SlipOpt

SlipOpt is a Fortran + MATLAB/MEX implementation for Stokes boundary integral workflows on smooth closed surfaces (including spherical-harmonic perturbations such as Y43).

Layout

• src/: Fortran sources (stokes_mod.f90, geometry_mod.f90, mex wrappers, etc.)
• matlab/: generated and hand-written MATLAB/MEX interface files
• test/: end-to-end MATLAB test scripts
• external/: external dependencies (including rotgrid)

Build

From this directory:

make

This builds matlab/stokes_mex.mexmaca64 and regenerates MATLAB wrappers from matlab/stokes.mw.

Core MEX APIs

• stokesKernelMat_mex: Stokes SLP self matrix
• kerneldSMatrix_mex: traction kernel self matrix
• Sto3dSLPmat_mex: dense Stokes SLP matrix (A output)
• Sto3dSLPnmat_mex: dense Stokes traction matrix (same role as Sto3dSLPmat second output)
• build_geometry_bvp_mex: geometry builder with shape name input ('sphere', 'Y43')
• sht_ana_rotgrid_mex, ynm_all_mex: harmonic helper routines

Geometry

Use:

np = (p+1)*(2*p);
r  = zeros(np,3); nx = zeros(np,3);
xu = zeros(np,3); xv = zeros(np,3); w = zeros(np,1);
[r, nx, xu, xv, w] = build_geometry_bvp_mex(p, np, Shape, r, nx, xu, xv, w);

build_geometry_bvp_mex is the geometry entry point.

Tests

Run from the test/ folder (or project root):

• test_stokes_dirichlet_bvp.m
• test_stokes_neumann_bvp.m
• test_stokes_mix_bvp.m

These scripts:

• build geometry and system matrices,
• solve with truncated SVD,
• evaluate on slice targets,
• visualize magnitude/error fields.

References

This code supports:

• Das, Kausik; Zhu, Hai; Bonnet, Marc; Veerapaneni, Shravan. Squirmers with arbitrary shape and slip: modeling, simulation, and optimization. arXiv:2602.19336
• Bonnet, Marc; Das, Kausik; Veerapaneni, Shravan; Zhu, Hai. Slip optimization on arbitrary 3D microswimmers: a reduced-dimension and boundary-integral framework. arXiv:2604.07310

This code depends on:

• rotgrid (Fortran)
• MATLAB files from ves3d/matlab for computing the Stokes single-layer self-evaluation matrix

Parts of this codebase were co-developed with AI coding assistants, including Codex and Claude Code.