TUHH Open Research (TORE)https://tore.tuhh.deTORE captures, stores, indexes, preserves, and distributes digital research material.Thu, 21 Oct 2021 08:24:53 GMT2021-10-21T08:24:53Z50381- Transparent boundary conditions for time-dependent problemshttp://hdl.handle.net/11420/7065Title: Transparent boundary conditions for time-dependent problems
Authors: Ruprecht, Daniel; Schädle, Achim; Schmidt, Frank; Zschiedrich, Lin
Abstract: A new approach to derive transparent boundary conditions (TBCs) for dispersive wave, Schrödinger, heat, and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physically reasonable and unreasonable solutions by the location of the singularities of the Laplace transform of the exterior solution. Here the Laplace transform is taken with respect to a generalized radial variable. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients. © 2008 Society for Industrial and Applied Mathematics.
Mon, 17 Aug 2020 09:10:23 GMThttp://hdl.handle.net/11420/70652020-08-17T09:10:23Z
- Performance of parallel-in-time integration for Rayleigh Bénard convectionhttp://hdl.handle.net/11420/7761Title: Performance of parallel-in-time integration for Rayleigh Bénard convection
Authors: Clarke, Andrew T.; Davies, Christopher J.; Ruprecht, Daniel; Tobias, Steven M.; Oishi, Jeffrey S.
Abstract: © 2020, The Author(s). Rayleigh–Bénard convection (RBC) is a fundamental problem of fluid dynamics, with many applications to geophysical, astrophysical, and industrial flows. Understanding RBC at parameter regimes of interest requires complex physical or numerical experiments. Numerical simulations require large amounts of computational resources; in order to more efficiently use the large numbers of processors now available in large high performance computing clusters, novel parallelisation strategies are required. To this end, we investigate the performance of the parallel-in-time algorithm Parareal when used in numerical simulations of RBC. We present the first parallel-in-time speedups for RBC simulations at finite Prandtl number. We also investigate the problem of convergence of Parareal with respect to statistical numerical quantities, such as the Nusselt number, and discuss the importance of reliable online stopping criteria in these cases.
Wed, 04 Nov 2020 11:12:03 GMThttp://hdl.handle.net/11420/77612020-11-04T11:12:03Z
- Parallel-in-time integration of kinematic dynamoshttp://hdl.handle.net/11420/5733Title: Parallel-in-time integration of kinematic dynamos
Authors: Clarke, Andrew T.; Davies, Christopher J.; Ruprecht, Daniel; Tobias, Steven M.
Abstract: The precise mechanisms responsible for the natural dynamos in the Earth and Sun are still not fully understood. Numerical simulations of natural dynamos are extremely computationally intensive, and are carried out in parameter regimes many orders of magnitude away from real conditions. Parallelization in space is a common strategy to speed up simulations on high performance computers, but eventually hits a scaling limit. Additional directions of parallelization are desirable to utilise the high number of processor cores now available. Parallel-in-time methods can deliver speed up in addition to that offered by spatial partitioning but have not yet been applied to dynamo simulations. This paper investigates the feasibility of using the parallel-in-time algorithm Parareal to speed up initial value problem simulations of the kinematic dynamo, using the open source Dedalus spectral solver. Both the time independent Roberts and time dependent Galloway-Proctor 2.5D dynamos are investigated over a range of magnetic Reynolds numbers. Speed ups beyond those possible from spatial parallelization are found in both cases. Results for the Galloway-Proctor flow are promising, with Parareal efficiency found to be close to 0.3. Roberts flow results are less efficient, but Parareal still shows some speed up over spatial parallelization alone. Parallel in space and time speed ups of ∼300 were found for 1600 cores for the Galloway-Proctor flow, with total parallel efficiency of ∼0.16.
