This talk will describe ongoing work on a method to enable density functional theory calculations of defects in crystals. Defects determine critical properties of crystalline materials even though they occur at relatively low concentrations. They can interact over long distances through slowly decaying fields whose strength depends on the electronic structure of the core. Thus the study of defects requires electronic resolutions with continuum range. After a general introduction, the talk will describe current work that builds on two ideas (i) reformulating DFT in a manner that is accessible to coarse-graining and (ii) developing a numerical discretization that adapts the resolution to the structure of the solution with no a priori ansatz or ad hoc patches. We demonstrate the idea and highlight key properties through examples.
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