TWO-GRID METHODS FOR MAXWELL EIGENVALUE PROBLEMS

Area of Science:

• Computational mathematics
• Electromagnetism theory
• Numerical analysis

Background:

• The Maxwell eigenvalue problem is crucial in various physics and engineering fields.
• Existing methods for solving the Maxwell eigenvalue problem can be computationally intensive.
• The two-grid methodology has shown promise for efficiently solving elliptic eigenvalue problems.

Purpose of the Study:

• To introduce two novel two-grid algorithms for the Maxwell eigenvalue problem.
• To adapt and extend the two-grid methodology for electromagnetic applications.
• To reduce the computational cost associated with solving the Maxwell eigenvalue problem.

Main Methods:

• The proposed methods utilize a two-grid approach, adapting techniques from elliptic eigenvalue problems.
• The algorithms reduce the problem on a fine grid to a Maxwell equation on the fine grid and an eigenvalue problem on a coarser grid.
• Error estimation and numerical experiments are employed to validate the algorithms.

Main Results:

• The new two-grid schemes significantly decrease the total computational cost.
• Asymptotically optimal accuracy is maintained by the proposed methods.
• Numerical experiments confirm the theoretical error estimates and the efficiency of the algorithms.

Conclusions:

• The developed two-grid algorithms provide an efficient and accurate solution for the Maxwell eigenvalue problem.
• These methods offer a practical approach for computational electromagnetics.
• The study demonstrates the effectiveness of the two-grid methodology in this domain.