TY - JOUR
AU - Yokota, Rio
AU - Turkiyyah, George
AU - Keyes, David
PY - 2014/06/18
Y2 - 2023/06/09
TI - Communication Complexity of the Fast Multipole Method and its Algebraic Variants
JF - Supercomputing Frontiers and Innovations
JA - superfri
VL - 1
IS - 1
SE - Articles
DO - 10.14529/jsfi140104
UR - https://superfri.susu.ru/index.php/superfri/article/view/22
SP - 63-84
AB - <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>
ER -