12 citations · 29 across the 14 of their papers we have counts for
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Space-Time Parallel Direct Numerical Simulation of Rayleigh-Bénard Convection
Thomas Saupe, Thibaut Lunet, Mathis Bode +3
Rayleigh-Bénard convection (RBC) is a model for turbulent flow and challenging to simulate by direct numerical simulation (DNS). Adequate resolution of all relevant length scales r…
Tracking in-silico Lagrangian sensors in a lab-scale stirred tank reactor
Vamika Rathi, Fatima Sehar, Finn Sommer +4
Lagrangian sensors have shown promise to improve operator awareness of conditions inside a chemical reactor but three-dimensional tracking remains a mostly unsolved challenge. We e…
Adjoint-based Perfusion Estimation from Dynamic Contrast-Enhanced Ultrasound: Advection-Diffusion and Two-Compartment Models
Sophie Externbrink, Ahmed El Kaffas, Dimitre Hristov +1
Tumor perfusion and vascular properties are important determinants of a cancer's response to therapy. In this paper, we discuss the estimation of spatially varying blood flow veloc…
Enforcing boundary conditions for physics-informed neural operators
Niklas Göschel, Sebastian Götschel, Daniel Ruprecht
Machine-learning based methods like physics-informed neural networks and physics-informed neural operators are becoming increasingly adept at solving even complex systems of partia…
Space-time parallel scaling of Parareal with a physics-informed Fourier Neural Operator coarse propagator applied to the Black-Scholes equation
Abdul Qadir Ibrahim, Sebastian Götschel, Daniel Ruprecht
Iterative parallel-in-time algorithms like Parareal can extend scaling beyond the saturation of purely spatial parallelization when solving initial value problems. However, they re…
Improving Efficiency of Parallel Across the Method Spectral Deferred Corrections
Gayatri Čaklović, Thibaut Lunet, Sebastian Götschel +1
Parallel-across-the method time integration can provide small scale parallelism when solving initial value problems. Spectral deferred corrections (SDC) with a diagonal sweeper, wh…
Adaptive time step selection for Spectral Deferred Correction
Thomas Saupe, Sebastian Götschel, Thibaut Lunet +2
Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial…
Spectral deferred correction methods for second-order problems
Ikrom Akramov, Sebastian Götschel, Michael Minion +2
Spectral deferred corrections (SDC) are a class of iterative methods for the numerical solution of ordinary differential equations. SDC can be interpreted as a Picard iteration to…
Parareal with a physics-informed neural network as coarse propagator
Abdul Qadir Ibrahim, Sebastian Götschel, Daniel Ruprecht
Parallel-in-time algorithms provide an additional layer of concurrency for the numerical integration of models based on time-dependent differential equations. Methods like Parareal…
Impact of spatial coarsening on Parareal convergence for the linear advection equation
Judith Angel, Sebastian Götschel, Daniel Ruprecht
The Parareal parallel-in-time integration method often performs poorly when applied to hyperbolic partial differential equations. This effect is even more pronounced when the coars…