This paper surveys the mathematics required for a typically challenging problem from
computational medicine: cancer therapy planning in deep regional hyperthermia. In the …

The assumptions underpinning the adiabatic Born–Oppenheimer (BO) approximation are
broken for molecules interacting with attosecond laser pulses, which generate complicated …

Introducing a unique, modular approach to modeling polymerization reactions, this useful
book will enable practitioners-chemists and engineers alike-to set up and structure their own …

Sequential-in-time methods solve a sequence of training problems to fit nonlinear
parametrizations such as neural networks to approximate solution trajectories of partial …

Spectral deferred correction methods for solving stiff ODEs are known to converge
reasonably fast towards the collocation limit solution on equidistant grids, but show a less …

Recent advances in attosecond science have made it increasingly important to develop
stable, reliable, and accurate algorithms and methods to model the time evolution of atoms …

While multilevel Monte Carlo (MLMC) methods for the numerical approximation of partial
differential equations with random coefficients enjoy great popularity, combinations with …

A new concept for the higher-order accurate approximation of partial differential equations
on manifolds is proposed where a surface mesh composed by higher-order elements is …

We propose and analyze two strategies for preconditioning linear operator equations that
arise in PDE constrained optimal control in the framework of conjugate gradient methods …

We show that the discrete operator stemming from time-space discretization of evolutionary
partial differential equations can be represented in terms of a single Sylvester matrix …