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Wednesday, March 15 • 4:40pm - 5:00pm
Algorithms and Performance: Improving Scalability and Performance of Linear System Solves in Pore-scale Simulations

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Pore-scale fluid simulation is an integral part of hydrocarbon exploration and production. The numerical solution of the Cahn-Hilliard equation, which governs the separation of a two-component fluid mixture, is an essential and computationally demanding part of our simulations. In this talk, we present two approaches to improve the performance and scalability of the solution of the large, sparse linear systems arising from the equation discretization, since these system solves are the main performance bottleneck of the simulation.

The iterative solvers used to solve these systems rely on fast sparse matrix-vector products (SpMVs), and the size of the problems require the distribution of the linear systems over multiple computing nodes. Thus, a fully asynchronous, hybrid parallel SpMV implementation is introduced, which overlaps computation and communication in order to achieve high scalability.

Our second approach to improve the performance of the linear systems solves is to exploit hierarchical scale separation (HSS), a recently developed multigrid-type scheme to solve linear systems arising from discontinuous Galerkin methods. HSS profits from the spatial locality of the numerical solution by splitting each linear system into a coarse-scale system of reduced size and a set of very small, decoupled fine-scale systems. For the former, a standard iterative solver is employed, while the latter are solved with a direct solver. This splitting improves the overall performance of the linear system solves, since the iterative solver benefits from the reduced system size, while the direct solves of the decoupled systems can be parallelized very efficiently. We also show a modification of the HSS algorithm that further improves scalability and performance.

Both approaches help improving the performance of linear systems solves in our application. The asynchronous SpMV implementation displays high scalability, and the modified HSS algorithm greatly accelerates the GMRES solve with its multigrid-type approach. Experimental results from the application of the above techniques to the Cahn-Hilliard equation are presented.

Moderators
HC

Henri Calandra

Total
Henri Calandra obtained his M.Sc. in mathematics in 1984 and a Ph.D. in mathematics in 1987 from the Universite des Pays de l’Adour in Pau, France. He joined Cray Research France in 1987 and worked on seismic applications. In 1989 he joined the applied mathematics department of the French Atomic Agency. In 1990 he started working for Total SA. After 12 years of work in high performance computing and as project leader for Pre-stack Depth... Read More →
avatar for Ernesto Prudencio

Ernesto Prudencio

Senior Software Engineer, Schlumberger
Ernesto E. Prudencio combines a BSc in electronics engineering (1990, Brazil), a MSc in applied mathematics (domain decomposition methods, 2001, Brazil), and a PhD in computer science / numerical analysis (PDE-constrained optimization, 2005, Boulder, CO), with professional experience in industry (IBM, Integris, Schlumberger), in national laboratories (ANL, SLAC) and academia (UT Austin). He has been working in Schlumberger since September of... Read More →

Speakers


Wednesday March 15, 2017 4:40pm - 5:00pm
Room 280

Attendees (1)