This version is based on the direct evaluation of volume integrals, putting it in a category with nonuniform grid (), Fast Fourier Transform methods (, ) and Tensor Grid methods (). The version presented in this paper is an extension to the class of Fast Multipole Codes. The Fast Multipole Method (FMM) was originally invented for p simulations. This can be further reduced to O(M log(M)) by the use of H-matrix approximation, , or fast summation techniques utilizing non-uniform fast Fourier transform (NUFFT).
For the computation of the potential at the boundary, hybrid FEM/BEM (Finite Element Method with Boundary Element Method Coupling) and the shell transformation approach add an additional complexity of O (M2), where M denotes the number of surface triangles. The demagnetization potential has open boundary conditions defined at infinity. * Corresponding author Email address: (P. Modern Finite Element Method (FEM) implementations, have linear scaling for the Poisson equation only for closed boundary conditions when a Direct solutions compute all pair-wise interactions and hence they scale with O (N2) operations, where N denotes the number of interaction partners. Numerous algorithms for solving the problem exist, e.g. More broadly Poisson's equation has to be solved in many areas of computational physics.
In micromagnetic simulations the demagnetization field is the most ¡-consuming part. Micromagnetic algorithms are an important tool for the simulation of ferromagnetic materials used in electric motors, storage systems and magnetic >rs. Keywords: Micromagnetic, Stray-field, Fast multipole method, High performance computing By using FMM the calculations scale linearly in time and memory. This approach tackles important issues like the vectorial and continuous nature of the magnetic field. We treat the near field directly and in use (exact) numerical integration on the multipole expansion in the far field. The novelty lies in extending FMM to linearly magnetized tetrahedral sources making it interesting also for other areas of computational physics. This work presents an efficient implementation of the Fast Multipole Method for the magnetic scalar potential as used in micromag-netics. Computational improvements can relieve problems related to this bottleneck. The long-range magnetic field is the most time-consuming part in micromag-netic simulations. SuessaĪ Christian Doppler Laboratory for Advanced Magnetic Sensing and Materials, Ins Solid State Physics, TU Wien, Vienna, Austria b Institute of Solid State Physics, TU Wien, Vienna, Austria cFaculty of Mathematics, University of Vienna, Vienna, Austrii Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. As a service to our customers we are providing this early version of the manuscript.
#IRIP 2.1.3 PDF#
This is a PDF file of an unedited manuscript that has been accepted for publication. Suess, Highly Parallel Demagnetization Field Calculation Using the Fast Multipole Method on Tetrahedral Meshes with Continuous Sources, Journal of Magnetism and Magnetic Materials (2017), doi: To appear in: Journal of Magnetism and Magnetic Materials Highly Parallel Demagnetization Field Calculation Using the Fast Multipole Method on Tetrahedral Meshes with Continuous Sources
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