## Section: Scientific Foundations

### Introduction

The methodological component of `HiePACS` concerns the expertise for
the design as well as the efficient and scalable implementation of
highly parallel numerical algorithms to perform frontier simulations.
In order to address these computational challenges a hierarchical
organization of the research is considered.
In this bottom-up approach, we first consider in
Section
3.2
generic topics concerning high performance computational science.
The activities described in this section are transversal to the
overall project and its outcome will support all the other research
activities at various levels in order to ensure the parallel
scalability of the algorithms.
The aim of this activity is not to study general purpose solution but
rather to address these problems in close relation with specialists of
the field in order to adapt and tune advanced approaches in our
algorithmic designs.
The next activity, described in
Section
3.3 , is
related to the study of parallel linear algebra techniques that currently
appear as promising approaches to tackle huge problems on millions of
cores.
We highlight the linear problems (linear systems or eigenproblems)
because they are in many large scale applications the main
computational intensive numerical kernels and often the main
performance bottleneck.
These parallel numerical techniques will be the basis of both academic
and industrial collaborations described in
Section
4.2
and Section
4.3 , but will
also be closely related to some functionalities developed in the
parallel Fast Multipole activity described in
Section
3.4 . Finally, as
the accuracy of the physical models increases, there is a real need
to go for parallel efficient algorithm implementation for
multiphysics and multiscale modelling in particular in the context of
code coupling.
The challenges associated with this activity will be addressed in the
framework of the activity described in
Section
3.5 .