Package author: Jukka Aho (@ahojukka5, [email protected])

FEMBase.jl is a base package for FEM codes. It implements all the basic data structures in an efficient way and aims to be the rock-solid backbone which can be used to build your very own FEM solver. The basis principle is that FEMBase is a tiny and well-optimized, efficient subset of larger finite element method software with pre- and postprocessors. FEMBase.jl is used in JuliaFEM.jl.

In order to make a stable package, all operations that are not closely related to the basic operations are left out. This encourages to develop a highly modular FEM where features are implemented in their own packages. The stragegy chosen is intentional. Pre- and posprocessing, physical models, file formats and things like that evolve in time, while the basic principles stay. We want that those evolving things stay in their own packages as much as possible.

FEMBase implements all kind of basic data types like Problem, Element, Node, IntegrationPoint, Analysis and so on so that user can define the discretized geometry and integration scheme. Each element does have a topology like Poi1, Seg2, Tri3, Quad4, Tet4, Hex8 for isoparametric linear elements having only corner nodes or Seg3, Tri6, Quad8, Tet10, Hex20 for isoparametric quadratic elements having nodes in middle of the edges. Then there is also elements having middle nodes like Tri7 and Quad9.

Data of model is repsented in fields. Data type can be scalar, vector, tensor or something user-defined for spesific needs. Data can be defined in analysis, problem, element, node or integration point. Data can depend on time and it can be interpolated with respect to time using different interpolation schemes.

Data can also be interpolated in spatial direction using basis functions, which are Lagrange basis functions at the moment.

FEMBase.jl doesn't solve the system of equations. You can define model and data, integrate and interpolate, but you need to write your own solver. And as a consequence it doesn't write the results to anywhere, so you need to implement your own results writer or use some of the existing solutions like XdmfWriter.jl.

FEMBase.jl doesn't have any physical models. FEMBase doesn't know anything about displacements, temperatures, velocities or pressures. FEMBase.jl does assemble a problem, but it doesn't define it. So you need to build your physical model in some other package or use some of the existing solutions like HeatTransfer.jl. Things related to geometry, like calculating Jacobians, are supported.

FEMBase does not parse mesh from other format. For that, you need to implement your own parser or use some existing solutions, like AbaqusReader.jl, AsterReader.jl or Gmsh.jl.

Given data and basis functions, we should be able to naturally interpolate any kind of data. In current implementation, we have an assumption that data is defined in nodes like it is done standard FE methods. Then we have things like hierarchical elements, NURBS, material particle method and so on, which should also be possible to implement using FEMBase.

Contributions in code and idea level are welcome and highly appreciated. If you have some great ideas how to improve package, raise an issue or drop me email.