Wed, 15 Apr 2020 08:22:30 GMThttp://hdl.handle.net/11420/57332020-04-15T08:22:30Z
- Shared memory pipelined pararealhttp://hdl.handle.net/11420/7070Title: Shared memory pipelined parareal
Authors: Ruprecht, Daniel
Abstract: For the parallel-in-time integration method Parareal, pipelining can be used to hide some of the cost of the serial correction step and improve its efficiency. The paper introduces a basic OpenMP implementation of pipelined Parareal and compares it to a standard MPI-based variant. Both versions yield almost identical runtimes, but, depending on the compiler, the OpenMP variant consumes about 7% less energy and has a significantly smaller memory footprint. However, its higher implementation complexity might make it difficult to use in legacy codes and in combination with spatial parallelisation.
Mon, 17 Aug 2020 10:45:12 GMThttp://hdl.handle.net/11420/70702020-08-17T10:45:12Z
- Parareal with a learned coarse model for robotic manipulationhttp://hdl.handle.net/11420/7444Title: Parareal with a learned coarse model for robotic manipulation
Authors: Agboh, Wisdom; Grainger, Oliver; Ruprecht, Daniel; Dogar, Mehmet R,
Abstract: A key component of many robotics model-based planning and control algorithms is physics predictions, that is, forecasting a sequence of states given an initial state and a sequence of controls. This process is slow and a major computational bottleneck for robotics planning algorithms. Parallel-in-time integration methods can help to leverage parallel computing to accelerate physics predictions and thus planning. The Parareal algorithm iterates between a coarse serial integrator and a fine parallel integrator. A key challenge is to devise a coarse model that is computationally cheap but accurate enough for Parareal to converge quickly. Here, we investigate the use of a deep neural network physics model as a coarse model for Parareal in the context of robotic manipulation. In simulated experiments using the physics engine Mujoco as fine propagator we show that the learned coarse model leads to faster Parareal convergence than a coarse physics-based model. We further show that the learned coarse model allows to apply Parareal to scenarios with multiple objects, where the physics-based coarse model is not applicable. Finally, we conduct experiments on a real robot and show that Parareal predictions are close to real-world physics predictions for robotic pushing of multiple objects. Videos are at https://youtu.be/wCh2o1rf-gA.
Thu, 01 Oct 2020 11:37:00 GMThttp://hdl.handle.net/11420/74442020-10-01T11:37:00Z
- Thermodynamic modelling of a stratified charge spark ignition enginehttp://hdl.handle.net/11420/7072Title: Thermodynamic modelling of a stratified charge spark ignition engine
Authors: Smith, Jamie Karl; Roberts, Phil; Kountouriotis, Alexandros; Richardson, David; Aleiferis, Pavlos; Ruprecht, Daniel
Abstract: © IMechE 2018. Combustion of a charge with spatially and temporally varying equivalence ratio in a spark ignition engine was modelled using the Leeds University Spark Ignition Engine quasi-dimensional thermodynamic code. New sub-models have been integrated into Leeds University Spark Ignition Engine that simulate the effect of burnt gas expansion and turbulent mixing on an initial equivalence ratio distribution. Realistic distribution functions were used to model the radially varying equivalence ratio. The new stratified fuel model was validated against experimental data, showing reasonable agreement for both the pressure trace and percentage heat released. Including the effect of turbulent mixing was found to be important to reproduce the trend in the differences between the stratified and homogeneous simulations.
Mon, 17 Aug 2020 12:02:27 GMThttp://hdl.handle.net/11420/70722020-08-17T12:02:27Z
- Performance of the BGSDC integrator for computing fast ion trajectories in nuclear fusion reactorshttp://hdl.handle.net/11420/9256Title: Performance of the BGSDC integrator for computing fast ion trajectories in nuclear fusion reactors
Authors: Tretiak, Krasymyr; Buchanan, James; Akers, Rob; Ruprecht, Daniel
Abstract: Modelling 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.
Wed, 14 Apr 2021 07:57:29 GMThttp://hdl.handle.net/11420/92562021-04-14T07:57:29Z
- Toward transient finite element simulation of thermal deformation of machine tools in real-timehttp://hdl.handle.net/11420/10503Title: Toward transient finite element simulation of thermal deformation of machine tools in real-time
Authors: Naumann, Andreas; Ruprecht, Daniel; Wensch, Jörg
Abstract: Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FE models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit–explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand.
