Theme D: Numerical methods for multi-scale problems

Theme Manager: Professor I.G. Graham, Mathematical Sciences

OVERVIEW

• Parallel elliptic solvers for diffusion in heterogeneous media in 2D and 3D which are robust to multiple scales in the problem, both in terms of their accuracy and their solution times.
• Solvers for frequency domain wave propagation in heterogeneous media which are able to locate band gap phenomena, using hybrid numerical/asymptotic methods.
• Application of codes to computation of band gap phenomena in periodic and non-periodic wave localization problems in photonic crystals.
• Application to porous media flow and verification of solver on benchmark problems from the Society of Petroleum Engineers and on real problems in oil recovery or waste management applications.
• Adaptive methods for 2D problems with singular and near singular solutions exploiting (emergent) scaling properties.
• Application to nonlinear optics problems and to blow-up problems in 2-D Boussinesq convection.
• World class workshop on numerical techniques for multi-scale problems.

CURRENT RESEARCH HIGHLIGHTS

Within Theme D there has been much progress in innovative numerical analysis and algorithm design in a number of application areas. Click here for further details.