This report describes the detailed implementation of MiniAMR - a software for octree-based adaptive mesh refinement (AMR) that can be used to study the communication costs in a typical AMR simulation. We have designed new data structures and refinement/coarsening algorithms for octree-based AMR and studied the performance improvements using a similar software from Sandia National Laboratory. We have also introduced the idea of amortized load balancing to AMR in this report. In addition to this, we have also provided a low-overhead distributed load balancing scheme for AMR applications that perform sub-cycling (refinement in time).
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