## Computational Electromagnetics and Its ApplicationsThomas G. Campbell, Roy A. Nicolaides, Manuel D. Salas This volume contains the proceedings of the first ICASE/LaRC Work shop on Computational Electromagnetics and Its Applications conducted by the Institute for Computer Applications in Science and Engineering and NASA Langley Research Center. We had several goals in mind when we decided, jointly with the Elec tromagnetics Research Branch, to organize this workshop on Computa tional Electromagnetics ( CEM). Among our goals were a desire to obtain an overview of the current state of CEM, covering both algorithms and ap plications and their effect on NASA's activities in this area. In addition, we wanted to provide an attractive setting for computational scientists with expertise in other fields, especially computational fluid dynamics (CFD), to observe the algorithms and tools of CEM at work. Our expectation was that scientists from both fields would discover mutually beneficial inter connections and relationships. Another goal was to learn of progress in solution algorithms for electromagnetic optimization and design problems; such problems make extensive use of field solvers and computational effi ciency is at a premium. To achieve these goals we assembled the renowned group of speakers from academia and industry whose talks are contained in this volume. The papers are printed in the same order in which the talks were pre sented at the meeting. The first paper is an overview of work currently being performed in the Electromagnetic Research Branch at the Langley Research Center. |

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### Contents

Overview of EM Research in the Electromagnetic Research | 15 |

Antenna Optimization Using the Genetic Algorithm | 53 |

Electromagnetic Analysis for Microwave Applications | 80 |

CEM for Radar Cross Section Application | 97 |

ReducedOrder Electromagnetic Modeling for DesignDriven | 126 |

vi | 143 |

The True Origin of Spurious Solutions and Their Avoidance | 155 |

A Note on the Use of Divergence Boundary Conditions | 185 |

Parallel Hierarchical Solvers and Preconditioners | 212 |

FiniteDifference TimeDomain FDTD Computational | 229 |

Large Hybrid Finite Element Methods for Electromagnetics | 287 |

List of Attendees | 308 |

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absorbing boundary condition accuracy algorithm analysis aperture applications approach approximation calculated cavity circuit coefficient complex Computational Electromagnetics configuration curl equations curl-curl equations derived developed dielectric discretization div-curl divergence equations domain edge efficiency electric field electromagnetic scattering electronic error class FDTD Figure finite difference finite element method formulation frequency response gain geometry Green's function grid Helmholtz equation hierarchical hybrid IEEE IEEE Trans integral equation iterative Jiang Langley Research Center laser least-squares linear load LSFEM matrix matrix-vector product Maxwell equations Maxwell's mesh method of moments microstrip NASA nodes numerical obtained optimization Padé approximation parallel parameters preconditioners problems processors propagation radiation reduced-order modeling scheme simulation solve solver spurious solutions structure subsections surface techniques Theorem time-domain tions transmission line unknowns vector Volakis voltage VSWR wave waveguide wavelength wire antennas