Time Domain Integral Equation Analysis of Scattering From Composite Bodies via Exact Evaluation of Radiation Fields

Accurate temporal discretization of time domain boundary integral equations

“…First, the collocation in time scheme is applied with second degree piecewise polynomial Lagrange interpolants as basis functions. All interaction integrals are computed as in [4]. Next, the simulation is repeated using the new scheme.…”

Parallel PWTD-Accelerated Explicit Solution of the Time-Domain Electric Field Volume Integral Equation

“…The implicit MOT scheme require at every time step solution of the linear system [3], which is traditionally constructed upon expanding the flux density with Schaubert-Wilton-Glisson (SWG) spatial basis functions [8] and piecewise polynomial temporal basis functions [9], followed by Galerkin and point testing in space and time, respectively. In addition, modern implicit MOT-based solution of time domain surface and volume integral equations can be made low-and high-frequency stable by using computationally more expensive space-time discretization techniques, such as bandlimited time discretization [7,10], space-time Galerkin testing [11,12], quasi-Helmholtz decomposition [13,14], and highly accurate evaluation of MOT matrix elements [12,[15][16][17][18][19][20]. In contrast, the explicit MOT scheme, usually leverages pulse spatial basis functions and low order temporal basis functions and point testing both in space and time.…”

1/R2-Kernel cancelation in classical marching-on-in-time schemes

“…Enforcing the boundary condition J = n × H, which sets the total (incident plus scattered) magnetic field tangential to the exterior surface conformal to S equal to the unknown induced surface current density J(r,t), finally results in the time-domain magnetic field integral equation (MFIE) [1][2][3][4][5][6][7]. Taking the existing curl operator into the integral and extracting the Cauchy principal value afterwards, the MFIE can be represented by…”

“…Time-domain surface integral equations, which are prefectly suited for the analysis of electromagnetic wave scattering from three-dimensional objects, are numerically solved using the time-domain boundary element methods [1][2][3][4][5][6][7]. Depending on the choice of time discretization approaches, several categories of integral solvers have been attained.…”