Coordinate-free numerics: all your variation points for free?

Abstract

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Whenever we develop software we know it will evolve over time, and it will need to be adapted to changing requirements. A variation point is where a program has been designed for change, or where it easily can be accommodated to change. Here we discuss variation points in numerical solvers for Partial Differential Equations (PDEs). Our experience is that an abstraction oriented approach based on coordinate-free numerics naturally provides most, if not all, variation points needed.