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Item type:Publication, Access status: with files , Quantum-inspired tensor-network fractional-step method for incompressible flow in curvilinear coordinates(Elsevier, 2026-04-22); ; ; ; We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.Publicationtype: Journal Article48 12 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Efficient numerical methods for the Maxey-Riley-Gatignol equations with Basset history termThe Maxey-Riley-Gatignol equations (MRGE) describe the motion of a finite-sized, spherical particle in a fluid. Because of wake effects, the force acting on a particle depends on its past trajectory. This is modeled by an integral term in the MRGE, also called Basset force, that makes its numerical solution challenging and memory intensive. A recent approach proposed by Prasath et al. (2019) [9] exploits connections between the integral term and fractional derivatives to reformulate the MRGE as a time-dependent partial differential equation on a semi-infinite pseudo-space. They also propose a numerical algorithm based on polynomial expansions. This paper develops a numerical approach based on finite difference instead, by adopting techniques by Koleva (2005) [35] and Fazio and Jannelli (2014) [37] to cope with the issues of having an unbounded spatial domain. We compare convergence order and computational efficiency for particles of varying size and density of the polynomial expansion by Prasath et al., our finite difference schemes and a direct integrator for the MRGE based on multi-step methods proposed by Daitche (2013) [29]. While all methods achieve their theoretical convergence order for neutrally buoyant particles with zero initial relative velocity, they suffer from various degrees of order reduction if the initial relative velocity is non-zero or the particle has a different density than the fluid.Publicationtype: Journal Article72 59 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Comparing open-source DEM frameworks for simulations of common bulk processes(Elsevier, 2023-12-19); ; Scopus© Citations 1 13 62 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , An incremental singular value decomposition approach for large-scale spatially parallel & distributed but temporally serial data – applied to technical flowsThe article presents a strategy and its algorithm to compile a simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The framework addresses state-of-the-art PDE solvers for computational science and engineering applications. An important characteristic of such applications is that the spatial size of the data is often time-invariant and significantly exceeds the temporal size due to the large computational grid in 3D applications. Typical examples, which are also considered in this article, relate to results extracted from unsteady flow simulations. Herein, the flow data, which progresses over time, is frequently calculated spatially parallel based on domain decomposition strategies, which allow to parallelize the simulation on distributed memory machines following a Single Instruction Multiple Data (SIMD) concept. With a view to the memory-efficient reuse of (compressed) simulation results and their CPU time-saving, sufficiently accurate generation, the paper scrutinizes the efficiency of incremental/parallel SVD approaches for such simulation examples. To improve the computational efficiency, the introduction of a bunch matrix is proposed, which enables the aggregation of multiple time steps and SVD updates, and significantly increases the efficiency. The suggested strategy is verified and validated by simple 2D laminar single-phase flows and subsequently applied to more complex 2D and 3D turbulent two-phase flows. Emphasis is given to (a) the accuracy of SVD-based reconstruction, (b) the physical realizability of the reconstructed quantities, (c) the independence of domain partitioning, (d) an efficient snapshot bunching, and (e) related implementation aspects. In addition, the influence of lower and (adaptive) upper rank thresholds on the effort and accuracy is evaluated. A final application renders the practical benefits of the approach and refers to a merchant ship in head waves at Re = 1.4×107 and Fn = 0.26. The simulation involves 2880 processor cores and the related full-rank snapshot matrix has (108×104) entries. With a numerical overhead of O(10%), this snapshot matrix can be incrementally generated and compressed by O(95%). The compression is accompanied by only small errors in the integral force and local wave elevation of O(10−2%). This qualifies the method for an efficient subsequent data processing.Publicationtype: Journal Article31 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A GPU-parallelized interpolation-based fast multipole method for the relativistic space-charge field calculationThe fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for the computation of the relativistic space-charge field. Different to the quasi-electrostatic model, our FMM is formulated in the lab-frame and can be applied without the assistance of the Lorentz transformation. In particular, we derive a modified admissibility condition which can effectively control the interpolation error of the proposed FMM. The algorithms and their GPU parallelization are discussed in detail. A package containing serial and GPU-parallelized solvers is implemented in the Julia programming language. The GPU-parallelized solver can reach a speedup of more than a hundred compared to the execution on a single CPU core.Publicationtype: Journal Article47 90 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Relativistic space-charge field calculation by interpolation-based treecodeSpace-charge effects are of great importance in particle accelerator physics. In the computational modeling, tree-based methods are increasingly used because of their effectiveness in handling non-uniform particle distributions and/or complex geometries. However, they are often formulated using an electrostatic force which is only a good approximation for low energy particle beams. For high energy, i.e., relativistic particle beams, the relativistic interaction kernel may need to be considered and the conventional treecode fails in this scenario. In this work, we formulate a treecode based on Lagrangian interpolation for computing the relativistic space-charge field. Two approaches are introduced to control the interpolation error. In the first approach, a modified admissibility condition is proposed for which the treecode can be used directly in the lab-frame. The second approach is based on the transformation of the particle beam to the rest-frame where the conventional admissibility condition can be used. Numerical simulation results using both methods will be compared and discussed.Publicationtype: Journal Article30 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Performance of the BGSDC integrator for computing fast ion trajectories in nuclear fusion reactorsModelling neutral beam injection (NBI) in fusion reactors requires computing the trajectories of large ensembles of particles. Slowing down times of up to one second combined with nanosecond time steps make these simulations computationally very costly. This paper explores the performance of BGSDC, a new numerical time stepping method, for tracking ions generated by NBI in the DIII-D and JET reactors. BGSDC is a high-order generalisation of the Boris method, combining it with spectral deferred corrections and the Generalized Minimal Residual method GMRES. Without collision modelling, where numerical drift can be quantified accurately, we find that BGSDC can deliver higher quality particle distributions than the standard Boris integrator at comparable cost or comparable distributions at lower cost. With collision models, quantifying accuracy is difficult but we show that BGSDC produces stable distributions at larger time steps than Boris.Publicationtype: Journal ArticleScopus© Citations 3 175 344 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , i-PI 2.0 : a universal force engine for advanced molecular simulationsProgress in the atomic-scale modelling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born-Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives.Publicationtype: Journal Article214 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Highly accurate quadrature-based Scharfetter–Gummel schemes for charge transport in degenerate semiconductorsWe introduce a family of two point flux expressions for charge carrier transport described by drift–diffusion problems in degenerate semiconductors with non-Boltzmann statistics which can be used in Voronoï finite volume discretizations. In the case of Boltzmann statistics, Scharfetter and Gummel derived such fluxes by solving a linear two point boundary value problem yielding a closed form expression for the flux. Instead, a generalization of this approach to the nonlinear case yields a flux value given implicitly as the solution of a nonlinear integral equation. We examine the solution of this integral equation numerically via quadrature rules to approximate the integral as well as Newton's method to solve the resulting approximate integral equation. This approach results into a family of quadrature-based Scharfetter–Gummel flux approximations. We focus on four quadrature rules and compare the resulting schemes with respect to execution time and accuracy. A convergence study reveals that the solution of the approximate integral equation converges exponentially in terms of the number of quadrature points. With very few integration nodes they are already more accurate than a state-of-the-art reference flux, especially in the challenging physical scenario of high nonlinear diffusion. Finally, we show that thermodynamic consistency is practically guaranteed.Publicationtype: Journal Article230