Long-range interactions: P3M, MMMxD, ELC, MEMD ... - ESPResSo

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http://www.icp.uni-stuttgart.deWhy to control errorsrms force error ∆F =√ 〈(F exact − F Ewald ) 2〉 =∆F1010.10.010.0010.0001r max=1, k max=10r max=2, k max=10r max=1, k max=201e-050 1 2 3 4 5α√1NN∑i=1∆F 2i• optimal α brings orders of magnitude of accuracy• at given required accuracy, find fastest cutoffs• compare algorithms at the same accuracyA. Arnold Long-range interactions 16/40
How to: error estimateshttp://www.icp.uni-stuttgart.deKolafa and Perram:∆F∆F real ≈1010.10.010.001total errorreal space estimatek-space estimate0.00010 1 2 3 4 5α∑ q2√Ni2)√(−αrmax L exp 2 r 23 maxHockney and Eastwood:∆F Fourier ≈√∑ q2√NiQ[Ĝopt(k)]L 3A. Arnold Long-range interactions 17/40
Page 1 and 2: http://www.icp.uni-stuttgart.deLong
Page 4 and 5: Electrostatics in periodic boundary
Page 6 and 7: Assigning chargeshttp://www.icp.uni
Page 8 and 9: Ewald: splitting the potentialhttp:
Page 10: The dipole termhttp://www.icp.uni-s
Page 13 and 14: Steps of P 3 Mhttp://www.icp.uni-st
Page 15: Optimal influence functionhttp://ww
Page 19 and 20: Partially periodic systemshttp://ww
Page 21 and 22: Taking the limit: MMM2D far formula
Page 23 and 24: MMM2D procedurehttp://www.icp.uni-s
Page 25 and 26: MMM2D and MMM1D in ESPResSo (AA)htt
Page 27 and 28: Electrostatic layer correction (ELC
Page 29 and 30: Maxwell Equation Molecular Dynamics
Page 31 and 32: Maxwell equationshttp://www.icp.uni
Page 33 and 34: Discretizationhttp://www.icp.uni-st
Page 35 and 36: Self energy correctionhttp://www.ic
Page 37 and 38: MEMD in ESPResSo (F. Fahrenberger)h
Page 39 and 40: ICC ∗ algorithmhttp://www.icp.uni

Long-range interactions: P3M, MMMxD, ELC, MEMD ... - ESPResSo

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