Most of the time spent to solve a numerical problem is taken by a linear system. There are cases
in which the solution is straightforward: lower triangular, upper triangular or diagonal matrices.
However, in every day life, solutions of linear systems are far for being trivial: usually partial
differential equation (PDE) problems lead to complicated linear systems and it could be even worse
when you have to deal with a system of PDEs.
This is the situation where HPC is not enough and the starting point of my thesis. Literature
and software libraries provide a huge amount of resources and it is very unlikely that you could
do better than thousand of scientists and billions of lines of code improved for years. You might
improve slightly your code, and not more but if you want to significantly improve your code, you
will have to take into account something else: what you need is a new High Performance Point of
View.
