The goal of this project is to design and develop large-scale parallel algorithms for dealing with optimization problems involving wave phenomena. Such problems arise in many practical applications: two examples are in seismic inversion, where one tries to deduce the geology of rock formations that best fits the available seismic data, and in wave localization, which can be used to improve the efficiency of wireless charging devices. To make the optimization tractable, parallel computers must be used to cope with the large amounts of data and intensive computation inherent to these problems. In the last decade, parallel-in-time methods have made enormous progress: for parabolic problems, a near-optimal scaling with respect to the number of processors has been achieved (scalability). For wave propagation, there has been no such success.
To achieve our goal of developing innovative, space-time parallel methods for solving such optimization problems, we will consider three interrelated aspects. The first aspect is the direct simulation of wave-type systems, which must be done repeatedly over the course of the optimization. The second aspect is the optimization over bounded time horizons, which is at the heart of both data assimilation and wave localization problems. Here, our approach is to split the full optimality system into many subsystems in time and in space, and to use transmission conditions to ensure consistency with the global solution. We will then exploit the control structure and use the discrete Hilbert Uniqueness Method to derive optimal transmission conditions. Approximating these conditions by local, easy-to-implement conditions will then lead to highly efficient methods. The third aspect concerns the assimilation of infinite streams of data, where one cannot benefit from adjoint techniques. We will tackle this problem by combining parallel simulation with observer approaches, so that the time integration benefits from the space-time parallel methods mentioned above. Our methods will be used to tackle two concrete problems, namely wave localization in complex geometries and data assimilation in geophysical and environmental systems.
- Parallélisation espace-temps
- Équation des ondes
- Hong-Kong : Felix Kwok (PI), Hongyu Liu, Xue-Cheng Tai .
- INRIA Paris : Julien Salomon
- LAGA, Université Paris 13 : Laurence Halpern (PI), Bérangère Delourme, Thanh Vuong DANG (PhD student)