Stability analysis of the marching-on-in-time boundary element method for electromagnetics

Stability of boundary element methods for the two dimensional wave equation in time domain revisited

“…|λ| > 1 holds. Eigenvalue problems of this type in 3D have been considered by many authors after converting them into equivalent linear eigenvalue problems for the companion matrices (e.g., [23,22,7,9,4,11]). As a matter of fact, there is no ambiguity in the choice of a sufficiently large l in 3D if the scatterer is bounded because the fundamental solution has a "tail" of a finite length.…”

“…Coding becomes easier if one uses variational approaches only spatially and use collocation in time. Van 't Wout et al [4] have shown a way to find a stable timecollocated variational approach based on fully variational methods. In spite of these efforts, the standard collocation approaches remain the preferred choice in engineering, although known mathematical stability results in collocation are rather limited (see Davies and Dancan [5] for example).…”

Time-Dependent Lorentz-Mie-Debye Formulation for Electromagnetic Scattering From Dielectric Spheres (Invited Paper)

“…This has been numerically demonstrated in [45]. However, ongoing work is focused on studying late time stability for this system and extending it to analyzing stabilities of TDIEs as applied to electromagnetics -a long standing problem where significant literature exists [56][57][58][59][60][61][62].…”

Radiation Gauge Potential-Based Time Domain Integral Equations for Penetrable Regions

“…Along these lines, it is essential for basis and testing functions to be selected from appropriate Sobolev spaces to achieve a stable marchingon-in-time (MOT) discretization of systems combining vector and scalar TDIEs [17]. In particular, basis functions are selected from the domain space of the integral operators, while testing functions are selected from the dual to the range space of the integral operators [25]. To support this, the Sobolev space properties of Eqs.…”