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A marching-on in time meshless kernel based solver for full-wave electromagnetic simulation. (English) Zbl 1269.78016
In their previous work, the authors developed an improved smoothed particle hydrodynamics (SPH) method and applied it to Maxwell’s equations, which led them to the smoothed particle electrodynamics method (SPEM). The SPEM is limited by the so-called Courant-Friedrichs-Lewy (CFL) stability condition, i.e., the size of the time step of SPEM is limited.
In this paper, the authors develop an unconditionally stable scheme by applying the alternating direction finite difference time domain (ADI-FDTD) method in a leapfrog way. They call it leapfrog alternating direction implicit finite difference (LAF) SPEM. The authors perform numerical tests of LAF-SPEM, and the computational results are compared to the exact solutions to demonstrate the efficiency of LAF-SPEM.

78M25 Numerical methods in optics (MSC2010)
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q61 Maxwell equations
65D25 Numerical differentiation
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