Moving domain decomposition methods for parabolic PDEs

The overall purpose of the project is to design and analyze new domain decomposition methods for parabolic partial differential equations (PDEs) on moving domains with dynamic boundary conditions.

These equations are frequently encountered in applications, and are numerically challenging due to the time-dependent geometries and the need for implicit time integration.

This results in large-scale computations that require the usage of parallel and distributed hardware.The numerical study of parabolic PDEs on moving domains is a very recent field focused on standard numerical schemes that do not allow for parallel implementations.

Thus, there is a large demand, from both industry and academia, to develop new parallel strategies tailored to time-dependent equations and geometries.The aim of this project is therefore to develop a genuinely new framework, by merging numerical analysis of domain decomposition methods with the recent theoretical developments associated with PDEs on moving domains and space-time finite elements.

This includes the extension of Sobolev-Bochner spaces to moving domains and variational formulations using fractional Sobolev spaces in time.

The methods developed in the project will be implemented and benchmarked in our interdisciplinary collaborations, e.g., in optimal surface control.