I feel that (physics) notation for tensor calculus is awful. Are there any alternative notations worth looking into?

I am reading through Fung and Tong's "Classical and Computational Solid Mechanics", and feel that the Einstein summation convention saves a few symbols, at the expense of a lot of clarity. Along with that, there is rampant misuse of superscripts, where they are sometimes used as labels for basis vectors, and sometimes used to denote (as is usually done) a power.

Are there any presentations of tensors/tensor calculus/continuum mechanics I could look into that use a better notation (I am okay with using a few more symbols, for the sake of clarity), or present the currently widespread notation in a better fashion?

Solution 1:

My personal favorite notation is the (relatively new) notation adopted in the following excellent review paper,

Kolda & Bader, Tensor Decompositions and Applications (SIAM Review 2009)

I feel it strikes a good balance between some of the more abstract pure math notations on one hand where elements of the tensor are not even considered, and the tedious physics index notation on the other hand.

Beware though, it's only really known/used in the numerical analysis and computational mathematics communities, but not the physics or geometry communities.