This review article serves to summarize the many advances in time-parallel computations
since the excellent review article by Gander,“50 years of Time Parallel Integration”(Gander …

This review article describes various multiscale approaches, development of which was
spurred by the emergence of nanotechnology. The multiscale approaches are grouped into …

We consider optimal-scaling multigrid solvers for the linear systems that arise from the
discretization of problems with evolutionary behavior. Typically, solution algorithms for …

Time parallel time integration methods have received renewed interest over the last decade
because of the advent of massively parallel computers, which is mainly due to the clock …

The parareal algorithm is a method to solve time-dependent problems parallel in time: it
approximates parts of the solution later in time simultaneously to parts of the solution earlier …

This book provides an introduction to some modern computational techniques for
optimization problems governed by partial differential equations (PDEs). The optimization …

We present and analyze a new space-time parallel multigrid method for parabolic equations.
The method is based on arbitrarily high order discontinuous Galerkin discretizations in time …

The Lanczos method is an iterative procedure to compute an orthogonal basis for the Krylov
subspace generated by a symmetric matrix A and a starting vector v. An interesting …

Research on multigrid methods for optimization problems is reviewed. Optimization
problems considered include shape design, parameter optimization, and optimal control …

Standard Krylov subspace solvers for self-adjoint problems have rigorous convergence
bounds based solely on eigenvalues. However, for non-self-adjoint problems, eigenvalues …