A fast algorithm for particle simulations
Journal of Computational Physics
An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
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
Multipole algorithms for molecular dynamics simulation on high performance computers
Multipole algorithms for molecular dynamics simulation on high performance computers
Fast Fourier Transform Accelerated Fast Multipole Algorithm
SIAM Journal on Scientific Computing
Modification of the carrier, Greengard, and Rokhlin FMM for independent source and target fields
Journal of Computational Physics
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
Efficient parallel implementations of multipole based n-body algorithms
Efficient parallel implementations of multipole based n-body algorithms
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Journal of Computational Physics
Minimizing development and maintenance costs in supporting persistently optimized BLAS
Software—Practice & Experience - Research Articles
Hybrid MPI-Thread Parallelization of the Fast Multipole Method
ISPDC '07 Proceedings of the Sixth International Symposium on Parallel and Distributed Computing
High performance BLAS formulation of the multipole-to-local operator in the fast multipole method
Journal of Computational Physics
FastCap: a multipole accelerated 3-D capacitance extraction program
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On well-separated sets and fast multipole methods
Applied Numerical Mathematics
An (almost) direct deployment of the Fast Multipole Method on the Cell processor
The Journal of Supercomputing
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In a previous work, we have presented a new formulation of the uniform version of the Fast Multipole Method (FMM) for the Laplace equation by using matrix products that can be efficiently computed thanks to the BLAS (Basic Linear Algebra Subprograms) routines. We propose here to extend this formulation to the adaptive version of the FMM: this requires the conception of a new data structure for the octree, namely the octree with indirections, which is efficient for both uniform and non-uniform distributions, as well as a detection mechanism of the available uniform areas in non-uniform distributions. In comparison with other M2L computation schemes (block FFT, rotations and plane wave expansions) in the case of non-uniform distributions of particles, our BLAS version appears to be the fastest for the common precisions used when one solves the Laplace equation.