An efficient explicit marching on in time solver for magnetic field volume integral equation

Abstract

Abstract-An efficient explicit marching on in time (MOT) scheme for solving the magnetic field volume integral equation is proposed. The MOT system is cast in the form of an ordinary differential equation and is integrated in time using a PE(CE) m multistep scheme. At each time step, a system with a Gram matrix is solved for the predicted/corrected field expansion coefficients. Depending on the type of spatial testing scheme Gram matrix is sparse or consists of blocks with only diagonal entries regardless of the time step size. Consequently, the resulting MOT scheme is more efficient than its implicit counterparts, which call for inversion of fuller matrix system at lower frequencies. Numerical results, which demonstrate the efficiency, accuracy, and stability of the proposed MOT scheme, are presented.

Explicit Time Marching Schemes for Solving the Magnetic Field Volume Integral Equation

“…5(b For the same set of simulations with ∆t = 6.667 ns, Fig. 5(c) Table III provides err RCS computed using (29) for this set of simulations and confirms that all four MOT schemes have the same level of accuracy. Table III's second and third groups of rows compares the efficiency and accuracy of the MOT schemes for the sets of PT is significantly faster than the other three.…”