Wed, 13 Oct 2021 06:52:09 GMThttp://hdl.handle.net/11420/105032021-10-13T06:52:09Z
- A multi-level spectral deferred correction methodhttp://hdl.handle.net/11420/10527Title: A multi-level spectral deferred correction method
Authors: Speck, Robert; Ruprecht, Daniel; Emmett, Matthew; Minion, Michael; Bolten, Matthias; Krause, Rolf
Abstract: The spectral deferred correction (SDC) method is an iterative scheme for computing a higher-order collocation solution to an ODE by performing a series of correction sweeps using a low-order timestepping method. This paper examines a variation of SDC for the temporal integration of PDEs called multi-level spectral deferred corrections (MLSDC), where sweeps are performed on a hierarchy of levels and an FAS correction term, as in nonlinear multigrid methods, couples solutions on different levels. Three different strategies to reduce the computational cost of correction sweeps on the coarser levels are examined: reducing the degrees of freedom, reducing the order of the spatial discretization, and reducing the accuracy when solving linear systems arising in implicit temporal integration. Several numerical examples demonstrate the effect of multi-level coarsening on the convergence and cost of SDC integration. In particular, MLSDC can provide significant savings in compute time compared to SDC for a three-dimensional problem.
Thu, 14 Oct 2021 10:28:52 GMThttp://hdl.handle.net/11420/105272021-10-14T10:28:52Z
- Toward fault-tolerant parallel-in-time integration with PFASSThttp://hdl.handle.net/11420/10520Title: Toward fault-tolerant parallel-in-time integration with PFASST
Authors: Speck, Robert; Ruprecht, Daniel
Abstract: We introduce and analyze different strategies for the parallel-in-time integration method PFASST to recover from hard faults and subsequent data loss. Since PFASST stores solutions at multiple time steps on different processors, information from adjacent steps can be used to recover after a processor has failed. PFASST's multi-level hierarchy allows to use the coarse level for correcting the reconstructed solution, which can help to minimize overhead. A theoretical model is devised linking overhead to the number of additional PFASST iterations required for convergence after a fault. The potential efficiency of different strategies is assessed in terms of required additional iterations for examples of diffusive and advective type.
Thu, 14 Oct 2021 09:54:52 GMThttp://hdl.handle.net/11420/105202021-10-14T09:54:52Z
- Spectral deferred corrections with fast-wave slow-wave splittinghttp://hdl.handle.net/11420/10521Title: Spectral deferred corrections with fast-wave slow-wave splitting
Authors: Ruprecht, Daniel; Speck, Robert
Abstract: The paper investigates a variant of semi-implicit spectral deferred corrections (SISDC) in which the stiff, fast dynamics correspond to fast propagating waves ("fast-wave slow-wave problem"). We show that for a scalar test problem with two imaginary eigenvalues i λfₐst, i λslₒw, having Δ t (| λfₐst | + | λslₒw | ) < 1 is sufficient for the fast-wave slow-wave SDC (FWSW-SDC) iteration to converge and that in the limit of infinitely fast waves the convergence rate of the non-split version is retained. Stability function and discrete dispersion relation are derived and show that the method is stable for essentially arbitrary fast-wave CFL numbers as long as the slow dynamics are resolved. The method causes little numerical diffusion and its semi-discrete phase speed is accurate also for large wave number modes. Performance is studied for an acoustic-advection problem and for the linearised Boussinesq equations, describing compressible, stratified flow. FWSW-SDC is compared to a diagonally implicit Runge-Kutta (DIRK) and IMEX Runge-Kutta (IMEX) method and found to be competitive in terms of both accuracy and cost.
