Post-Doctoral Research Visit F/M Low-Rank Compression Algorithms for H-matrices

The Inria center at the University of Bordeaux is one of the nine Inria centers in France and has about twenty research teams.. The Inria centre is a major and recognized player in the field of digital sciences. It is at the heart of a rich R&D and innovation ecosystem: highly innovative SMEs, large industrial groups, competitiveness clusters, research and higher education players, laboratories of excellence, technological research institute...

This project will be carried out within the framework of CONCACE, a joint Inria-Industry team involving Airbus, Cerfacs and Inria, focusing on the theme of composability applied to high-performance computing.
For wave propagation simulations in electromagnetics or acoustics, Airbus makes extensive use of H-matrix solvers to solve surface integral formulations. These techniques use a hierarchical partitioning of the physical object under consideration (e.g. an aircraft) to produce a hierarchical partitioning of the (dense) matrix of the linear system. Most of the matrix blocks thus created are numerically low-rank, and can therefore be stored in compressed form, occupying much less memory space. The H-matrix solver enables us to store these blocks, use them for matrix-vector products and factorize the matrices in our problems while keeping them in this storage format. This is a crucial tool for modeling certain aircraft physics.
The development of the h-matrix library is the fruit of a collaboration since 2010 between Airbus and Inria, it is in C++ and uses the task-based programming paradigm with the StarPU execution engine.  The proposed topic will lead to further development of this h-matrice tool, in collaboration with the industrial partner.

The aim of this 2-year mission - co-funded by Airbus and Inria - is to work on low-rank compression algorithms, which are a fundamental building block of the H-matrix approach. There is a huge variety of algo's fulfilling this role, between classical approaches (SVD, ACA, CUR, ID, ...), randomized variants, reconciliations between these methods and other usual algo's (ACA is for instance a way to rewrite LU), ... Today, H-matrix contains only a few of these algorithms. The aim of the post-doc is :

• enrich the available choice of low-rank compression algo ;
• implement them in a composable way, so that they can be used in the h-matrice library as well as in any other software library;
• to know for each algo its range of effectiveness, in terms of input data (size), target machine (CPU, GPU), precision, execution time, etc.
• be able to dynamically select the most suitable algo at runtime.

As the H-matrices tools at Airbus and Concace are halfway between industry and academic research, the aim of the research within this mission is to identify the most efficient numerical techniques and pass them on to industry for implementation in design offices.

To do this, the various stages of this post-doc will be :

• clarify this diversity of algorithms, identifying the strengths and weaknesses of each, and isolating those that are truly innovative;
• explore and extend the most promising variants (such as geometry-based ACA);
• to implement the most useful methods in the ComposyX software library, the composable linear algebra tool of the Concace project serving to consolidate our work;
• Publication (articles, conferences) of the theoretical and practical results of this work

•     Linear algebra, algorithms, parallelism
•     C, C++, Python programming
•     Writing articles, oral presentations
•     Ability to alternate collaborative work and autonomy
  
  Language: French or English

• subsidized meals
• partial reimbursement of public transport costs
• possibility of partial teleworking and flexible organization of working hours
• professional equipment avilable (videoconferencing, loan of computer equipment...)
• access to vocational training
• social security coverage

The gross monthly salary will be 2788€ (before social security contributions and monthly witholding tax)