2021/01/07 by Min Cai, Cai, Min, Ehsan Kharazmi +5
Computer Science · Engineering · Mathematics · #Boundary (topology) #Boundary value problem #Bounded function #Collocation (remote sensing) #Computer science #Discretization #Dissipation #Domain (mathematical analysis) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Fractional calculus #Function (biology) #Mathematical analysis #Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Optics #Perfectly matched layer #Physics #Reflection (computer programming) #Variable (mathematics) #Wave equation #Wave propagation #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.2101.02355
arxiv created 2021/01/07 · openalex publication_date 2021/01/07 · arxiv updated 2021/01/08 · openalex created_date 2021/01/18 · openalex updated_date 2026/08/05
We develop fractional buffer layers (FBLs) to absorb propagating waves without reflection in bounded domains. Our formulation is based on variable-order spatial fractional derivatives. We select a proper variable-order function so that dissipation is induced to absorb the coming waves in the buffer layers attached to the domain. In particular, we first design proper FBsL for the one-dimensional one-way and two-way wave propagation. Then, we extend our formulation to two-dimensional problems, where we introduce a consistent variable-order fractional wave equation. In each case, we obtain the fully discretized equations by employing a spectral collocation method in space and Crank-Nicolson or Adams-Bashforth method in time. We compare our results with the perfectly matched layer (PML) method and show the effectiveness of FBL in accurately suppressing any erroneously reflected waves, including corner reflections in two-dimensional rectangular domains. FBLs can be used in conjunction with any discretization method appropriate for fractional operators describing wave propagation in bounded or truncated domains.