Solution of two-dimensional electromagnetic scattering problem by FDTD with optimal step size, based on a semi-norm analysis

• Published in: AIP conference proceedings Vol. 1637; no. 1
• Main Authors: Monsefi Farid, Carlsson Linus, Rančić Milica, Otterskog Magnus, Silvestrov Sergei
• Format: Conference Proceeding Journal Article
• Language: English
• Published: Melville American Institute of Physics 10.12.2014
• Subjects: ALGORITHMS; BOUNDARY CONDITIONS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; CONVERGENCE; Current sources; ELECTROMAGNETIC RADIATION; Electromagnetic scattering; FINITE DIFFERENCE METHOD; Finite difference time domain method; IMPLEMENTATION; INSTABILITY; MAXWELL EQUATIONS; SCATTERING; SPACE; STABILITY; SURFACES; Time domain analysis; TWO-DIMENSIONAL CALCULATIONS
• ISSN: 0094-243X; 1551-7616
• DOI: 10.1063/1.4904639

To solve the electromagnetic scattering problem in two dimensions, the Finite Difference Time Domain (FDTD) method is used. The order of convergence of the FDTD algorithm, solving the two-dimensional Maxwell’s curl equations, is estimated in two different computer implementations: with and without an obstacle in the numerical domain of the FDTD scheme. This constitutes an electromagnetic scattering problem where a lumped sinusoidal current source, as a source of electromagnetic radiation, is included inside the boundary. Confined within the boundary, a specific kind of Absorbing Boundary Condition (ABC) is chosen and the outside of the boundary is in form of a Perfect Electric Conducting (PEC) surface. Inserted in the computer implementation, a semi-norm has been applied to compare different step sizes in the FDTD scheme. First, the domain of the problem is chosen to be the free-space without any obstacles. In the second part of the computer implementations, a PEC surface is included as the obstacle. The numerical instability of the algorithms can be rather easily avoided with respect to the Courant stability condition, which is frequently used in applying the general FDTD algorithm.