M-Adapting Low Order Mimetic Finite Differences for Dielectric Interface Problems

McGregor, Duncan A.¹  Gyrya, Vitaliy²  Manzini, Gianmarco² 

[1]Oregon State Univ., Corvallis, OR (United States)

[2]Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

关键词: Mathematics;    dielectric interface;    dispersion;    mimetic finite difference;    m-adaptation;   

DOI  :  10.2172/1240815
RP-ID  :  LA--UR-16-21424
PID  :  OSTI ID: 1240815

学科分类：数学（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

We consider a problem of reducing numerical dispersion for electromagnetic wave in the domain with two materials separated by a at interface in 2D with a factor of two di erence in wave speed. The computational mesh in the homogeneous parts of the domain away from the interface consists of square elements. Here the method construction is based on m-adaptation construction in homogeneous domain that leads to fourth-order numerical dispersion (vs. second order in non-optimized method). The size of the elements in two domains also di ers by a factor of two, so as to preserve the same value of Courant number in each. Near the interface where two meshes merge the mesh with larger elements consists of degenerate pentagons. We demonstrate that prior to m-adaptation the accuracy of the method falls from second to rst due to breaking of symmetry in the mesh. Next we develop m-adaptation framework for the interface region and devise an optimization criteria. We prove that for the interface problem m-adaptation cannot produce increase in method accuracy. This is in contrast to homogeneous medium where m-adaptation can increase accuracy by two orders.