This book deals with the general topic “Numerical solution of partial differential equations
(PDEs)” with a focus on adaptivity of discretizations in space and time. By and large …

Adjoint methods are a key ingredient of gradient-based full-waveform inversion schemes.
While being conceptually elegant, they face the challenge of massive memory requirements …

Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of
partial differential equations, aimed at supporting application-oriented research in numerical …

This paper presents concepts and implementation of the finite element toolbox Kaskade 7, a
flexible C++ code for solving elliptic and parabolic PDE systems, based on the Dune …

For the solution of optimal control problems governed by nonlinear parabolic PDEs,
methods working on the reduced objective functional are often employed to avoid solving …

This paper proposes a new method that combines checkpointing methods with error-
controlled lossy compression for large-scale high-performance full-waveform inversion …

In high accuracy numerical simulations and optimal control of time-dependent processes,
often both many timesteps and fine spatial discretizations are needed. Adjoint gradient …

This paper presents efficient computational techniques for solving an optimization problem
in cardiac defibrillation governed by the monodomain equations. Time-dependent electrical …

Parallel-in-time methods for solving initial value problems are a means to increase the
parallelism of numerical simulations. Hybrid parareal schemes interleaving the parallel-in …

Full waveform inversion or adjoint tomography has routinely been performed to image the
internal structure of the Earth at high resolution. This is typically done using the Fréchet …