74 citations · 199 across the 21 of their papers we have counts for
27 papers
Spectral deferred corrections parallelized across the method for differential-algebraic equations
Matthias Bolten, Lisa Wimmer
In this work, the performance of different spectral deferred corrections (SDC) methods applied to initial value problems for differential-algebraic equations (DAEs) of index one is…
Multigrid preconditioning for regularized least-squares problems
Matthias Bolten, Scott P. MacLachlan, Misha E. Kilmer
In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regu…
Non-convex shape optimization by dissipative Hamiltonian flows
Matthias Bolten, Onur Tanil Doganay, Hanno Gottschalk +1
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to comput…
Symbol based convergence analysis in multigrid methods for saddle point problems
Matthias Bolten, Marco Donatelli, Paola Ferrari +1
Saddle point problems arise in a variety of applications, e.g., when solving the Stokes equations. They can be formulated such that the system matrix is symmetric, but indefinite,…
A note on the spectral analysis of matrix sequences via GLT momentary symbols: from all-at-once solution of parabolic problems to distributed fractional order matrices
Matthias Bolten, Sven-Erik Ekström, Isabella Furci +1
The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization with space-time grid for a…
Symbol based Convergence Analysis in Block Multigrid Methods with Applications for Stokes Problems
Marco Donatelli, Matthias Bolten, Paola Ferrari +1
The main focus of this paper is the study of efficient multigrid methods for large linear systems with a particular saddle-point structure. Indeed, when the system matrix is symmet…
Using ODE waveform-relaxation methods to efficiently include gap junctions in distributed neural network simulations
Matthias Bolten, Jan Hahne
Waveform-relaxation methods divide systems of differential equations into subsystems and therefore allow for parallelization across the system. Here we present an application for O…
A symbol based analysis for multigrid methods for Block-Circulant and Block-Toeplitz Systems
Matthias Bolten, Marco Donatelli, Paola Ferrari +1
In the literature, there exist several studies on symbol-based multigrid methods for the solution of linear systems having structured coefficient matrices. In particular, the conve…
Towards Real-Time Magnetic Dosimetry Simulations for Inductive Charging Systems
Norman Haussmann, Martin Zang, Robin Mease +3
The exposure of a human by magneto-quasistatic fields from wireless charging systems is to be determined from magnetic field measurements in near real-time. This requires a fast li…
Krylov Subspace Recycling for Evolving Structures
Matthias Bolten, Eric de Sturler, Camilla Hahn
Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear natural…
Toeplitz Momentary Symbols: definition, results, and limitations in the spectral analysis of Structured Matrices
Matthias Bolten, Sven-Erik Ekström, Isabella Furci +1
A powerful tool for analyzing and approximating the singular values and eigenvalues of structured matrices is the theory of GLT sequences. By the GLT theory one can derive a functi…
Event-based update of synapses in voltage-based learning rules
Jonas Stapmanns, Jan Hahne, Moritz Helias +3
Due to the point-like nature of neuronal spiking, efficient neural network simulators often employ event-based simulation schemes for synapses. Yet many types of synaptic plasticit…
Non-overlapping block smoothers for the Stokes equations
Lisa Claus, Matthias Bolten
Overlapping block smoothers efficiently damp the error contributions from highly oscillatory components within multigrid methods for the Stokes equations but they are computational…
PyMGRIT: A Python Package for the parallel-in-time method MGRIT
Jens Hahne, Stephanie Friedhoff, Matthias Bolten
In this paper, we introduce the Python framework PyMGRIT, which implements the multigrid-reduction-in-time (MGRIT) algorithm for solving the (non-)linear systems arising from the d…
Tracing locally Pareto optimal points by numerical integration
Matthias Bolten, Onur Tanil Doganay, Hanno Gottschalk +1
We suggest a novel approach for the efficient and reliable approximation of the Pareto front of sufficiently smooth unconstrained bi-criteria optimization problems. Optimality cond…
GivEn -- Shape Optimization for Gas Turbines in Volatile Energy Networks
Jan Backhaus, Matthias Bolten, Onur Tanil Doganay +19
This paper describes the project GivEn that develops a novel multicriteria optimization process for gas turbine blades and vanes using modern "adjoint" shape optimization algorithm…
Parallel-in-Time Simulation of an Electrical Machine using MGRIT
Matthias Bolten, Stephanie Friedhoff, Jens Hahne +1
We apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To reso…
Shape optimization to decrease failure probability
Matthias Bolten, Hanno Gottschalk, Camilla Hahn +1
Ceramic is a material frequently used in industry because of its favorable properties. Common approaches in shape optimization for ceramic structures aim to minimize the tensile st…
Asymptotic convergence of the parallel full approximation scheme in space and time for linear problems
Matthias Bolten, Dieter Moser, Robert Speck
For time-dependent partial differential equations, parallel-in-time integration using the "parallel full approximation scheme in space and time" (PFASST) is a promising way to acce…
Integration of continuous-time dynamics in a spiking neural network simulator
Jan Hahne, David Dahmen, Jannis Schuecker +4
Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based…
A multigrid perspective on the parallel full approximation scheme in space and time
Matthias Bolten, Dieter Moser, Robert Speck
For the numerical solution of time-dependent partial differential equations, time-parallel methods have recently shown to provide a promising way to extend prevailing strong-scalin…
Multigrid methods for tensor structured Markov chains with low rank approximation
Matthias Bolten, Karsten Kahl, Sonja Sokolović
Tensor structured Markov chains are part of stochastic models of many practical applications, e.g., in the description of complex production or telephone networks. The most interes…
Interweaving PFASST and Parallel Multigrid
Michael Minion, Robert Speck, Matthias Bolten +2
The parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and disc…
Minimal failure probability for ceramic design via shape control
Matthias Bolten, Hanno Gottschalk, Sebastian Schmitz
We consider the probability of failure for components made of brittle mate- rials under one time application of a load as introduced by Weibull and Batdorf - Crosse and more recent…