On enforcing Gauss' law in electromagnetic particle-in-cell codes

✍ Scribed by A. Bruce Langdon

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 326 KB
• Volume: 70
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(92)90105-8

✦ Synopsis

During the 20 years in which two-dimensional electromagnetic particle-in-cell codes have been in intensive use, discussion has continued as to how best to honor both the Ampere-Maxwell equation and Gauss' law in spite of compromises made in the collection of the density and current terms from the particle coordinates. Boris' popular and very effective method corrects the divergence of the electric field, but that requires solution of a Poisson's equation. Marder has recently popularized a partial correction that is very simple and fast, even with complex meshes.

A new viewpoint on Marder's correction suggests improvements and new possibilities. In this note, I restate Marder's procedure and analyze a simple modification that improves it and clarifies its relation to Boris' divergence correction. Finally, I show that the improved Marder scheme gives the same results as an "incomplete Boris" correction in which the exact Poisson solve is replaced by a single accelerated point-Jacobi iteration. This observation suggests further improvements.