A weak Galerkin method for diffraction gratings

Abstract

This paper concerns a weak Galerkin method (WGM) for the diffraction of a time-harmonic incident wave impinging upon a one-dimensional periodic grating structure. The existence and uniqueness of the weak Galerkin solution to the grating problem are established using a variational approach. The convergence rate of the proposed WGM is systematically analyzed. Numerical simulations are presented to verify the efficiency of the WGM for solving grating problems.

Keywords:

• Weak Galerkin method
• diffraction grating

AMS Subject Classifications:

• 65N30
• 65N12
• 65M12

Acknowledgements

The authors wish to thank Professor Haijun Wu for many suggestions on FEM programming of the grating problems. They also wish to thank the High Performance Computing Center of Jilin University and Computing Center of Jilin Province for essential computing support.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11471141]; the basic research of the science and technology development program of Jilin province [grant number 20150101058JC]; by the NSF of China [grant number 11201453], [grant number 11571161]; and Shenzhen Sci-Tech fund [grant number JCYJ20140509143748226].