Yves Ineichen

An extreme-scale implicit solver for complex PDEs: highly heterogeneous flow in earth's mantle

Mantle convection is the fundamental physical process within earths interior responsible for the thermal and geological evolution of the planet, including plate tectonics. The mantle is modeled as a viscous, incompressible, non-Newtonian fluid. The wide range of spatial scales, extreme variability and anisotropy in material properties, and severely nonlinear rheology have made global mantle convection modeling with realistic parameters prohibitive. Here we present a new implicit solver that exhibits optimal algorithmic performance and is capable of extreme scaling for hard PDE problems, such as mantle convection. To maximize accuracy and minimize runtime, the solver incorporates a number of advances, including aggressive multi-octree adaptivity, mixed continuous-discontinuous discretization, arbitrarily-high-order accuracy, hybrid spectral/geometric/algebraic multigrid, and novel Schur-complement preconditioning. These features present enormous challenges for extreme scalability. We demonstrate that---contrary to conventional wisdom---algorithmically optimal implicit solvers can be designed that scale out to 1.5 million cores for severely nonlinear, ill-conditioned, heterogeneous, and anisotropic PDEs.

A fast and scalable low dimensional solver for charged particle dynamics in large particle accelerators

Particle accelerators are invaluable tools for research in the basic and applied sciences, in fields such as materials science, chemistry, the biosciences, particle physics, nuclear physics and medicine. The design, commissioning, and operation of accelerator facilities is a non-trivial task, due to the large number of control parameters and the complex interplay of several conflicting design goals.We propose to tackle this problem by means of multi-objective optimization algorithms which also facilitate massively parallel deployment. In order to compute solutions in a meaningful time frame, that can even admit online optimization, we require a fast and scalable software framework. In this paper, we focus on the key and most heavily used component of the optimization framework, the forward solver. We demonstrate that our parallel methods achieve a strong and weak scalability improvement of at least two orders of magnitude in today’s actual particle beam configurations, reducing total time to solution by a substantial factor.Our target platform is the Blue Gene/P (Blue Gene/P is a trademark of the International Business Machines Corporation in the United States, other countries, or both) supercomputer. The space-charge model used in the forward solver relies significantly on collective communication. Thus, the dedicated TREE network of the platform serves as an ideal vehicle for our purposes. We demonstrate excellent strong and weak scalability of our software which allows us to perform thousands of forward solves in a matter of minutes, thus already allowing close to online optimization capability.

A scalable randomized least squares solver for dense overdetermined systems

We present a fast randomized least-squares solver for distributed-memory platforms. Our solver is based on the Blendenpik algorithm, but employs a batchwise randomized unitary transformation scheme. The batchwise transformation enables our algorithm to scale the distributed memory vanilla implementation of Blendenpik by up to ×3 and provides up to ×7.5 speedup over a state-of-the-art scalable least-squares solver based on the classic QR based algorithm. Experimental evaluations on terabyte scale matrices demonstrate excellent speedups on up to 16384 cores on a Blue Gene/Q supercomputer.

Improvements of a fast parallel poisson solver on irregular domains

We discuss the scalable parallel solution of the Poisson equation on irregularly shaped domains discretized by finite differences. The symmetric positive definite system is solved by the preconditioned conjugate gradient algorithm with smoothed aggregation (SA) based algebraic multigrid (AMG) preconditioning. We investigate variants of the implementation of SA-AMG that lead to considerable improvements in the execution times. The improvements are due to a better data partitioning and the iterative solution of the coarsest level system in AMG. We demonstrate good scalability of the solver on a distributed memory parallel computer with up to 2048 processors.