| Budget Amount *help |
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥2,500,000 (Direct Cost: ¥2,500,000)
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| Research Abstract |
To compress the costs of the molecular dynamics simulations of biomolecules, Coulomb interactions are usually calculated using fast algorithms, such as the fast multipole method (FMM) and particle mesh Ewald (PME). On the other hand, in biomembrane simulations, it is usual to repeat membranes in the z-axis direction so as to constitute a three-dimensional periodicity, which can then be directly handled by PME and periodic FMM. However, the artificial repeat of the membrane may cause undesirable artifacts on the simulations. In this work, we originally aimed at developing a periodic FMM that will circumvent such artifacts. We first derived the formula for virials in the framework of the FMM theory, which are necessary for constant-pressure simulation. We found that the conversion of the multipole to local expansion, which is the key operation of FMM, affects the virials in two ways : through lattice-dependence of the conversion matrix and through that of the multipoles. The latter contribution has not been reported previously. The FMM computation is then O(NlogN) instead of O(N). The results of numerical tests also suggest that the net dipole of the unit cell produces a serious effect on the precision of the Coulomb interactions and hence it is equally important to develop an effective strategy for removing the effect, although the development is left for future work. On the other hand, periodic FMMs generally suffer from great deal of computation regarding interaction between neighboring cells. In this work, a cluster computing system, which is based on the cooperation of FMM algorithm and dedicated hardware for the Coulomb-force evaluation, was developed and improved. Currently, further investigation on the accurate virial calculation is being undertaken, which is necessary for producing accurate FMM calculation as well as for reducing artifacts that may be caused by the periodicity.
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