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James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
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Related Experiment Video

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Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
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TWO-GRID METHODS FOR MAXWELL EIGENVALUE PROBLEMS.

J Zhou1, X Hu2, L Zhong3

  • 1School of Mathematical and Computational Sciences, Xiangtan University, Xiangtan 411105, China.

SIAM Journal on Numerical Analysis
|July 21, 2015
PubMed
Summary
This summary is machine-generated.

Two new algorithms efficiently solve Maxwell eigenvalue problems by reducing complex calculations to simpler ones on coarser grids. These methods offer significant computational savings while maintaining accuracy.

Keywords:
Maxwell eigenvalue problemedge elementtwo-grid method

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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.