Thu, 14 Oct 2021 09:58:04 GMThttp://hdl.handle.net/11420/105212021-10-14T09:58:04Z
- A high-order Boris integratorhttp://hdl.handle.net/11420/10522Title: A high-order Boris integrator
Authors: Winkel, Mathias; Speck, Robert; Ruprecht, Daniel
Abstract: This work introduces the high-order Boris-SDC method for integrating the equations of motion for electrically charged particles in an electric and magnetic field. Boris-SDC relies on a combination of the Boris-integrator with spectral deferred corrections (SDC). SDC can be considered as preconditioned Picard iteration to compute the stages of a collocation method. In this interpretation, inverting the preconditioner corresponds to a sweep with a low-order method. In Boris-SDC, the Boris method, a second-order Lorentz force integrator based on velocity-Verlet, is used as a sweeper/preconditioner. The presented method provides a generic way to extend the classical Boris integrator, which is widely used in essentially all particle-based plasma physics simulations involving magnetic fields, to a high-order method. Stability, convergence order and conservation properties of the method are demonstrated for different simulation setups. Boris-SDC reproduces the expected high order of convergence for a single particle and for the center-of-mass of a particle cloud in a Penning trap and shows good long-term energy stability.
Thu, 14 Oct 2021 10:01:44 GMThttp://hdl.handle.net/11420/105222021-10-14T10:01:44Z
- Verification of cardiac mechanics software: Benchmark problems and solutions for testing active and passivematerial behaviourhttp://hdl.handle.net/11420/10525Title: Verification of cardiac mechanics software: Benchmark problems and solutions for testing active and passivematerial behaviour
Authors: Land, Sander; Gurev, Viatcheslav; Arens, Sander; Augustin, Christoph M.; Baron, Lukas; Blake, Robert; Bradley, Chris; Castro, Sebastian; Crozier, Andrew; Favino, Marco; Fastl, Thomas E.; Fritz, Thomas; Gao, Hao; Gizzi, Alessio; Griffith, Boyce E.; Hurtado, Daniel E.; Krause, Rolf; Luo, Xiaoyu; Nash, Martyn P.; Pezzuto, Simone; Plank, Gernot; Rossi, Simone; Ruprecht, Daniel; Seemann, Gunnar; Smith, Nicolas P.; Sundnes, Joakim; Jeremy Rice, J.; Trayanova, Natalia; Wang, Dafang; Wang, Zhinuo Jenny; Niederer, Steven A.
Abstract: Models of cardiac mechanics are increasingly used to investigate cardiac physiology. These models are characterized by a high level of complexity, including the particular anisotropic material properties of biological tissue and the actively contracting material. A large number of independent simulation codes have been developed, but a consistent way of verifying the accuracy and replicability of simulations is lacking. To aid in the verification of current and future cardiac mechanics solvers, this study provides three benchmark problems for cardiac mechanics. These benchmark problems test the ability to accurately simulate pressure-Type forces that depend on the deformed objects geometry, anisotropic and spatially varying material properties similar to those seen in the left ventricle and active contractile forces. The benchmark was solved by 11 different groups to generate consensus solutions, with typical differences in higher-resolution solutions at approximately 0.5%, and consistent results between linear, quadratic and cubic finite elements as well as different approaches to simulating incompressible materials. Online tools and solutions are made available to allow these tests to be effectively used in verification of future cardiac mechanics software.
Thu, 14 Oct 2021 10:18:24 GMThttp://hdl.handle.net/11420/105252021-10-14T10:18:24Z
- Modulation of internal gravity waves in a multiscale model for deep convection on mesoscaleshttp://hdl.handle.net/11420/10530Title: Modulation of internal gravity waves in a multiscale model for deep convection on mesoscales
Authors: Ruprecht, Daniel; Klein, Rupert; Majda, Andrew J.
