Formation of an extensional sedimentary basin.
Side view of sediment layers in Grand Canyon, USA.
Sample computational domain of a basin simulation. This model has about 8.5 million tetrahedral elements, and large material parameter variations from layer to layer.
Joachim Berdal Haga received a BSc/Hons in computer science from Heriot-Watt University in 1998, and worked as a programmer the next four years. Following a BSc in physics (2004) and a MSc in computational physics (2006), both at the University of Oslo, he joined Simula in the summer of 2006. He is currently occupied with a PhD in numerical methods for modelling of coupled deformation and fluid flow in sedimentary basins.
Research interests
I am at the moment focused on efficient iterative solvers and preconditioners for finite element discretisations of large geomechanical (poroelastic) problems. Such large-scale problems arise (for example) in sedimentary basins. In particular, two major difficulties for iterative solvers are the tight coupling of the equations and the contrasts (discontinuities) of the material parameters. These must be handled in order to allow the simulation of basin-scale problems.
- The finite element method
- Numerical methods
- Parallel computing (mainly of the distributed type, i.e., no shared memory)
- Architectural solutions and frameworks for the topics above: high-level languages for numerics, abstractions, etc.
Research projects
Research activities
We have implemented a simulator based on a finite element discretisation of Biot's equations, which describe the poroelastic problem in terms of two coupled partial differential equations; one for the displacement of the solid (porous) matrix, and one for the pressure of the fluid in the pore space. Depending on the needs of the particular problem, the introduction of fluid velocity or solid pressure as primary variables is also possible. The main obstacle to the simulation of basin-scale processes is however the solution of the algebraic equations on parallel computers. For this, an iterative solution process is necessary, which requires robust preconditioning. Hence, the following list of activities, which is reflected in my recent publications.
- Stable finite element discretisation of Biot's equations.
- Block preconditioners for 2-by-2 saddle point problems with ill-conditioned blocks (such as Biot's equations with large permeability contrasts).
- Parallel block preconditioners.
