Effect of preconditioning on the convergence rate in the Krylov subspace method for computing Brownian forces. For this test, an intracellular suspension of 1152 particles with a volume fraction of 0.51 is used.
Comparison of E k exact and E k in the preconditioned Krylov subspace method for computing Brownian noise. An incomplete Cholesky preconditioner was used. The simulated system is an intracellular-like suspension. E k with k = 1 was set to 1.
Scaling of computational time for 10 time steps of FLD and SD simulations of a monodisperse suspension model at a volume fraction of 0.5 with periodic boundary conditions. In the SD simulation, the far-field hydrodynamic interaction term and its inverse were calculated only in the first time step. Dashed lines are a guide to the eye to show the approximate scaling with the number of particles.
(Upper) Normalized short-time and (lower) long-time diffusion coefficients of various particle radii in the intracellular-like suspension model obtained from SD, FLD, and FD simulations.
Normalized pair correlation function, C ij , for the 24 Å–24 Å and 66 Å–66 Å pairs in the intracellular-like suspension model obtained from SD, FLD, and FD simulations. Time and surface distance are normalized by a 2/D 0 and a, respectively.
Breakdown of computational time for FLD with different preconditioning methods, and with and without initial guesses for the first linear system. Timings are shown in seconds. Iteration counts are shown in brackets. For iterative convergence criteria, E k < 10−3 for the Brownian noise approximation and the relative residual norm < 10−6 for CG are used. The simulated system is an intracellular suspension of 1152 particles with volume fraction 0.51. Occupancy of non-zero elements in the resistance tensor is 2%. All values are averaged over ten independent calculations using different particle configurations.
Number of iterations (and time in units of seconds) in the Krylov Brownian noise approximation for various convergence criteria E k and the subsequent preconditioned CG method using the initial guesses constructed from the available Krylov subspace. Convergence criterion of preconditioned CG is relative residual norm < 10−6. For this test, an intracellular suspension of 1152 particles with a volume fraction of 0.51 is used. All values are averaged over ten independent calculations using different particle configurations.
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