Towards a taxonomy for multiscale methods in computational mechanics: building blocks of existing methods

Existing multiscale methods in computational mechanics are analyzed with respect to their computational building blocks, considering methods in both solid and fluid mechanics. From this analysis, a step towards a taxonomy for multiscale methods in computational mechanics is taken. The present article is not intended as a closed story; it is rather hoped that it may provide some basis for future discussions. Moreover, it might even provide a point of view to more clearly identify differences and similarities in the variety of multiscale methods currently existing or being developed in the future. The methods or their building blocks, respectively, are investigated with a view on their multiscale features regarding the underlying problem, spatial scale processing, and temporal scale processing. As expected, it turns out that the mechanics of the underlying problem strongly influences the necessary building blocks of an adequate multiscale method.