in the repository root and initialize the path:

setup_project_paths

Result	MATLAB command
CAV two-grid spectrum	run('scripts/experiments/verify_cav_twogrid_spectrum.m')
Membrane spectra and FGMRES convergence	run('scripts/experiments/run_membrane_spectra_experiment.m')
Beam and target-point refinement	run('scripts/experiments/run_forcing_refinement_study.m')
ASZ fiber grid refinement	run('scripts/experiments/run_asz_fixed_time_grid_refinement.m')
ASZ parameter robustness	run('scripts/experiments/run_asz_parameter_robustness.m')

Output is written below results/.

To run the validation suite:

run_validation_suite

The membrane and box-relaxation studies require N >= 16 because the overlapped B(4,2) patch is not unique on smaller periodic grids.