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In this paper, we propose an approach to generate high quality force and deformation using a novel automatic space and time adaptive level of detail technique in combination with a parallel computation using a graphics processing unit (GPU). The elastic object is represented by a multi-resolution hierarchy of tetrahedral adaptive volume mesh. The tetrahedral adaptive volume mesh and the time step of the deformation simulation are locally refined by online re-mesh and multi-rate simulation to concentrate the computational load into the regions that deform the most. In order to compute the online re-mesh and multi-rate deformation simulation on a GPU efficiently, we propose a novel data structure which consists of an extended and transposed connection table, a node list and a separated mass list. This effective computation is achieved by the relocatability of the connection table and optimized memory access at the computation of both deformation and re-meshing. Through evaluation experiments, we confirm the feasibility and the effectiveness of the proposed approach.