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Yeo and M. R. Maxey, J. Fluid Mech. 649, 205\u2013231 (2010)] for computing hydrodynamic interactions among particles confined to a doubly periodic geometry with either a single bottom wall or two walls (slit channel) in the aperiodic direction. Our spectrally accurate Stokes solver uses the fast Fourier transform in the periodic xy plane and Chebyshev polynomials in the aperiodic z direction normal to the wall(s). We decompose the problem into two problems. The first is a doubly periodic subproblem in the presence of particles (source terms) with free-space boundary conditions in the z direction, which we solve by borrowing ideas from a recent method for rapid evaluation of electrostatic interactions in doubly periodic geometries [Maxian et al., J. Chem. Phys. 154, 204107 (2021)]. The second is a correction subproblem to impose the boundary conditions on the wall(s). Instead of the traditional Gaussian kernel, we use the exponential of a semicircle kernel to model the source terms (body force) due to the presence of particles and provide optimum values for the kernel parameters that ensure a given hydrodynamic radius with at least two digits of accuracy and rotational and translational invariance. The computation time of our solver, which is implemented in graphical processing units, scales linearly with the number of particles, and allows computations with about a million particles in less than a second for a sedimented layer of colloidal microrollers. We find that in a slit channel, a driven dense suspension of microrollers maintains the same two-layer structure as above a single wall, but moves at a substantially lower collective speed due to increased confinement.<\/jats:p>","DOI":"10.1063\/5.0141371","type":"journal-article","created":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T11:36:38Z","timestamp":1681731398000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":16,"title":["Computing hydrodynamic interactions in confined doubly periodic geometries in linear time"],"prefix":"10.1063","volume":"158","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7639-5665","authenticated-orcid":false,"given":"Aref","family":"Hashemi","sequence":"first","affiliation":[{"name":"Courant Institute, New York University 1 , New York, New York 10012, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3393-7329","authenticated-orcid":false,"given":"Ra\u00fal P.","family":"Pel\u00e1ez","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University 1 , New York, New York 10012, USA"},{"name":"Departamento F\u00edsica Te\u00f3rica de la Materia Condensada, Universidad Aut\u00f3noma de Madrid 2 , Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0877-891X","authenticated-orcid":false,"given":"Sachin","family":"Natesh","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University 1 , New York, New York 10012, USA"},{"name":"Department of Applied Mathematics, University of Colorado Boulder 3 , Boulder, Colorado 80309, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6005-1668","authenticated-orcid":false,"given":"Brennan","family":"Sprinkle","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University 1 , New York, New York 10012, USA"},{"name":"Department of Applied Mathematics and Statistics, Colorado School of Mines 4 , Golden, Colorado 80401, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4770-1723","authenticated-orcid":false,"given":"Ondrej","family":"Maxian","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University 1 , New York, New York 10012, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7752-2136","authenticated-orcid":false,"given":"Zecheng","family":"Gan","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University 1 , New York, New York 10012, USA"},{"name":"Department of Mathematics, The Hong Kong University of Science and Technology 5 , Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-6057-9543","authenticated-orcid":false,"given":"Aleksandar","family":"Donev","sequence":"additional","affiliation":[{"name":"Courant Institute, New York University 1 , New York, New York 10012, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2023,4,17]]},"reference":[{"key":"2024041700021415400_c1","doi-asserted-by":"publisher","first-page":"041002","DOI":"10.1143\/jpsj.78.041002","article-title":"Hydrodynamic interaction in confined geometries","volume":"78","year":"2009","journal-title":"J. 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