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After more than a decade of development, adaptive methods - in which the computational grid is refined or coarsened to follow the solution's structure - still haven't gained wide acceptance in atmospheric modeling. One main reason is weak technology. Although mathematicians - and physicists and meteorologists - tend to neglect the technical details, the combination of techniques behind efficient and successful adaptive atmospheric modeling forms an interesting case study of scientific computing. This article combines many diverse topics - including grid generation, computational geometry, graph partitioning, and the solution of partial differential equations - to solve a problem related to ozone depletion in the Arctic stratosphere.