We have made innovative contributions to a wide range of FEM technologies, including
- Adaptive FEM based on a posteriori error estimates
- Coupled problems, such as fluid-structure interaction
- Cut FEM for problems with dynamic domains
- Isogeometric analysis using splines as basis functions
- Multiscale mixed FEM for flow in porous media
- Reduced-order modelling for fast numerical solution of parameterized PDEs
- Virtual element methods for meshes with general polyhedral elements
As an example, we have developed an open-source object oriented adaptive parallel isogeometric FEM module called IFEM (Isogeometric Finite Element Module) available at github.com/OPM/IFEM, which has been applied to a range of problems:
- 1D, 2D and 3D linear and non-linear solid mechanics
- Beam, membrane, plates, and shell structural mechanics
- Poisson problems e.g. heat equation
- Advection–diffusion problems
- 2D and 3D Stokes problems
- 2D and 3D (including high Reynolds flow) Navier–Stokes problems
- 2D and 3D Boussinesq equations
- Porous media flow
- Coupled problems:
- Thermoelasticity
- Poroelasticity
- Fluid-structure interaction
We can combine our high-fidelity FEM-models with reduced-order modelling (ROM), which is a technique for delivering numerical solutions of parametrized PDEs in real-time with reasonable accuracy.
We also have expertise in the FEniCS computing platform (fenicsproject.org) and proficiency in mesh generation methods and standard software such as Gmsh , or our own UPR module for constrained Voronoi grids.