Landau Gauge Fixing on GPUs

In this paper we present and explore the performance of Landau gauge fixing in GPUs using CUDA. We consider the steepest descent algorithm with Fourier acceleration, and compare the GPU performance with a parallel CPU implementation. Using $32^4$ lattice volumes, we find that the computational power of a single Tesla C2070 GPU is equivalent to approximately 256 CPU cores.Comment: 10 pages, 3 figures and 3 table

Generating optimized Fourier interpolation routines for density function theory using SPIRAL

© 2015 IEEE.Upsampling of a multi-dimensional data-set is an operation with wide application in image processing and quantum mechanical calculations using density functional theory. For small up sampling factors as seen in the quantum chemistry code ONETEP, a time-shift based implementation that shifts samples by a fraction of the original grid spacing to fill in the intermediate values using a frequency domain Fourier property can be a good choice. Readily available highly optimized multidimensional FFT implementations are leveraged at the expense of extra passes through the entire working set. In this paper we present an optimized variant of the time-shift based up sampling. Since ONETEP handles threading, we address the memory hierarchy and SIMD vectorization, and focus on problem dimensions relevant for ONETEP. We present a formalization of this operation within the SPIRAL framework and demonstrate auto-generated and auto-tuned interpolation libraries. We compare the performance of our generated code against the previous best implementations using highly optimized FFT libraries (FFTW and MKL). We demonstrate speed-ups in isolation averaging 3x and within ONETEP of up to 15%

Distributed-memory large deformation diffeomorphic 3D image registration

We present a parallel distributed-memory algorithm for large deformation diffeomorphic registration of volumetric images that produces large isochoric deformations (locally volume preserving). Image registration is a key technology in medical image analysis. Our algorithm uses a partial differential equation constrained optimal control formulation. Finding the optimal deformation map requires the solution of a highly nonlinear problem that involves pseudo-differential operators, biharmonic operators, and pure advection operators both forward and back- ward in time. A key issue is the time to solution, which poses the demand for efficient optimization methods as well as an effective utilization of high performance computing resources. To address this problem we use a preconditioned, inexact, Gauss-Newton- Krylov solver. Our algorithm integrates several components: a spectral discretization in space, a semi-Lagrangian formulation in time, analytic adjoints, different regularization functionals (including volume-preserving ones), a spectral preconditioner, a highly optimized distributed Fast Fourier Transform, and a cubic interpolation scheme for the semi-Lagrangian time-stepping. We demonstrate the scalability of our algorithm on images with resolution of up to $1024^3$ on the "Maverick" and "Stampede" systems at the Texas Advanced Computing Center (TACC). The critical problem in the medical imaging application domain is strong scaling, that is, solving registration problems of a moderate size of $256^3$---a typical resolution for medical images. We are able to solve the registration problem for images of this size in less than five seconds on 64 x86 nodes of TACC's "Maverick" system.Comment: accepted for publication at SC16 in Salt Lake City, Utah, USA; November 201