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With advances in reconfigurable hardware, especially field-programmable gate arrays (FPGAs), it has become possible to use reconfigurable hardware to accelerate complex applications such as those in scientific computing. There has been a resulting development of reconfigurable computers, that is, computers that have both general-purpose processors and reconfigurable hardware, as well as memory and high-performance interconnection networks. In this paper, we describe the acceleration of molecular dynamics simulations with reconfigurable computers. We evaluate several design alternatives for the implementation of the application on a reconfigurable computer. We show that a single node accelerated with reconfigurable hardware, utilizing fine-grained parallelism in the reconfigurable hardware design, is able to achieve a speedup of about two times over the corresponding software-only simulation. We then parallelize the application and study the effect of acceleration on performance and scalability. Specifically, we study strong scaling, in which the problem size is fixed. We find that the unaccelerated version actually scales better, because it spends more time in computation than the accelerated version does. However, we also find that a cluster of P accelerated nodes gives better performance than a cluster of 2P unaccelerated nodes.