Participating institutions:
Scientific Computing, Institute of Information Technology, Uppsala University	Maya Neytcheva, Ali Dorostkar
Geophysics, Department of Earth Sciences, Uppsala University	Björn Lund
Nordic Volcanological Center, Institute of Earth Sciences, University of Iceland	Thora Árnadóttir
Department of Physics and Mathematics, University of Insubria, Italy	Stefano Serra Capizzano

Project aims and scope:

This project aims at providing accurate and efficient computer simulation tools for glacial isostatic adjustment (GIA) models.

GIA describes the response of the solid Earth to redistribution of surface loads due to the growth or decay of large ice masses. Ice advance and recession, as well as the recent global warming trend, induce sea-level changes and migration of coast lines, which we need to predict. GIA processes involve time scales of a glacial cycle, 100000 years, and spatially encompass the entire Earth. The complexity and the enormous space and time scales leave computer simulations as the only viable option to study GIA phenomena. The need to model complex geometries and 3D Earth structures has prompted an interest to use the finite element method (FEM). Currently, no publicly available FEM codes implement the main GIA complexities; commercial codes are used with inappropriate description of the physics.

This project will develop and analyse FEM-based methods to simulate a more complete description of the GIA process, allowing accurate simulations of complex 3D models with material inhomogeneities. Novel robust and scalable numerical solvers will be developed, including optimal order preconditioned iterative methods. The outcome, a freely available, accurate and efficient simulation code will be a valuable tool box for the GIA community and will enable better understanding of the GIA process in regions with laterally varying Earth properties, such as Iceland.

The driving force for the project is the need to address applied problems of very high complexity, the solution of which is of utmost importance for our society. Such problems are characterized by complicacy, heterogeneity, mutual dependencies, unknown parameters and large space and time domains, that preclude analytical approaches and promote numerical simulations as the only feasible way to approximate the solution.

As the main reference application we consider the Glacial Isostatic Adjustment (GIA) processes, i.e., the response of the solid Earth to redistribution of mass due to alternating glaciation and deglaciation periods. In mathematical terms these processes are described by a coupled system of integro-differential equations that have to be discretized appropriately and accurately enough, and solved using efficient numerical solution methods that are robust with respect to problem, discretization and method parameters.

Accuracy, robustness and efficiency in terms of computational cost are to be achieved answering the following major questions with mathematical rigor:

• What is the estimated approximation error in the numerical solution, consisting of error due to discretization in space and time, numerical integration error for the integral term and operator splitting error.
• What is the sensitivity of the model with respect to the above set of parameters.
• Can we use the general technique of 'Approximating Classes of Sequences', developed by the invited guest researcher, to derive spectral properties and convergence estimates for the matrices in the discrete GIA models, that can not be fully studied by currently available techniques due to nonsymmetricity and noncoerciveness but possessing certain algebraic structure.
• How to utilize the algebraic structure to construct numerically and computationally efficient preconditioners to speed up the solution of the algebraic systems, balancing the overall discretization error with the iteration error.