#5499. A hierarchical matrix approach for computing hydrodynamic interactions

August 2026publication date
Proposal available till 20-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Applied Mathematics;
Numerical Analysis;
Computational Mathematics;
Modeling and Simulation;
Physics and Astronomy (all);
Physics and Astronomy (miscellaneous);
Computer Science Applications;
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Abstract:
For simulations of large numbers of small, spherical particles in a Stokes flow, the long-range hydrodynamic interactions approximated by the Rotne–Prager–Yamakawa (RPY) kernel can be summed rapidly using, for example, the fast multipole method (FMM) or the particle-mesh Ewald (PME) method. In this paper, we develop new fast methods for computing these sums using the H2 hierarchical matrix representation, for open and for periodic boundary conditions. To the best of our knowledge, the method for infinite periodic sums using the H2 hierarchical matrix representation is the first such method developed. We also consider a more general RPY kernel that handles polydisperse particle radii, and show analytically and experimentally that the proxy surface method for efficiently constructing the H2 hierarchical matrix representation remains effective in this case.
Keywords:
H2 matrix; Interpolative decomposition; Proxy surface method; Rotne–Prager–Yamakawa tensor

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