Treating late-time instability of hybrid finite-element/finite-difference time-domain method

Time-domain finite-difference/finite-element hybrid simulations of radio frequency coils in magnetic resonance imaging

“…The third type of spurious solution is linear growth (Hwang and Wu 1999). Mathematically, linear growth can be traced to the non-diagonalizable system amplification matrix (Wang and Teixeira 2004).…”

“…Mathematically, linear growth can be traced to the non-diagonalizable system amplification matrix (Wang and Teixeira 2004). Alternatively, one can explain it by noticing that E = E + t • ∇V is also a valid solution of equation ( 2) in a source-free lossless medium (Hwang and Wu 1999). In practice, the linear growth can be excited in different ways.…”

Electric and magnetic losses modeled by a stable hybrid with explicit–implicit time-stepping for Maxwell’s equations

“…Wu and Itoh proposed FEM-FDTD hybridizations for both two [6] and three [7] dimensions. These schemes suffer from late-time instabilities that may be damped by temporal filtering [8]. Abenius et al [9] combine the FDTD scheme with an implicit FEM and numerical studies indicate that it is stable, although no formal proof of stability is given.…”

A brick-tetrahedron finite-element interface with stable hybrid explicit–implicit time-stepping for Maxwell’s equations

“…The unphysical late-time instabilities can be artificially damped by e.g. spectral filtering [12]. The finite-volume method in the time domain has also been used to connect unstructured grids to an FDTD scheme [13] and the inherent late-time instabilities can be treated with a dissipative time-integration scheme [14].…”