GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A fast algorithm for particle simulations
Journal of Computational Physics
Rapid solution of integral equations of scattering theory in two dimensions
Journal of Computational Physics
The parallel multipole method on the connection machine
SIAM Journal on Scientific and Statistical Computing
Mapping the adaptive fast multipole algorithm onto MIMD systems
Unstructured scientific computation on scalable multiprocessors
Astrophysical N-body simulations using hierarchical tree data structures
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
A parallel hashed Oct-Tree N-body algorithm
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
SIAM Journal on Scientific Computing
Journal of Parallel and Distributed Computing
Parallel matrix-vector product using approximate hierarchical methods
Supercomputing '95 Proceedings of the 1995 ACM/IEEE conference on Supercomputing
Field Computation by Moment Methods
Field Computation by Moment Methods
Scalable parallel formulations of the barnes-hut method for n-body simulations
Proceedings of the 1994 ACM/IEEE conference on Supercomputing
A Parallel Version of the Fast Multipole Method-Invited Talk
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
Many-to-many personalized communication with bounded traffic
FRONTIERS '95 Proceedings of the Fifth Symposium on the Frontiers of Massively Parallel Computation (Frontiers'95)
Efficient parallel formulations of hierarchical methods and their applications
Efficient parallel formulations of hierarchical methods and their applications
Compression of particle data from hierarchical approximate methods
ACM Transactions on Mathematical Software (TOMS)
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The method of moments is an important tool for solving boundary integral equations arising in a variety of applications. It transforms the physical problem into a dense linear system. Due to the large number of variables and the associated computational requirements, these systems are solved iteratively using methods such as GMRES, CG and its variants. The core operation of thes itertive solvers is the application of the system matrix to a vector. This requres O(n2) operations and memory using accurate dense methods. The computational complexity can be reduced to O(n log n) and the memory requirement to O(n) using hierarchical approximation techniques. The algorithmic speedup from approximation can be combined with parallelism to yield very fast dense solvers. In this paper, we present efficient parallel formulations of dense iterative solvers based on hierarchical approximations for solving the integral form of Laplace equation. We study the impact of various parameters on the accuracy and performance of the parallel solver. We present two preconditioning techniques for accelerating the convergence of the iterative solver. Thes techniques are based on an inner-outer scheme and a block diagonal scheme based on a truncated Green's function. We present detailed experimental results on up to 256 processors of a Cray T3D.