@article {1341,
	title = {Accelerating Tensor Contractions in High-Order FEM with MAGMA Batched},
	year = {2017},
	month = {2017-03},
	publisher = {SIAM Conference on Computer Science and Engineering (SIAM CSE17), Presentation},
	address = {Atlanta, GA},
	author = {Ahmad Abdelfattah and Marc Baboulin and Veselin Dobrev and Jack Dongarra and Christopher Earl and Jo{\"e}l Falcou and Azzam Haidar and Ian Karlin and Tzanio Kolev and Ian Masliah and Stanimire Tomov}
}
@techreport {929,
	title = {High-Performance Tensor Contractions for GPUs},
	journal = {University of Tennessee Computer Science Technical Report},
	number = {UT-EECS-16-738},
	year = {2016},
	month = {2016-01},
	publisher = {University of Tennessee},
	abstract = {We present a computational framework for high-performance tensor contractions on GPUs. High-performance is difficult to obtain using existing libraries, especially for many  independent contractions where each contraction is very small, e.g., sub-vector/warp in size. However, using our framework to batch contractions plus application-specifics, we demonstrate close to peak performance results. In particular, to accelerate large scale tensor-formulated high-order finite element method (FEM) simulations, which is the main focus and motivation for this work, we represent contractions as tensor index reordering plus matrix-matrix multiplications (GEMMs). This is a key factor to achieve algorithmically many-fold acceleration (vs. not using it) due to possible reuse of data loaded in fast memory. In addition to using this context knowledge, we design tensor data-structures, tensor algebra interfaces, and new tensor contraction algorithms and implementations to achieve 90+\% of a theoretically derived peak on GPUs. On a K40c GPU for contractions resulting in GEMMs on square matrices of size 8 for example, we are 2.8{\texttimes} faster than CUBLAS, and 8.5{\texttimes} faster than MKL on 16 cores of Intel Xeon ES-2670 (Sandy Bridge) 2.60GHz CPUs. Finally, we apply autotuning and code generation techniques to simplify tuning and provide an architecture-aware, user-friendly interface.},
	author = {Ahmad Abdelfattah and Marc Baboulin and Veselin Dobrev and Jack Dongarra and Christopher Earl and Jo{\"e}l Falcou and Azzam Haidar and Ian Karlin and Tzanio Kolev and Ian Masliah and Stanimire Tomov}
}
@conference {942,
	title = {High-Performance Tensor Contractions for GPUs},
	booktitle = {International Conference on Computational Science (ICCS{\textquoteright}16)},
	year = {2016},
	month = {2016-06},
	address = {San Diego, CA},
	abstract = {We present a computational framework for high-performance tensor contractions on GPUs. High-performance is difficult to obtain using existing libraries, especially for many independent contractions where each contraction is very small, e.g., sub-vector/warp in size. However, using our framework to batch contractions plus application-specifics, we demonstrate close to peak performance results. In particular, to accelerate large scale tensor-formulated high-order finite element method (FEM) simulations, which is the main focus and motivation for this work, we represent contractions as tensor index reordering plus matrix-matrix multiplications (GEMMs). This is a key factor to achieve algorithmically many-fold acceleration (vs. not using it) due to possible reuse of data loaded in fast memory. In addition to using this context knowledge, we design tensor data-structures, tensor algebra interfaces, and new tensor contraction algorithms and implementations to achieve 90+\% of a theoretically derived peak on GPUs. On a K40c GPU for contractions resulting in GEMMs on square matrices of size 8 for example, we are 2.8{\texttimes} faster than CUBLAS, and 8.5{\texttimes} faster than MKL on 16 cores of Intel Xeon E5-2670 (Sandy Bridge) 2.60GHz CPUs. Finally, we apply autotuning and code generation techniques to simplify tuning and provide an architecture-aware, user-friendly interface.},
	keywords = {Applications, Batched linear algebra, FEM, gpu, Tensor contractions, Tensor HPC},
	author = {Ahmad Abdelfattah and Marc Baboulin and Veselin Dobrev and Jack Dongarra and Christopher Earl and Jo{\"e}l Falcou and Azzam Haidar and Ian Karlin and Tzanio Kolev and Ian Masliah and Stanimire Tomov}
}
@article {1346,
	title = {Towards a High-Performance Tensor Algebra Package for Accelerators},
	year = {2015},
	month = {2015-09},
	publisher = {moky Mountains Computational Sciences and Engineering Conference (SMC15)},
	address = {Gatlinburg, TN},
	author = {Marc Baboulin and Veselin Dobrev and Jack Dongarra and Christopher Earl and Jo{\"e}l Falcou and Azzam Haidar and Ian Karlin and Tzanio Kolev and Ian Masliah and Stanimire Tomov}
}
