Applications of potentials to finite element modeling of Maxwell's equations

• Published in: IEEE transactions on magnetics Vol. 29; no. 2; pp. 1333 - 1336
• Main Authors: Boyse, W.E., Minerbo, G.N., Paulsen, K.D., Lynch, D.R.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: New York, NY IEEE 01.03.1993; Institute of Electrical and Electronics Engineers
• Subjects: 440400 - Well Logging Instrumentation; 580000 - Geosciences; 990200 - Mathematics & Computers; BOUNDARY CONDITIONS; CALCULATION METHODS; Classical and quantum physics: mechanics and fields; Classical electromagnetism, maxwell equations; Classical field theories; Design automation; DIFFERENTIAL EQUATIONS; Educational institutions; Electric potential; ELECTRICAL SURVEYS; ELECTROMAGNETIC SURVEYS; EQUATIONS; Exact sciences and technology; FINITE ELEMENT METHOD; Finite element methods; Frequency; GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; GEOPHYSICAL SURVEYS; GEOSCIENCES; HELMHOLTZ THEOREM; Hyperthermia; Laboratories; Magnetic materials; MATHEMATICAL MODELS; MAXWELL EQUATIONS; NUMERICAL SOLUTION; OTHER INSTRUMENTATION; PARTIAL DIFFERENTIAL EQUATIONS; Physics; POTENTIALS; SURVEYS; USES; Finite element method; Proceedings; Potentials; Computerized simulation; Electromagnetic fields; Well logging; Maxwell equations; Hyperthermia
• ISSN: 0018-9464; 1941-0069
• DOI: 10.1109/20.250644

A scalar and vector potential formulation for Maxwell's equations at low frequency is presented which is suitable for discretization with conventional node-based finite elements. The formulation is based on the Lorentz gauge and results in coupled Helmholtz equations for the potentials. With a proper combination of boundary conditions, the solutions are free of spurious modes for the nonresonant cases of interest. Examples are presented for cases of electromagnetic borehole sonde modeling and hyperthermia treatment planning.< >