Abstract: Starting from the conservation laws for mass, momentum, and energy together with a three-species bulk microphysics model, a model for the interaction of internal gravity waves and deep convective hot towers is derived using multiscale asymptotic techniques. From the leading-order equations, a closed model for the large-scale flow is obtained analytically by applying horizontal averages conditioned on the small-scale hot towers. No closure approximations are required besides adopting the asymptotic limit regime on which the analysis is based. The resulting model is an extension of the anelastic equations linearized about a constant background flow. Moist processes enter through the area fraction of saturated regions and through two additional dynamic equations describing the coupled evolution of the conditionally averaged small-scale vertical velocity and buoyancy.Atwo-way coupling between the large-scale dynamics and these small-scale quantities is obtained: moisture reduces the effective stability for the large-scale flow, and microscale up-and downdrafts define a large-scale averaged potential temperature source term. In turn, large-scale vertical velocities induce small-scale potential temperature fluctuations due to the discrepancy in effective stability between saturated and nonsaturated regions. The dispersion relation and group velocity of the system are analyzed and moisture is found to have several effects: (i) it reduces vertical energy transport by waves, (ii) it increases vertical wavenumbers but decreases the slope at which wave packets travel, (iii) it introduces a new lower horizontal cutoff wavenumber in addition to the well-known high wavenumber cutoff, and (iv)moisture can cause critical layers. Numerical examples reveal the effects of moisture on steady-state and time-dependent mountain waves in the present hot-tower regime. © 2010 American Meteorological Society.
Thu, 14 Oct 2021 10:36:14 GMThttp://hdl.handle.net/11420/105302021-10-14T10:36:14Z
- Time parallel gravitational collapse simulationhttp://hdl.handle.net/11420/10519Title: Time parallel gravitational collapse simulation
Authors: Kreienbuehl, Andreas; Benedusi, Pietro; Ruprecht, Daniel; Krause, Rolf
Abstract: This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in time, a tailored load balancing scheme is proposed and compared to load balancing based on number of time steps alone. The performance of Parareal is studied for both the sub-critical and black hole case; our experiments show that Parareal generates substantial speedup and, in the super-critical regime, can reproduce Choptuik's black hole mass scaling law.
Thu, 14 Oct 2021 09:51:56 GMThttp://hdl.handle.net/11420/105192021-10-14T09:51:56Z
- Explicit Parallel-in-time Integration of a Linear Acoustic-Advection Systemhttp://hdl.handle.net/11420/10529Title: Explicit Parallel-in-time Integration of a Linear Acoustic-Advection System
Authors: Ruprecht, Daniel; Krause, Rolf
Abstract: The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather prediction (NWP), is addressed. Parallel-in-time schemes are a possible way to increase, on the algorithmic level, the amount of parallelism, a requirement arising from the rapidly growing number of CPUs in high performance computer systems. A recently introduced modification of the "parallel implicit time-integration algorithm" could successfully solve hyperbolic problems arising in structural dynamics. It has later been cast into the framework of Parareal. The present paper adapts this modified Parareal and employs it for the solution of a hyperbolic flow problem, where the initial value problem solved in parallel arises from the spatial discretization of a partial differential equation by a finite difference method. It is demonstrated that the modified Parareal is stable and can produce reasonably accurate solutions while allowing for a noticeable reduction of the time-to-solution. The implementation relies on integration schemes already widely used in NWP (RK-3, partially split forward Euler, forward-backward). It is demonstrated that using an explicit partially split scheme for the coarse integrator allows to avoid the use of an implicit scheme while still achieving speedup.
Thu, 14 Oct 2021 10:34:50 GMThttp://hdl.handle.net/11420/105292021-10-14T10:34:50Z
- A stencil-based implementation of Parareal in the C++ domain specific embedded language STELLAhttp://hdl.handle.net/11420/10523Title: A stencil-based implementation of Parareal in the C++ domain specific embedded language STELLA
Authors: Arteaga, Andrea; Ruprecht, Daniel; Krause, Rolf
Abstract: In view of the rapid rise of the number of cores in modern supercomputers, time-parallel methods that introduce concurrency along the temporal axis are becoming increasingly popular. For the solution of time-dependent partial differential equations, these methods can add another direction for concurrency on top of spatial parallelization. The paper presents an implementation of the time-parallel Parareal method in a C++ domain specific language for stencil computations (STELLA). STELLA provides both an OpenMP and a CUDA backend for a shared memory parallelization, using the CPU or GPU inside a node for the spatial stencils. Here, we intertwine this node-wise spatial parallelism with the time-parallel Parareal. This is done by adding an MPI-based implementation of Parareal, which allows us to parallelize in time across nodes. The performance of Parareal with both backends is analyzed in terms of speedup, parallel efficiency and energy-to-solution for an advection-diffusion problem with a time-dependent diffusion coefficient.
