# Nvidia GTC 2013 Accepted Talks

I’m fortunate to work with some very talented people 🙂 Work supported in part by a generous donation of 50 M2070 Nvidia Tesla cards from HP

**Accelerating and Scaling Lanczos Diagonalization with GPGPU**

W. J. Brouwer, Sreejith G.J., F. Spiga

Lanczos diagonalization (LD) is an important algorithm for calculating eigenvalues and eigenvectors of large matrices, used in many applications. A example performed countless times throughout the world on a daily basis involves latent semantic analysis of documents for search and retrieval. This presentation details work devoted to exploiting the massive parallelism and scalability of GPUs, in order to enhance LD for key aspects of condensed matter physics. One significant application area is the diagonalization of the Hamiltonian for large, dense matrices encountered in studies of the fractional quantum Hall effect. A second application discussed in this work is to the Self Consistent Field (SCF) cycle of a Density Functional Theory (DFT) code, Quantum Espresso. Initial results are promising, demonstrating a 18x speedup using GPU, over an optimized CPU implementation. Further, the use of MPI in conjunction with NVIDIA GPUDirect allows for scaling to all GPUs across the cluster used in this work.

**Estimating Fracture Size in Gas Shale Formations using Smart Proppants and GPGPU**

M. K. Hassan, W. J. Brouwer, R. Mittra

This presentation considers a system containing specially engineered particles called smart proppants, which have the potential to serve as sensors in estimating the effective length of fractures in gas shale formation, a significant factor in predicting the yield of a reservoir. The proppants are suspended and randomly distributed in a background medium, the fracturing fluid. A Monte Carlo method is used to generate the properties and position of smart proppants within a volume that approximates the fracture zone. Modeling the particles as dipoles, one can construct a large and unwieldy matrix equation, simplified by the application of characteristic basis functions (CBF). The CBF method involves application of LU decomposition and SVD based methods to matrix sub blocks, in order to produce subsequent solutions. This presentation will discuss the overall application and solution method, as well as the results of using GPU implementations of the key algorithms, effectively providing 30-40x performance improvement over using a single CPU.