Marcin Krotkiewski

• Vembe, Johanne Elise; Krotkiewski, Marcin; Bjørgve, Magnar; Førre, Morten & Agueny, Hicham (2025). GaDE - GPU-acceleration of time-dependent Dirac equation for exascale. Computer Physics Communications. ISSN 0010-4655. 321. doi: 10.1016/j.cpc.2025.110015. Full text in Research Archive Show summary

  Modern heterogeneous high-performance computing (HPC) systems powered by advanced graphics processing unit (GPU) architectures enable accelerating computing with unprecedented performance and scalability. Here, we present a GPU-accelerated solver for the three-dimensional (3D) time-dependent Dirac Equation optimized for distributed HPC systems. The solver named GaDE is designed to simulate the electron dynamics in atoms induced by electromagnetic fields in the relativistic regime. It combines MPI with CUDA/HIP to target both NVIDIA and AMD GPU architectures. We discuss our implementation strategies in which the majority of the computations are carried out on GPUs, taking advantage of the GPU-aware MPI feature to optimize communication performance. We evaluate GaDE on the pre-exascale supercomputer LUMI, powered by AMD MI250X GPU and the HPE’s Slingshot interconnect. Single GPU performance on NVIDIA A100, GH200 and AMD MI250X shows comparable performance between A100 and MI250X in compute and memory bandwidth, with GH200 delivering higher performance. Weak scaling on LUMI demonstrates excellent scalability, achieving 85% parallel efficiency across 2048 GPUs, while strong scaling delivers a 16× speedup on 32 GPUs - 50% efficiency for a communication-intensive, time-dependent Dirac equation solver. These results demonstrate GaDE’s high scalability, making it suitable for exascale systems and enabling predictive simulations for ultra-intense laser experiments probing relativistic quantum effects.

• Hawkins, Christopher; Angheluta, Luiza; Krotkiewski, Marcin & Jamtveit, Bjørn (2016). Reynolds-number dependence of the longitudinal dispersion in turbulent pipe flow. Physical Review E (PRE). ISSN 2470-0045. 93(4). doi: 10.1103/PhysRevE.93.043119. Full text in Research Archive
• Jamtveit, Bjørn; Krotkiewski, Marcin; Kobchenko, Maya; Renard, Francois Marie Paul L & Angheluta, Luiza (2014). Pore-space distribution and transport properties of an andesitic intrusion. Earth and Planetary Science Letters. ISSN 0012-821X. 400, p. 123–129. doi: 10.1016/j.epsl.2014.05.042. Full text in Research Archive
• Krotkiewski, Marcin & Dabrowski, Marcin (2013). Efficient 3D stencil computations using CUDA. Parallel Computing. ISSN 0167-8191. 39(10), p. 533–548. doi: 10.1016/j.parco.2013.08.002. Full text in Research Archive
• Krotkiewski, Marcin; Ligaard, Ingeborg S; Lie, Knut-Andreas & Schmid, Daniel Walter (2011). On the importance of the Stokes-Brinkman equations for computing effective permeability in karst reservoirs. Communications in Computational Physics. ISSN 1815-2406. 10(5), p. 1315–1332. doi: 10.4208/cicp.290610.020211a. Full text in Research Archive Show summary

  Cavities and fractures significantly affect the flow paths in carbonate reservoirs and should be accurately accounted for in numerical models. Herein, we consider the problem of computing the effective permeability of rock samples based on high-resolution 3D CT scans containing millions of voxels. We use the Stokes-Brinkman equations in the entire domain, covering regions of free flow governed by the Stokes equations, porous Darcy flow, and transitions between them. The presence of different length scales and large (ten orders of magnitude) contrasts in permeability leads to highly ill-conditioned linear systems of equations, which are difficult to solve. To obtain a problem that is computationally tractable, we first analyze the relative importance of the Stokes and Darcy terms for a set of idealized 2D models. We find that, in terms of effective permeability, the Stokes-Brinkman equations are only applicable for a special parameter set where the effective free-flow permeability is less than four orders of magnitude different from the matrix permeability. All other cases can be accurately modeled with either the Stokes or the Darcy end-member flows, depending on if there do or do not exist percolating free-flow regions. The insights obtained are used to perform a direct computation of the effective permeability of a rock sample model with more than 8 million cells.

