A fast algorithm for particle simulations
Journal of Computational Physics
An implementation of the fast multipole method without multipoles
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Fast Fourier Transform Accelerated Fast Multipole Algorithm
SIAM Journal on Scientific Computing
A fast method of moments solver for efficient parameter extraction of MCMs
DAC '97 Proceedings of the 34th annual Design Automation Conference
Generalized Gaussian Quadratures and Singular Value Decompositions of Integral Operators
SIAM Journal on Scientific Computing
Yet another fast multipole method without multipoles—pseudoparticle multipole method
Journal of Computational Physics
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Journal of Computational Physics
A Generalized Fast Multipole Method for Nonoscillatory Kernels
SIAM Journal on Scientific Computing
An Improved Fast Multipole Algorithm for Potential Fields on the Line
SIAM Journal on Numerical Analysis
IES3: Efficient Electrostatic and Electromagnetic Simulation
IEEE Computational Science & Engineering
A new version of the fast multipole method for screened Coulomb interactions in three dimensions
Journal of Computational Physics
A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
A precorrected-FFT method for electrostatic analysis of complicated 3-D structures
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Developing design tools for biological and biomedical applications of micro- and nano-technology
CODES+ISSS '05 Proceedings of the 3rd IEEE/ACM/IFIP international conference on Hardware/software codesign and system synthesis
A wideband fast multipole method for the Helmholtz equation in three dimensions
Journal of Computational Physics
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
A fast multipole method for the three-dimensional Stokes equations
Journal of Computational Physics
Low-constant parallel algorithms for finite element simulations using linear octrees
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Algorithm for direct numerical simulation of emulsion flow through a granular material
Journal of Computational Physics
A Cartesian treecode for screened coulomb interactions
Journal of Computational Physics
Hierarchical molecular interfaces and solvation electrostatics
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
The black-box fast multipole method
Journal of Computational Physics
A Sixth-order Image Approximation to the Ionic Solvent Induced Reaction Field
Journal of Scientific Computing
A massively parallel adaptive fast-multipole method on heterogeneous architectures
Proceedings of the Conference on High Performance Computing Networking, Storage and Analysis
Journal of Computational Physics
On the limits of GPU acceleration
HotPar'10 Proceedings of the 2nd USENIX conference on Hot topics in parallelism
Fast and accurate numerical methods for solving elliptic difference equations defined on lattices
Journal of Computational Physics
Diagnosis, Tuning, and Redesign for Multicore Performance: A Case Study of the Fast Multipole Method
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
A fast algorithm for simulating vesicle flows in three dimensions
Journal of Computational Physics
A fast directional algorithm for high-frequency electromagnetic scattering
Journal of Computational Physics
A Fourier-series-based kernel-independent fast multipole method
Journal of Computational Physics
Journal of Computational Physics
Scalable fast multipole methods on distributed heterogeneous architectures
Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
SIAM Journal on Scientific Computing
Fast Evaluation of Multiquadric RBF Sums by a Cartesian Treecode
SIAM Journal on Scientific Computing
A massively parallel adaptive fast multipole method on heterogeneous architectures
Communications of the ACM
High performance BLAS formulation of the adaptive Fast Multipole Method
Mathematical and Computer Modelling: An International Journal
Proceedings of the twenty-fourth annual ACM symposium on Parallelism in algorithms and architectures
A Butterfly Algorithm for Synthetic Aperture Radar Imaging
SIAM Journal on Imaging Sciences
Scaling fast multipole methods up to 4000 GPUs
Proceedings of the ATIP/A*CRC Workshop on Accelerator Technologies for High-Performance Computing: Does Asia Lead the Way?
A tuned and scalable fast multipole method as a preeminent algorithm for exascale systems
International Journal of High Performance Computing Applications
A fast multipole method for the Rotne-Prager-Yamakawa tensor and its applications
Journal of Computational Physics
Second kind integral equation formulation for the modified biharmonic equation and its applications
Journal of Computational Physics
2HOT: an improved parallel hashed oct-tree n-body algorithm for cosmological simulation
SC '13 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
A fast solver for Poisson problems on infinite regular lattices
Journal of Computational and Applied Mathematics
Beyond first-order finite element schemes in micromagnetics
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
A CPU: GPU Hybrid Implementation and Model-Driven Scheduling of the Fast Multipole Method
Proceedings of Workshop on General Purpose Processing Using GPUs
Advances in Computational Mathematics
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We present a new fast multipole method for particle simulations. The main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel, and it is based only on kernel evaluations. Instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical FMM tree, we use a continuous distribution of an equivalent density on a surface enclosing the box. To find this equivalent density, we match its potential to the potential of the original sources at a surface, in the far field, by solving local Dirichlet-type boundary value problems. The far-field evaluations are sparsified with singular value decomposition in 2D or fast Fourier transforms in 3D. We have tested the new method on the single and double layer operators for the Laplacian, the modified Laplacian, the Stokes, the modified Stokes, the Navier, and the modified Navier operators in two and three dimensions. Our numerical results indicate that our method compares very well with the best known implementations of the analytic FMM method for both the Laplacian and modified Laplacian kernels. Its advantage is the (relative) simplicity of the implementation and its immediate extension to more general kernels.