Sparse space-time boundary element methods for the heat equation

The goal of this work is the efficient solution of the heat equation with Dirichlet or Neumann boundary conditions using the Boundary Elements Method (BEM). Efficiently solving the heat equation is useful, as it is a simple model problem for other types of parabolic problems. In complicated spatial domains as often found in engineering, BEM can be beneficial since only the boundary of the domain has to be discretised. This makes BEM easier than domain methods such as finite elements and finite differences, conventionally combined with time-stepping schemes to solve this problem. The contribution of this work is to further decrease the complexity of solving the heat equation, leading both to speed gains (in CPU time) as well as requiring smaller amounts of memory to solve the same problem. To do this we will combine the complexity gains of boundary reduction by integral equation formulations with a discretisation using wavelet bases. This reduces the total work to O(h

Evaluation of simulated sea-ice concentrations from sea-ice/ocean models using satellite data and polynya classification methods

Sea-ice concentrations in the Laptev Sea simulated by the coupled North Atlantic-Arctic Ocean-Sea-Ice Model and Finite Element Sea-Ice Ocean Model are evaluated using sea-ice concentrations from Advanced Microwave Scanning Radiometer-Earth Observing System satellite data and a polynya classification method for winter 2007/08. While developed to simulate largescale sea-ice conditions, both models are analysed here in terms of polynya simulation. The main modification of both models in this study is the implementation of a landfast-ice mask. Simulated sea-ice fields from different model runs are compared with emphasis placed on the impact of this prescribed landfast-ice mask. We demonstrate that sea-ice models are not able to simulate flaw polynyas realistically when used without fast-ice description. Our investigations indicate that without landfast ice and with coarse horizontal resolution the models overestimate the fraction of open water in the polynya. This is not because a realistic polynya appears but due to a larger-scale reduction of ice concentrations and smoothed ice-concentration fields. After implementation of a landfast-ice mask, the polynya location is realistically simulated but the total open-water area is still overestimated in most cases. The study shows that the fast-ice parameterization is essential for model improvements. However, further improvements are necessary in order to progress from the simulation of large-scale features in the Arctic towards a more detailed simulation of smaller-scaled features (here polynyas) in an Arctic shelf sea.