A fast algorithm for particle simulations
Journal of Computational Physics
On the numerical solution of the biharmonic equation in the plane
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Multipole translation theory for the three-dimensional Laplace and Helmholtz equations
SIAM Journal on Scientific Computing
Integral equation methods for Stokes flow and isotropic elasticity in the plane
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
Fast Evaluation of Radial Basis Functions: Methods for Generalized Multiquadrics in $\RR^\protectn$
SIAM Journal on Scientific Computing
A New Parallel Kernel-Independent Fast Multipole Method
Proceedings of the 2003 ACM/IEEE conference on Supercomputing
A scalar potential formulation and translation theory for the time-harmonic Maxwell equations
Journal of Computational Physics
A fast multipole method for the three-dimensional Stokes equations
Journal of Computational Physics
Fast multipole methods on graphics processors
Journal of Computational Physics
Journal of Computational Physics
Delaunay space division for RBF image reconstruction
Proceedings of the 26th Spring Conference on Computer Graphics
Journal of Computational Physics
Efficient FMM accelerated vortex methods in three dimensions via the Lamb-Helmholtz decomposition
Journal of Computational Physics
Hi-index | 31.48 |
The evaluation of sums (matrix-vector products) of the solutions of the three-dimensional biharmonic equation can be accelerated using the fast multipole method, while memory requirements can also be significantly reduced. We develop a complete translation theory for these equations. It is shown that translations of elementary solutions of the biharmonic equation can be achieved by considering the translation of a pair of elementary solutions of the Laplace equations. The extension of the theory to the case of polyharmonic equations in R^3 is also discussed. An efficient way of performing the FMM for biharmonic equations using the solution of a complex valued FMM for the Laplace equation is presented. Compared to previous methods presented for the biharmonic equation our method appears more efficient. The theory is implemented and numerical tests presented that demonstrate the performance of the method for varying problem sizes and accuracy requirements. In our implementation, the FMM for the biharmonic equation is faster than direct matrix-vector product for a matrix size of 550 for a relative L"2 accuracy @e"2=10^-^4, and N=3550 for @e"2=10^-^1^2.