Conservative treatment of curvilinear perfect-conductor boundaries in the energy-conserving implicit Darwin-PIC algorithm.

We discuss the extension of the recently developed fully implicit, curvilinear Darwin particle-in-cell algorithm¹ to deal with arbitrary curvilinear perfect-conductor boundaries. Unlike standard explicit PIC schemes, fully implicit PIC algorithms allow exact discrete energy and charge conservation, and feature superior stability properties.^1,2,3,4 However, Darwin-PIC formulations are notoriously brittle when dealing with realistic boundaries in multiple dimensions, as they often require artificial boundary conditions.⁵ Here, we extend the implicit Darwin-PIC algorithm to deal with arbitrary curvilinear perfect-conductor boundaries while retaining its exact conservation properties.⁶ We will introduce the formulation and demonstrate its accuracy and efficiency properties with various numerical experiments.

1. Chacon and Chen, JCP, 316 (2016)

2. Chen, Chacon, and Barnes, JCP 230 (2011)

3. Chen and Chacon, CPC, 185 (2014)

4. Chen and Chacon, CPC 197 (2015)

5. Hewett, CPC 84 (1994)

6. Chacon and Chen, JCP, submitted (2018)