Modern science is computational science. We use computers to simulate models of reality, thus exchanging the classic laboratory with a digital one. In some fields this is the most efficient way to test solutions, e.g. aerodynamics of aircrafts, market models and electric circuit simulations. In other fields it is the only way: when trying to understand the basic “rules” of our universe, numerical simulations provide the only window into many rich and unexplored phenomena in the world of elementary particle and nuclear physics.
The Computational Science section consists of the groups Computational Quantum Field Theory and Numerical Analysis.
In the Numerical Analysis group we don’t limit ourselves to one specific area of mathematics. Since we’re working to make problems “computational” for all mathematical areas, we require a basic understanding of every potentially helpful tool, be it discrete mathematics or functional analysis, differential geometry or optimization.
In the Computational Quantum Field Theory group we similarly make use of a wide variety of mathematical tools to develop state-of-the-art algorithms and efficient numerical techniques to perform simulations of elementary particle interactions on supercomputers.
The work and research of our section at IMADA covers a wide span of topics such as: testing candidate theories of new particle interactions; create novel numerical algorithms to simulate complex physical quantum models; make problems from physics, chemistry, biology and economics “computational”; and cooperate with industries from Volkswagen to nVidia.
Topics of research
- Algorithms with geometric constraints
- Computational modeling in molecular biology
- High Performance Computing algorithms (e.g. efficient coding and parallelization methods, GPGPU computing, infrastructure for efficient data analysis)
- Lattice Quantum Field Theory (first principle models for quantum physics)
- High-resolution shock simulations
- New models of particle physics (composite Higgs Boson, novel strong dynamics)
- Numerical linear algebra and model reduction
- Phase transitions (matter under extreme conditions, quantum phase transitions, renormalization group)
- Strong Nuclear Force (precision tests of Quantum Chromodynamics)
- The simulation of uncertain dynamic processes by stochastic differential equations and their optimal control
Funding and external collaborations/partners
Our external partners include: German Aerospace Center (DLR), Volkswagen Group Research, Newtec Engineering A/S, CERN, nVidia, Google, CRAY.
Our section has received funding from:
· (2019-2022) EU ITN ETN EuroPLEx “European network for Particle physics, Lattice field theory and Extreme computing”. Local coordinator: C. Pica. Grant: ~4.000.000 EUR
· (2018-2019) DDF project grant: The hadronic contribution to the muon anomaly beyond leading order. PI: M. Della Morte. Grant: 2.600.000 DKK
· (2013-2018) Lundbeckfonden fellow 2012. PI: C. Pica. Grant: 10.000.000 DKK
· (2016-2018) National e-infrastructure project “National Science App Store” funded DeIC (Danish e-Infratructure Cooperation) and DEFF (Denmark’s electronic research library). PI: C. Pica Grant: 1.400.000 DKK
· (2016-2021) Outreach project “Quantum Rascals” funded by the “A.P. Møller og Hustru Chastine Mc-Kinney Møllers” Foundation. Co-PI: C. Pica. Grant: 4.000.000 DKK.
· (2015-2017) Outreach project “SDU Supercomputing Challenge”, 2 editions. Funded by the “A.P. Møller og Hustru Chastine Mc-Kinney Møllers” Foundation, Industriens Fond, Knud Højgaards Fond, Tuborg Fondet and the Otto Bruuns Fond. PI: C. Pica. Total of grants: 3.725.000 DKK
· (2010-2015) Several European PRACE grants for HPC. PI: C. Pica. Total of Grants: 36.8M core*hour (value ~4.000.000 DKK)
· (2013-2019) Co-PI for the DG Centre of Excellence “CP3-Origins” (director Prof. F. Sannino). CO-PI: C.Pica. Grant: 40.000.000 DKK
· (2013) DeIC grant for HPC hardware. PI: C. Pica. Grant: 417.500 DKK
Members of group
Zimmermann, R. A matrix-algebraic algorithm for the Riemannian logarithm on the Stiefel manifold, SIAM Journal on Matrix Analysis and Applications, 38(2):322-342, 2017.
G. Aarts, F. Attanasio, B. Jäger, and D. Sexty, The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics, JHEP 09 (2016) 087, arXiv:1606.05561
M. Della Morte, B. Jäger, A. Jüttner, and H. Wittig, Towards a precise lattice determination of the leading hadronic contribution to (g−2)μ, JHEP 1203 (2012) 055, arXiv:1112.2894
C. Pica, F. Sannino, UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond, Phys.Rev. D83 (2011) 035013, arXiv:1011.5917 [hep-ph].
L. Del Debbio, A. Patella, C. Pica, Higher representations on the lattice: Numerical simulations. SU(2) with adjoint fermions, Phys.Rev. D81 (2010) 094503, arXiv:0805.2058 [hep-lat].
Bokanowski and K. Debrabant, Backward diﬀerentiation formula ﬁnite diﬀerence schemes for diﬀusion equations with an obstacle term, IMA J. Numer. Anal. 41, no. 2 (2021), pp. 900–934.
Debrabant, A. Kværnø, and N. C. Mattsson, Runge–Kutta Lawson schemes for stochastic diﬀerential equations, BIT 61, no. 2 (2021), pp. 381–409.
A. Schroll, J. Lorenz, Hyperbolic systems with relaxation: characterization of stiff well-posedness and asymptotic expansions, Journal of Mathematical Analysis and Applications 235, no. 2 (1999), pp. 497-532.
A. Schroll, A. Tveito, R. Winther, An L1-error bound for a semi-implicit difference scheme applied to a stiff system of conservation laws, SIAM Journal on Numerical Analysis 34, no. 3 (1997), pp. 1152-1166.
E.A. Abdi, H.J. Schroll, An Adaptive Viscosity E–scheme for Degenerate Conservation and Balance Laws, International Journal of Numerical Analysis and Modeling 17, no. 3 (2020), pp. 434-456.