13,353 research outputs found
Polynomial Interpretation of Multipole Vectors
Copi, Huterer, Starkman and Schwarz introduced multipole vectors in a tensor
context and used them to demonstrate that the first-year WMAP quadrupole and
octopole planes align at roughly the 99.9% confidence level. In the present
article the language of polynomials provides a new and independent derivation
of the multipole vector concept. Bezout's Theorem supports an elementary proof
that the multipole vectors exist and are unique (up to rescaling). The
constructive nature of the proof leads to a fast, practical algorithm for
computing multipole vectors. We illustrate the algorithm by finding exact
solutions for some simple toy examples, and numerical solutions for the
first-year WMAP quadrupole and octopole. We then apply our algorithm to Monte
Carlo skies to independently re-confirm the estimate that the WMAP quadrupole
and octopole planes align at the 99.9% level.Comment: Version 1: 6 pages. Version 2: added uniqueness proof to Corollary 2;
added proper citation (to Starkman et al.) for Open Question; other minor
improvement
A broadband stable addition theorem for the two dimensional MLFMA
Integral equations arising from the time-harmonic Maxwell equations contain the Green function of the Helmholtz equation as the integration kernel. The structure of this Green function has allowed the development of so-called fast multipole methods (FMMs), i.e. methods for accelerating the matrix-vector products that are required for the iterative solution of integral equations. Arguably the most widely used FMM is the multilevel fast multipole algorithm (MLFMA). It allows the simulation of electrically large structures that are intractable with direct or iterative solvers without acceleration. The practical importance of the MLFMA is made all the more clear by its implementation in various commercial EM software packages such as FEKO and CST Microwave studio
Performing large full-wave simulations by means of a parallel MLFMA implementation
In this paper large full-wave simulations are performed using a parallel Multilevel Fast Multipole Algorithm (MLFMA) implementation. The data structures of the MLFMA-tree are partitioned according to the so-called hierarchical partitioning scheme, while the radiation patterns are partitioned in a blockwise way. To test the implementation of the algorithm, a full-wave simulation of a canonical example with more than 50 millions of unknowns has been performed
Particle-Particle, Particle-Scaling function (P3S) algorithm for electrostatic problems in free boundary conditions
An algorithm for fast calculation of the Coulombic forces and energies of
point particles with free boundary conditions is proposed. Its calculation time
scales as N log N for N particles. This novel method has lower crossover point
with the full O(N^2) direct summation than the Fast Multipole Method. The
forces obtained by our algorithm are analytical derivatives of the energy which
guarantees energy conservation during a molecular dynamics simulation. Our
algorithm is very simple. An MPI parallelised version of the code can be
downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic
Error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem
The numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate -but fast - methods such as the fast multipole method; however, since these methods are only approximate, it is important to have an estimate for the error introduced in such calculations. An analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained. The error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed. The total error introduced in a multilevel implementation is also investigated numerically.published_or_final_versio
Error minimization of multipole expansion
In this paper, we focus on the truncation error of the multipole expansion for the fast multipole method and the multilevel fast multipole algorithm. When the buffer size is large enough, the error can be controlled and minimized by using the conventional selection rules. On the other hand, if the buffer size is small, the conventional selection rules no longer hold, and the new approach which we have recently proposed is needed. However, this method is still not sufficient to minimize the error for small buffer cases. We clarify this fact and show that the information about the placement of true worst-case interaction is needed. A novel algorithm to minimize the truncation error is proposed. © 2005 Society for Industrial and Applied Mathematics.published_or_final_versio
- …