The field of numerical methods and model reduction is moving towards the development of more efficient and accurate techniques for simulating complex systems. Researchers are focusing on creating innovative methods that can handle large-scale problems, such as linear time-periodic systems, and nonlinear systems, like those found in proton transport and magnetic drug targeting. Noteworthy papers in this area include the development of a partial Floquet transformation for model reduction of linear time-periodic systems, and a high-order deterministic dynamical low-rank method for proton transport in heterogeneous media. Additionally, a unified framework for the analysis and numerical approximation of linear operator equations has been proposed, laying the foundation for future work in model reduction and numerical methods.
Advances in Model Reduction and Numerical Methods
Sources
Partial Floquet Transformation and Model Order Reduction of Linear Time-Periodic Systems
A new addition theorem for the 3-D Navier-Lam\'e system and its application to the method of fundamental solutions
Floquet stability of periodically stationary pulses in a short-pulse fiber laser
POD-based reduced order modeling of global-in-time iterative decoupled algorithms for Biot's consolidation model
Derivation and Numerical Simulation of a Thermodynamically Consistent Magneto Two-Phase Flow Model for Magnetic Drug Targeting
A high-order deterministic dynamical low-rank method for proton transport in heterogeneous media
Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors
A unified framework for the analysis, numerical approximation and model reduction of linear operator equations, Part I: Well-posedness in space and time