Parallel Algorithms for High Performance Computing

Domain decompostion, parallel-in-time, waveform relaxation

Parallel in space and time

Partial or differential-algebraic equations are commonly solved in time domain by integration methods like the backward Euler scheme. Those methods subdivide the time axis into small time steps, replace for each step sequentially the derivatives by difference quotients and solve in each time step for all unknowns a nonlinear equation system. This may become very time-consuming or impossible for long time intervals and large systems of equations, in particular if the system stems from a coupled problem that consists of subproblems with different properties. Often each subproblem describes a different physical effect (multiphysics), for example electromagnetic fields and heat distribution. The subproblems are mutually connected by coupling conditions (connecting ‘inputs’ and ‘outputs’). Often, the various phenomena evolve on different time and spatial scales (multiscale). This given decomposition in subproblems can be exploited to parallelize the simulation (in space and time) and thus reduce the time to solution considerably.

We are working on parallel-in-time methods, e.g. co-simulation, waveform-relaxation or Parareal methods. They aim at solving problems more efficiently. The ideas are similar to iterative methods for linear equation systems.

Iryna Kulchytska-Ruchka ; Sebastian Schöps ; Michael Hinze. PASIROM: Parallel Simulation and Robust Optimization of Electro-Mechanical Energy Converters. In KoMSO Success Stories, Mathematics in Industry. Springer, 2020.

Idoia Cortes Garcia ; Iryna Kulchytska-Ruchka ; Sebastian Schöps (2020):
Efficient Simulation of Field/Circuit Coupled Systems with Parallelised Waveform Relaxation.
In: IEEE Transactions on Magnetics, 56, (2), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2019.2952695, ARXIV: 1909.08895. [Article]

Matthias Bolten ; Stephanie Friedhoff ; Jens Hahne ; Sebastian Schöps (2020):
Parallel-in-Time Simulation of an Electrical Machine using MGRIT.
In: Computing and Visualization in Science, ARXIV: 1912.03106. [Article]

Denys Bast ; Iryna Kulchytska-Ruchka ; Sebastian Schöps ; Oliver Rain (2020):
Accelerated Steady-State Torque Computation for Induction Machines using Parallel-In-Time Algorithms.
In: IEEE Transactions on Magnetics, 56, (2), pp. 1–9, ISSN: 0018-9464, DOI: 10.1109/TMAG.2019.2945510, ARXIV: 1902.08277. [Article]

Iryna Kulchytska-Ruchka ; Herbert De Gersem ; Sebastian Schöps (2019):
An efficient steady-state analysis of the eddy current problem using a parallel-in-time algorithm.
In: The Tenth International Conference on Computational Electromagnetics (CEM 2019). ISBN: 978-1-83953-066-1, DOI: 10.1049/cp.2019.0113, ARXIV: 1905.13076. [In Proceedings]

Stephanie Friedhoff ; Jens Hahne ; Iryna Kulchytska-Ruchka ; Sebastian Schöps (2019):
Exploring Parallel-in-Time Approaches for Eddy Current Problems.
In: Progress in Industrial Mathematics at ECMI 2018, volume 30 of The European Consortium for Mathematics in Industry, 373–379. Springer. ISBN: 9783030275495, DOI: 10.1007/978-3-030-27550-1_47, ARXIV: 1810.13263. [In Proceedings]

Sebastian Schöps ; Innocent Niyonzima ; Markus Clemens (2018):
Parallel-in-time Simulation of Eddy Current Problems using Parareal.
In: IEEE Transactions on Magnetics, 54, (3), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2017.2763090, ARXIV: 1706.05750. [Article]

Jennifer Susanne Dutiné ; Markus Clemens ; Sebastian Schöps (2018):
Survey on semi-explicit time integration of eddy current problems.
In: Scientific Computing in Electrical Engineering SCEE 2016, volume 28 of Mathematics in Industry. Springer. ISBN: 978-3-319-75537-3, DOI: 10.1007/978-3-319-75538-0_13. [In Proceedings]

Christian Richter ; Sebastian Schöps ; Markus Clemens (2017):
GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields.
In: IEEE Transactions on Magnetics, 53, (6), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2017.2662234, ARXIV: 1612.09447. [Article]

Melina Merkel ; Innocent Niyonzima ; Sebastian Schöps (2017):
ParaExp using Leapfrog as Integrator for High-Frequency Electromagnetic Simulations.
In: Radio Science, 52, (12), pp. 1558–1569, DOI: 10.1002/2017RS006357, ARXIV: 1705.08019. [Article]

