| Abstract |
Computational science is a highly multidisciplinary field that makes use of computational resources to simulate complex phenomena. It
enables researchers to understand a variety problems that cannot be reproduced in a laboratory and are far from being solved using
analytical methods thus impacting in many fields (e.g., climate modeling, aircraft design, fusion reactors).
The level of complexity and accuracy of these simulations is limited by the amount of computational resources. The most complex
phenomena require the use of the most powerful supercomputers. State-of-the-art supercomputers are distributed memory machines
composed of interconnected processors; the largest supercomputers today can have millions of cores and reach a peak performance of
about 10 petaflop/s. As the increase of processor's speed, based on increasing the number of transistors is reaching a limit (as the
miniaturization of transistors will reach an atomic level), the only way to increase computing power is increasing concurrency. The next
generation of supercomputers, able to reach 1 exaflop/s, are expected to reach billions of cores. Further, memory per core will likely be
reduced, hardly exceeding 1 GB, bandwidth limitations are likely to increase and deeper memory hierarchies are to be expected.
In this context, the efficient exploitation of the vast amount of the available computational resources, already a difficult task, will become a
key challenge of computational science and engineering. This challenge involves the development of new algorithms and their
implementation in scientific software. Our vision is that commercial software, more focused on conservative and well-established solutions,
will unlikely permit to efficiently work on extreme core counts required in the next future. Instead, free software will permit to perform
numerical simulation of complex phenomena providing a framework for collaborative work between teems at different institutions,
concentrating efforts in the respective expertise areas.
In this project we focus on the scalable finite element (FE) approximation of partial differential equations (PDEs). The objective is to
develop new domain decomposition (DD) algorithms and to implement them in FEMPAR, an ambitious high performance scientific
computing software based on massively parallel FE solvers. FEMPAR has been developed in our group and is released under the GNU
GPL license.
In contrast to widely used free source scientific computing libraries devoted to the approximation of PDEs, which rely on external libraries
to solve linear system with appropriate interfaces, FEMPAR provides the whole range of algorithms from the physics to the solution of
linear systems in a unified framework. It currently provides state-of-the-art implementations of DD algorithms as well as new algorithms
recently developed in the group which are not available elsewhere.
Our specific goals include: the implementation and scalability analisis of multilevel DD algorithms to boost the scalability of FEMPAR to
millons of cores, to extend and enhance the DD algorithms to include nonlinear and time dependent problems as well as nonsymmetric
and indefinite problems, to develop DD methods for adaptive and advanced (e.g. discontinuous) discretizations and to make FEMPAR
more widely used, i.e. by users not affiliated to CIMNE. Achieving these goals will produce a strong impact in the scientific community. |