# Why are molecular dynamics problems so parallelizable?

### Abstract

A widely used method for the numerical simulation of a system of charged particles is the Particle-In-Cell (PIC) method. The PIC method uses the concept of quasiparticles, which move in electromagnetic fields according to classical equations of motion. The quasiparticles deposit electrical currents on a numerical grid according to their form factors. The Maxwell equations, which are also defined on the grid, are solved with the help of a Maxwell solver, usually the FTDT method. The calculated electromagnetic fields, in turn, have an effect on the quasiparticles. The main peculiarity of the PIC process is that the form factors of the quasiparticles must be matched to the lattice. The finite size of the quasiparticles implies that scattering processes cannot be correctly resolved with small distances between the latter, since the fields generated by the quasiparticles tend to zero close to the center of the latter and, as a result, very high lattice resolutions would be required. On the other hand, it is precisely the small distances that usually contain the essential parts of interaction physics. The MicPIC method offers an approach to correctly deal with physics at small distances. This method corresponds to the PIC method, with the interaction between closely neighboring particles being supplemented by the Coulomb interaction of point particles. Form factors for the particles are used for the current deposition. The above-mentioned problem - the disappearance of the fields of quasiparticles near their center - should thus be compensated for by adding an electrostatic point-particle interaction at small distances. The MicPIC method is used in the simulation of laser-driven high-density nanoplasms. In contrast to MicPIC, the dynamic framework used in the present work is based entirely on relativistic molecular dynamics for point particles supplemented by self-forces. The current deposition on the grid used in the context of the PIC method cannot, however, be adopted for point particles. This is also not necessary, since the fields required within the dynamic framework are analytical solutions of the Maxwell equations for point particles. If viewed naively, the numerical complexity of the resulting molecular dynamic equations of motion would scale quadratically with the number of quasiparticles. By introducing a hybrid concept of near and far fields, an integration process can be developed that scales better than the square of the number of particles. The particle-particle interaction for particles in the near-field range can be mapped directly using the analytically calculated potentials, while the latter for particles that are far away is calculated using numerically calculated fields on a grid. The current deposition method used in the PIC method is replaced in the present work by suitable boundary values for electromagnetic fields on the Maxwell grating at the border of the near-field area, which are then propagated into the far-field area with the help of a Maxwell solver. The presented numerical concept can be parallelized so that simulations with many particles can be carried out on a distributed mainframe computer. Thus, at least for the simulation of nanoplasmas, a numerical alternative to the PIC method is available, which offers significant improvements in the treatment of physics at small distances, radiation attenuation and the grid-independent representation of electromagnetic fields. The concept developed in this work is not limited to the solution of the Vlasov-Maxwell system, but can be applied to many other interacting many-body systems in the future. As is easy to see, all many-body systems in which interactions are described by fields can be divided into near-field and far-field areas, with the interactions in the near-field areas being calculated directly via analytical functions and in the far-field areas on a numerical grid. It is to be expected that with the method presented in this thesis, further long-range many-particle systems can be simulated with high precision at small distances and good scaling with the number of particles.

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