Time-domain integration of the Maxwell equations on finite elements

An explicit time-domain integration scheme is developed for finite-element spatial discretization of the Maxwell equations. A generalized wave equation is used in weak form, which is free of vector parasites when discretized on single C⁰ elements. The use of integral lumping renders the mass matrix diagonal with no necessary degradation in accuracy. The explicit method which results combines the economy of established finite-difference techniques with the geometric flexibility of finite elements. Test problems representative of practical hyperthermia applications show agreement with analytic and frequency-domain finite-element methods, and confirm scaling arguments on run-time and memory