• Krotkiewski, Marcin & Dabrowski, Marcin (2010). Parallel symmetric sparse matrix-vector product on scalar multi-core CPUs. Parallel Computing. ISSN 0167-8191. 36(4), p. 181–198. doi: 10.1016/j.parco.2010.02.003. Full text in Research Archive
• Mazzini, Adriano; Nermoen, Anders; Krotkiewski, Marcin; Podladtchikov, Iouri; Planke, Sverre & Svensen, Henrik (2009). Strike-slip faulting as a trigger mechanism for overpressure release through piercement structures. Implications for the Lusi mud volcano, Indonesia. Marine and Petroleum Geology. ISSN 0264-8172. 26(9), p. 1751–1765. doi: 10.1016/j.marpetgeo.2009.03.001. Full text in Research Archive
• Schmid, Daniel Walter; Dabrowski, Marcin & Krotkiewski, Marcin (2008). Evolution of large amplitude 3D fold patterns: A FEM study. Physics of the Earth and Planetary Interiors. ISSN 0031-9201. 171(1-4), p. 400–408. doi: 10.1016/j.pepi.2008.08.007. Full text in Research Archive
• Krotkiewski, Marcin; Dabrowski, Marcin & Podladchikov, Yuri P. (2008). Fractional Steps methods for transient problems on commodity computer architectures. Physics of the Earth and Planetary Interiors. ISSN 0031-9201. 171(1-4), p. 122–136. doi: 10.1016/j.pepi.2008.08.008. Full text in Research Archive
• Dabrowski, Marcin; Krotkiewski, Marcin & Schmid, Daniel Walter (2008). MILAMIN: MATLAB-based finite element method solver for large problems. Geochemistry Geophysics Geosystems. 9. doi: 10.1029/2007GC001719. Full text in Research Archive

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• Krotkiewski, Marcin & Dabrowski, Marcin (2011). Efficient solution of Poisson's equation on modern GPUs using structured grids. Full text in Research Archive
• Krotkiewski, Marcin & Dabrowski, Marcin (2011). Efficient stencil computations and geometric multigrid on modern GPUs. Full text in Research Archive
• Krotkiewski, Marcin & Dabrowski, Marcin (2011). High-performance unstructured 3D modeling on modern clusters with thousands of CPUs. Full text in Research Archive
• Dabrowski, Marcin; Krotkiewski, Marcin & Schmid, Daniel Walter (2009). Unraveling the puzzle of numerical modeling. Full text in Research Archive
• Nermoen, Anders; Mazzini, Adriano; Podladchikov, Yuri; Gisler, Galen Ross; Krotkiewski, Marcin & Planke, Sverre [Show all 7 contributors for this article] (2008). A Multidisciplinary approach to mud volcano eruptions - Lusi. Full text in Research Archive
• Krotkiewski, Marcin; Dabrowski, Marcin & Schmid, Daniel Walter (2008). Towards TeraFLOP sparse matrix-vector product: Efficient 3D computations on unstructured grids. Full text in Research Archive
• Nermoen, Anders; Mazzini, Adriano; Gisler, Galen Ross; Krotkiewski, Marcin; Podladchikov, Yuri & Svensen, Henrik [Show all 8 contributors for this article] (2008). A multidiciplinary approach for mud volcano eruptions - Lusi. Full text in Research Archive Show summary

  We present a multi-diciplinary study of mud volcanism. The study is inspired by the formation of the Lusi mud volcano on East Java, Indonesia where scientists for the first time in history have been able to follow the birth of a mud volcano. It is a common observation that piercement structures form along strike-slip faults, so also Lusi. We present here experimental, numerical and analytical evidence for the existence of an apparent weakening mechanism in the shear zone that reduces the critical fluid pressure at which deformation occur. This mechanism may, given a fluid over-pressure at depth, explain why fluidization is localized within strike-slip faults.

• Dabrowski, Marcin; Krotkiewski, Marcin; Schmid, Daniel Walter & Podladtchikov, Iouri (2007). 3D Deformation Modeling. Full text in Research Archive
• Dabrowski, Marcin; Krotkiewski, Marcin & Schmid, Daniel Walter (2007). Fold morphologies and effective mechanical properties in 3D. Full text in Research Archive
• Schmid, Daniel Walter; Dabrowski, Marcin & Krotkiewski, Marcin (2007). Direct numerical modelling of effective material properties and deformation processes in 3D. Full text in Research Archive
• Schmid, Daniel Walter; Dabrowski, Marcin & Krotkiewski, Marcin (2007). Research results of the microstructures group of PGP. Full text in Research Archive
• Krotkiewski, Marcin & Podladtchikov, Iouri (2007). High-resolution 3D modeling of acoustic wave propagation using ADI methods. Full text in Research Archive
• Krotkiewski, Marcin; Dabrowski, Marcin & Podladtchikov, Iouri (2007). High-resolution 3D modeling of wave scattering by an oil reservoir. Full text in Research Archive
• Krotkiewski, Marcin; Dabrowski, Marcin; Schmid, Daniel Walter & Podladtchikov, Iouri (2007). High resolution 3D models: approaches, implementation, parallelization. Full text in Research Archive
• Krotkiewski, Marcin; Dabrowski, Marcin; Schmid, Daniel Walter & Podladtchikov, Iouri (2007). Efficient Large Scale 3D Modelling. Full text in Research Archive
• Krotkiewski, Marcin; Dabrowski, Marcin & Podladchikov, Yuri (2006). High performance geo-computing with commodity architecture. Full text in Research Archive
• Krotkiewski, Marcin & Podladchikov, Yuri (2006). Benchmarking of structured and unstructured mesh approaches in large material contrast Stokes problem. Full text in Research Archive
• Schmid, Daniel Walter; Dabrowski, Marcin & Krotkiewski, Marcin (2005). Supercomputing at PGP. Full text in Research Archive

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