Finite Volume

Any numerical implementation requires the discretization of continuous functions into discrete approximations. These approximations are typically organized in a mesh, which defines boundaries, locations, and connectivity. Of specific interest to geophysical simulations, we require that averaging, interpolation and differential operators be defined for any mesh. In SimPEG, we have implemented a staggered mimetic finite volume approach (Hyman and Shashkov, 1999). This approach requires the definitions of variables at either cell-centers, nodes, faces, or edges as seen in the figure below.

• SimPEG Meshes
  • Overview of Meshes Available
  • Variable Locations and Terminology
  • The API
• Differential Operators
• Inner Products
  • Example problem for DC resistivity
  • Defining Tensor Properties
  • Structure of Matrices
  • Taking Derivatives
  • The API