2019/09/23 by Yann-Meing Law, Law, Yann-Meing, Jean‐Christophe Nave +1 · 1 citation
Engineering · Physics and Astronomy · #35Q61 #65M06 #78M20 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Microwave Engineering and Waveguides #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1909.10570
openalex publication_date 2019/09/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In this work, we propose staggered FDTD schemes based on the correction\nfunction method (CFM) to discretize Maxwell's equations with embedded perfect\nelectric conductor (PEC) boundary conditions. The CFM uses a minimization\nprocedure to compute a correction to a given FD scheme in the vicinity of the\nembedded boundary to retain its order. The minimization problem associated with\nCFM approaches is analyzed in the context of Maxwell's equations with embedded\nboundaries. In order to obtain a well-posed problem, we propose fictitious\ninterface conditions to fulfill the lack of information, namely the surface\ncurrent and charge density, on the embedded boundary. Fictitious interfaces can\ninduce some issues for long time simulations and therefore the penalization\ncoefficient associated with fictitious interface conditions must be chosen\nsmall enough. We introduce CFM-FDTD schemes based on the well-known Yee scheme\nand a fourth-order staggered FDTD scheme. Long time simulations and convergence\nstudies are performed in 2-D for various geometries of the embedded boundary.\nCFM-FDTD schemes have shown high-order convergence.\n