3 papers
math.NA2025
Carleman Linearization of Parabolic PDEs: Well-posedness, convergence, and efficient numerical methods
Bernhard Heinzelreiter, John W. Pearson
We explore how the analysis of the Carleman linearization can be extended to dynamical systems on infinite-dimensional Hilbert spaces with quadratic nonlinearities. We demonstrate…
math.NA2024
A Framework for the Solution of Tree-Coupled Saddle-Point Systems
Christoph Hansknecht, Bernhard Heinzelreiter, John W. Pearson +1
We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then…
math.NA2024
Diagonalization-Based Parallel-in-Time Preconditioners for Instationary Fluid Flow Control Problems
Bernhard Heinzelreiter, John W. Pearson
We derive a new parallel-in-time approach for solving large-scale optimization problems constrained by time-dependent partial differential equations arising from fluid dynamics. Th…