Solving for the low-rank tensor components of a scattering wave function
Atomic and molecular breakup reactions, such as multiple-ionisation, are described by a driven Schr\"odinger equation. This equation is equivalent to a high-dimensional Helmholtz equation and it...
Projected Newton method for noise constrained $\ell_p$ regularization
Choosing an appropriate regularization term is necessary to obtain a meaningful solution to an ill-posed linear inverse problem contaminated with measurement errors or noise. The $\ell_p$ norm...
Projected Newton Method for noise constrained Tikhonov regularization
Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter...
The Communication-Hiding Conjugate Gradient Method with Deep Pipelines
Krylov subspace methods are among the most efficient solvers for large scale linear algebra problems. Nevertheless, classic Krylov subspace algorithms do not scale well on massively parallel...
Krylov-Simplex method that minimizes the residual in $\ell_1$-norm or $\ell_\infty$-norm
The paper presents two variants of a Krylov-Simplex iterative method that combines Krylov and simplex iterations to minimize the residual $r = b-Ax$. The first method minimizes $\|r\|_\infty$,...
The communication-hiding pipelined BiCGStab method for the parallel solution of large unsymmetric linear systems
A High Performance Computing alternative to traditional Krylov subspace methods, pipelined Krylov subspace solvers offer better scalability in the strong scaling limit compared to standard Krylov...
Improving strong scaling of the Conjugate Gradient method for solving large linear systems using global reduction pipelining
This paper presents performance results comparing MPI-based implementations of the popular Conjugate Gradient (CG) method and several of its communication hiding (or 'pipelined') variants....
Initialization of lattice Boltzmann models with the help of the numerical Chapman-Enskog expansion
We extend the applicability of the numerical Chapman-Enskog expansion as a lifting operator for lattice Boltzmann models to map density and momentum to distribution functions. In earlier work...
An efficient multigrid calculation of the far field map for Helmholtz and Schr\"odinger equations
In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by...
Numerical extraction of a macroscopic pde and a lifting operator from a lattice Boltzmann model
Lifting operators play an important role in starting a lattice Boltzmann model from a given initial density. The density, a macroscopic variable, needs to be mapped to the distribution functions,...