Finite element solution techniques for large-scale problems in computational fluid dynamics

Element-by-element approximate factorization, implicit-explicit and adaptive implicit-explicit approximation procedures are presented for the finite-element formulations of large-scale fluid dynamics problems. The element-by-element approximation scheme totally eliminates the need for formation, storage and inversion of large global matrices. Implicit-explicit schemes, which are approximations to implicit schemes, substantially reduce the computational burden associated with large global matrices. In the adaptive implicit-explicit scheme, the implicit elements are selected dynamically based on element level stability and accuracy considerations. This scheme provides implicit refinement where it is needed. The methods are applied to various problems governed by the convection-diffusion and incompressible Navier-Stokes equations. In all cases studied, the results obtained are indistinguishable from those obtained by the implicit formulations

Uncertainty quantification for problems in radionuclide transport

The field of radionuclide transport has long recognised the stochastic nature of the problems encountered. Many parameters that are used in computational models are very difficult, if not impossible, to measure with any great degree of confidence. For example, bedrock properties can only be measured at a few discrete points, the properties between these points may be inferred or estimated using experiments but it is difficult to achieve any high levels of confidence. This is a major problem when many countries around the world are considering deep geologic repositories as a disposal option for long-lived nuclear waste but require a high degree of confidence that any release of radioactive material will not pose a risk to future populations. In this thesis we apply Polynomial Chaos methods to a model of the biosphere that is similar to those used to assess exposure pathways for humans and associated dose rates by many countries worldwide. We also apply the Spectral-Stochastic Finite Element Method to the problem of contaminated fluid flow in a porous medium. For this problem we use the Multi-Element generalized Polynomial Chaos method to discretise the random dimensions in a manner similar to the well known Finite Element Method. The stochastic discretisation is then refined adaptively to mitigate the build up errors over the solution times. It was found that these methods have the potential to provide much improved estimates for radionuclide transport problems. However, further development is needed in order to obtain the necessary efficiency that would be required to solve industrial problems

Schnelle Löser für Partielle Differentialgleichungen

The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch (Leipzig), and Gabriel Wittum (Frankfurt am Main), was held May 22nd–May 28th, 2011. This meeting was well attended by 54 participants with broad geographic representation from 7 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds