Pseudo-particle Fast Multipole Surface Charge Method using a Triangular Patch with a Variable Interior Control Point

Electrical Engineering Japan

Yamamoto

Kobayashi

2006

Self Cite

SUMMARYThis paper presents a generalized equivalent multipole-moment method for calculating three-dimensional Laplacian fields in a multispherical system. Greengard and Rokhlin's M2M, M2L, and L2L formulas enable the multipole-moment method to calculate the fields in general arrangement of multispheres, which involve exclusive and multilayered spherical arrangement. We applied this method to electric field calculation in biological structures induced by ELF magnetic fields. The induced electric fields in a system of three eccentric and exclusive spheres, which models the human head with two eyeballs, are calculated under the application of homogeneous and magnetic-dipole fields. The validity of this method is successfully confirmed by comparing the calculated fields with those by the fastmultipole surface-charge-simulation method.

Section: Calculating Anmentioning

confidence: 99%

Analysis of electric field induced by ELF magnetic field utilizing generalized equivalent multipole‐moment method

Electrical Engineering Japan

Yamamoto

Kobayashi

2006

Self Cite

“…The radius, relative permittivity, and field strength are 1 cm, 10 kV/cm, and 1 kV/cm, respectively. The spherical surface is divided into 19 200 curved triangular patches [8], as shown in Fig. 1.…”

Section: A Parameter Settingmentioning

confidence: 99%

Effective precondition technique to solve a full linear system for the fast multipole method

Takuma

2003

IEEE Trans. Magn.

The fast multipole method (FMM) is an ( ) solver of a full linear system appearing in integral equation methods. We propose a precondition technique for the FMM using the Bi-CGSTAB2 method, which employs a nested FMM having intentionally deteriorated precision. This enables us to utilize the global information residing in the system matrix.Index Terms-Boundary element methods, fast multipole method (FMM), iterative methods, Laplace equations, precondition.

“…The main specifications of the utilized SCM and FMM are summarized as follows: The surface is represented by the cubic triangular Bezier patch with a variable interior control point [3]. This realizes smooth surface connections between neighhoring patches along the element sides.…”

Section: Surface Charge Simulation Methodsmentioning

confidence: 99%

Electrostatic field calculation of multi-particle systems with and without contact points by the surface charge simulation method

Proceedings of the 7th International Conference on Properties and Applications of Dielectric Materials (Cat. No.03CH37417)

Takuma²

This paper describes three-dimensional electrostatic field calculations in multi-particle systems by a surface charge simulation method (SCM), one of the integral equation methods, sometimes called the indirect boundary element method. The utilized SCM adopts the fast multipole method (FMM), an O(N) algorithm for solving a dense linear system appearing in the SCM, where N is the number of unknowns. The calculated arrangements consist of spherical dielectrics, the radius of which is lcm, in the form of (a) a string of beads (2 to 12 particles) or (h) a simple three-dimensional lattice (23 or lo3 particles) under a homogeneous applied field. The half-length of the gap between the particles is (i) zero (with contact points) or (ii) 0.Olcm to OScm (without contact points). The charge and field distributions on the particles are numerically determined using up to 432000 curved triangular elements and 866000 unknowns in the quadratic basis function.