Ellipsis 3D: A particle-in-cell finite-element hybrid code for modelling mantle convection and lithospheric deformation

We have extended the two-dimensional geodynamics finite-element code “Ellipsis” to three-dimensions. Ellipsis uses a hybrid particle in a cell scheme, which combines a fixed mesh of computational points and a dense arrangement of mobile material points. The fixed Eulerian mesh allows very fast computation, performed in Ellipsis via a multigrid iteration method, while the Lagrangian particle reference frame allows the tracking of material interfaces and history-dependent properties such as strain history for strain-softening materials. The method is exceptionally useful in very large deformation analyses, where purely Lagrangian approaches would be severely hampered by the need for remeshing to minimize element distortion. The Gnu Public Licensed Ellipsis3D code lends itself to combined 2D/3D model prototyping, and has proven to be an excellent geodynamics teaching tool for modelling, covering mantle convection, lithospheric extension and plume–lithosphere interaction.