An Adaptive Discrete Geometric Approach is proposed for high-accuracy simulations of 2-D elliptic problems on the coarse grid. The idea is to reduce the error coming from the discretization of the constitutive equations by using the patch recovery technique. The integration-oriented scheme is adopted for the recovery procedure due to the high-precision of the regression functions. The accuracy and efficiency of the proposed approach are verified by the numerical tests.
CodecasaL.SpecognaR. and TrevisanF., A New Set of Basis Functions for the Discrete Geometric Approach, Journal of Computational Physics229 (2010), 7401–7410.
2.
SakataY.WashioN.MifuneT. and MatsuoT., Multiple-division Subgrid Construction for Space-time Finite Integration Electromagnetic Field Computation, International Journal of Applied Electromagnetics and Mechanics52 (2016), 617–622.
3.
FujitaY. and KawaguchiH., Development of Improved Memory Architecture FDTD/FIT Dedicated Computer Based on SDRAM for Large Scale Microwave Simulation, International Journal of Applied Electromagnetics and Mechanics32 (2010), 145–157.
4.
SchreiberaU.ClemensbM. and van RienenaU., Conformal FIT Formulation for Simulations of Electro-quasistatic Fields, International Journal of Applied Electromagnetics and Mechanics19 (2004), 193–197.
5.
MarroneM., Computational Aspects of the Cell Method in Electrodynamics, Progress in Electromagnetics Research32 (2001), 317–356.
6.
CodecasaL.SpecognaR. and TrevisanF., Discrete Constitutive Equations over Hexahedral Grids for Eddy-current Problems, Computer Modeling in Engineering1(1) (2008), 1–14.
7.
CodecasaL. and TrevisanF., Constitutive Equations for Discrete Electromagnetic Problems over Polyhedral Grids, Journal of Computational Physics225 (2007), 1894–1918.
8.
CodecasaL.SpecognaR. and TrevisanF., Base Functions and Discrete Constitutive Relations for Staggered Polyhedral Grids, Computer Methods in Applied Mechanics and Engineering198(1) (2009), 1117–1123.
9.
JänickeL. and KostA., Efficiency Properties of Adaptive Mesh Generation, International Journal of Applied Electromagnetics and Mechanics13 (2001/2002), 387–392.
10.
ChienW.HuangC.-H. and ChiuC.-C., Cubic-spline Expansion for A Two-dimensional PeriodicConductor in Free Space, International Journal of Applied Electromagnetics and Mechanics24 (2006), 105–114.
