@article{Yokota_Turkiyyah_Keyes_2014, title={Communication Complexity of the Fast Multipole Method and its Algebraic Variants}, volume={1}, url={https://superfri.susu.ru/index.php/superfri/article/view/22}, DOI={10.14529/jsfi140104}, abstractNote={<p class="p1">A combination of hierarchical tree-like data structures and data access patterns from fast multipole methods and hierarchical low-rank approximation of linear operators from H-matrix methods appears to form an algorithmic path forward for efficient implementation of many linear algebraic operations of scientific computing at the exascale. The combination provides asymptot- ically optimal computational and communication complexity and applicability to large classes of operators that commonly arise in scientific computing applications. A convergence of the mathe- matical theories of the fast multipole and H-matrix methods has been underway for over a decade. We recap this mathematical unification and describe implementation aspects of a hybrid of these two compelling hierarchical algorithms on hierarchical distributed-shared memory architectures, which are likely to be the first to reach the exascale. We present a new communication complexity estimate for fast multipole methods on such architectures. We also show how the data structures and access patterns of H-matrices for low-rank operators map onto those of fast multipole, leading to an algebraically generalized form of fast multipole that compromises none of its architecturally ideal properties.</p>}, number={1}, journal={Supercomputing Frontiers and Innovations}, author={Yokota, Rio and Turkiyyah, George and Keyes, David}, year={2014}, month={Jun.}, pages={63–84} }