sponsored byIEEEACMThe International Conference for High Performance 
Computing, Networking, Storage and Analysis
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SCHEDULE: NOV 16-21, 2014

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A Volume Integral Equation Stokes Solver for Problems with Variable Coefficients

SESSION: Heterogeneity and Scaling in Applications

EVENT TYPE: Papers, Best Student Paper Finalists

TIME: 11:30AM - 12:00PM

SESSION CHAIR: Justin Luitjens

AUTHOR(S):Dhairya Malhotra, Amir Gholami, George Biros



We present a novel numerical scheme for solving the Stokes equation
with variable coefficients in the unit box. Our scheme is based on a
volume integral equation formulation. We employ a novel adaptive fast
multipole method for volume integrals to obtain a scheme that is
algorithmically optimal. To increase performance, we have integrated
our code with both NVIDIA and Intel accelerators. Overall, our scheme
supports non-uniform discretizations and is spectrally accurate. In
our largest run we solved a problem with 20 billion unknowns, using a
14-order approximation for the velocity, on 2048 nodes of the Stampede
platform at the Texas Advanced Computing Center. We achieved 0.656
PetaFLOPS for the overall code (20% efficiency) and 1 PetaFLOPS for
the fast multipole part (40% efficiency). As an application example, we simulate Stokes flow in a porous medium with highly complex pore structure using a penalty formulation to enforce the no slip condition.

Chair/Author Details:

Justin Luitjens (Chair) - NVIDIA Corporation

Dhairya Malhotra - University of Texas at Austin

Amir Gholami - University of Texas at Austin

George Biros - University of Texas at Austin

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Paper provided by the ACM Digital Library

Paper also available from IEEE Computer Society