Towards Efficient and Stable Low Frequency Time Domain Integral Equation Solvers

This paper proposes some improvements to the electric field time domain integral equation (TDIE) solvers. Tree and loop functions were used to test the differential and integral forms of TDIE separately. This testing procedure removed the DC instability. The basis rearrangement was adopted to reduce the condition numbers of the impedance matrices. At each time step in the marching on in time (MOT) solution procedure, a "block pre-conditioner" was invoked. Likewise, the bandlimited extrapolator was used to provide a better initial guess for the iterative matrix equations solver. Collectively, improvements drastically reduced the iteration count of the iterative solver. A fast algorithm was integrated with the low-frequency MOT (LF-MOT) solver to accelerate the evaluation of transient fields due to past currents, which is by far the most costly in the entire MOT process, so it greatly reduces the cost of the overall solver. Numerical experiments below show significant efficiency and stability gains