Jennifer Susanne Dutiné ; Markus Clemens ; Sebastian Schöps (2017):
Explicit time integration of eddy current problems using a selective matrix update strategy.
In: COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 36, (5), pp. 1364–1371, DOI: 10.1108/COMPEL-02-2017-0100. [Article]

Christian Richter ; Sebastian Schöps ; Markus Clemens (2016):
GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields.
In: Proceedings of 17th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2016). ISBN: 978-1-5090-1032-5, DOI: 10.1109/CEFC.2016.7816199, URL: http://cefc2016.org, Digest. [In Proceedings]

Christian Richter ; Sebastian Schöps ; Markus Clemens (2016):
Multi-GPU Acceleration of Algebraic Multigrid Preconditioners.
In: Scientific Computing in Electrical Engineering SCEE 2014, number 23 in Mathematics in Industry, 83–90. Springer. ISBN: 978-3-319-30399-4, DOI: 10.1007/978-3-319-30399-4_9. [In Proceedings]

Christian Richter ; Sebastian Schöps ; Jennifer Susanne Dutiné ; Robert Schreiber ; Markus Clemens (2016):
Transient Simulation of Nonlinear Electro-Quasistatic Field Problems Accelerated by Multiple GPUs.
In: IEEE Transactions on Magnetics, ISSN: 0018-9464, DOI: 10.1109/TMAG.2015.2466602. [Article]

Innocent Niyonzima ; Markus Clemens ; Sebastian Schöps (2016):
Investigation of the Time Integration Methods on the Parareal Method for Field Computation of Eddy Currents Problems.
In: Proceedings of 17th Biennial IEEE Conference on Electromagnetic Field Computation (CEFC 2016). ISBN: 978-1-5090-1032-5, DOI: 10.1109/CEFC.2016.7816372, URL: http://cefc2016.org, Digest. [In Proceedings]

Melina Merkel ; Innocent Niyonzima ; Sebastian Schöps (2016):
An Application of ParaExp to Electromagnetic Waves.
In: 2016 URSI International Symposium on Electromagnetic Theory (EMTS), 121–124. IEEE. ISBN: 978-1-5090-2503-9, DOI: 10.1109/URSI-EMTS.2016.7571330, ARXIV: 1607.00368. [In Proceedings]

Christian Richter ; Sebastian Schöps ; Markus Clemens (2015):
Multi-GPU Acceleration of Algebraic Multigrid Preconditioners for Elliptic Field Problems.
In: IEEE Transactions on Magnetics, 51, (3), pp. 1–4, ISSN: 0018-9464, DOI: 10.1109/TMAG.2014.2357332. [Article]

Christian Richter ; Sebastian Schöps ; Markus Clemens. Jan Sykulski (editor) (2014):
GPU-Accelerated Mixed Precision Algebraic Multigrid Preconditioners for Discrete Elliptic Field Problems.
In: 9th IET International Conference on Computation in Electromagnetics (CEM 2014). IET. DOI: 10.1049/cp.2014.0185. [In Proceedings]

Christian Richter ; Sebastian Schöps ; Markus Clemens (2014):
GPU-Acceleration of Algebraic Multigrid Preconditioners for Discrete Elliptic Field Problems.
In: IEEE Transactions on Magnetics, 50, (2), pp. 461–464, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2283099. [Article]

Andreas Bartel ; Timo Hülsmann ; Jan Kühn ; Roland Pulch ; Sebastian Schöps (2014):
Influence of Measurement Errors on Transformer Inrush Currents Using Different Material Models.
In: IEEE Transactions on Magnetics, 50, (2), pp. 485–488, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2284072. [Article]

Eike Scholz ; Hanyu Ye ; Sebastian Schöps ; Markus Clemens (2013):
A Parallel FEM Matrix Assembly for Electro-Quasistatic Problems on GPGPU Systems.
In: IEEE Transactions on Magnetics, 49, (5), pp. 1801–1804, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2239624. [Article]

Christian Richter ; Sebastian Schöps ; Markus Clemens (2013):
GPU Acceleration of Finite Difference Schemes Used in Coupled Electromagnetic/Thermal Field Simulations.
In: IEEE Transactions on Magnetics, 49, (5), pp. 1649–1652, ISSN: 0018-9464, DOI: 10.1109/TMAG.2013.2238662. [Article]