## Abstract

We discuss the solution of the Maxwell's equations from static to microwave frequencies. First, we review the fast multipole method and the multilevel fast multipole algorithm we have developed for electrodynamic problems. Next, we discuss the problem encountered when electromagnetic problems are solved at very low frequencies. For such problems, we develop a new method to precondition the matrix equation resulting from applying method of moments (MOM) to the EFIE. This preconditioning method is based on first applying the loop-tree or loop-star decomposition of the currents to arrive at a Helmholtz decomposition of the unknown currents. However, the MOM matrix thus obtained cannot be solved efficiently by iterative solvers still due to the required large number of iterations. We propose a permutation of the loop-tree or loop-star currents by a connection matrix, to arrive at a current basis that yields a MOM matrix that can be solved efficiently by iterative solvers.

Original language | English (US) |
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Pages | 379-384 |

Number of pages | 6 |

State | Published - 1999 |

Event | 1999 Asia Pacific Microwave Conference (APMC'99) 'Microwaves Enter the 21st Century' - Singapore, Singapore Duration: Nov 30 1999 → Dec 3 1999 |

### Conference

Conference | 1999 Asia Pacific Microwave Conference (APMC'99) 'Microwaves Enter the 21st Century' |
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City | Singapore, Singapore |

Period | 11/30/99 → 12/3/99 |

## ASJC Scopus subject areas

- General Engineering