Thu, 14 Oct 2021 10:05:43 GMThttp://hdl.handle.net/11420/105232021-10-14T10:05:43Z
- A model for nonlinear interactions of internal gravity waves with saturated regionshttp://hdl.handle.net/11420/10531Title: A model for nonlinear interactions of internal gravity waves with saturated regions
Authors: Ruprecht, Daniel; Klein, Rupert
Abstract: A model for interactions between non-hydrostatic gravity waves and deep convective narrow hot towers is presented. The starting point of the derivation are the conservation laws for mass, momentum and energy for compressible flows combined with a bulk micro-physic model. Using multiscale asymptotics, a set of leading order equations is extracted, valid for the specific scales of the investigated regime. These are a timescale of 100 s, a horizontal and vertical lengthscale of 10 km for the wave dynamics plus a second horizontal lengthscale of 1 km for the narrow hot towers. Because of the comparatively short horizontal scales, Coriolis effects are negligible in this regime. The leading order equations are then closed by applying conditional averages over the hot tower lengthscale, leading to a closed model for the wave-scale that retains the net effects of the smaller scale dynamics. By assuming a systematically small saturation deficit in the ansatz, the small vertical displacements arising in this regime suffice to induce leading order changes of the saturated area fraction. The latter is the essential parameter in the model arising from the micro-physics.
Thu, 14 Oct 2021 10:37:39 GMThttp://hdl.handle.net/11420/105312021-10-14T10:37:39Z
- An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fieldshttp://hdl.handle.net/11420/10487Title: An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields
Authors: Tretiak, Krasymyr; Ruprecht, Daniel
Abstract: The Lorentz equations describe the motion of electrically charged particles in electric and magnetic fields and are used widely in plasma physics. The most popular numerical algorithm for solving them is the Boris method, a variant of the St\"ormer-Verlet algorithm. Boris' method is phase space volume conserving and simulated particles typically remain near the correct trajectory. However, it is only second order accurate. Therefore, in scenarios where it is not enough to know that a particle stays on the right trajectory but one needs to know where on the trajectory the particle is at a given time, Boris method requires very small time steps to deliver accurate phase information, making it computationally expensive. We derive an improved version of the high-order Boris spectral deferred correction algorithm (Boris-SDC) by adopting a convergence acceleration strategy for second order problems based on the Generalised Minimum Residual GMRES) method. Our new algorithm is easy to implement as it still relies on the standard Boris method. Like Boris-SDC it can deliver arbitrary order of accuracy through simple changes of runtime parameter but possesses better long-term energy stability. We demonstrate for
two examples, a magnetic mirror trap and the Solev'ev equilibrium, that the new method can deliver better accuracy at lower computational cost compared to the standard Boris method. While our examples are motivated by tracking ions in the magnetic field of a nuclear fusion reactor, the introduced algorithm can potentially deliver similar improvements in efficiency for other applications.
Wed, 13 Oct 2021 06:36:48 GMThttp://hdl.handle.net/11420/104872021-10-13T06:36:48Z
- Inexact spectral deferred correctionshttp://hdl.handle.net/11420/10537Title: Inexact spectral deferred corrections
Authors: Speck, Robert; Ruprecht, Daniel; Minion, Michael; Emmett, Matthew; Krause, Rolf
Fri, 15 Oct 2021 07:30:25 GMThttp://hdl.handle.net/11420/105372021-10-15T07:30:25Z
- A comparison of EGR correction factor models based on SI engine datahttp://hdl.handle.net/11420/10502Title: A comparison of EGR correction factor models based on SI engine data
Authors: Smith, Jamie Karl; Ruprecht, Daniel; Roberts, Philip John; Kountouriotis, Alexandros; Aleiferis, Pavlos; Richardson, David
Abstract: The article compares the accuracy of different exhaust gas recirculation (EGR) correction factor models under engine conditions. The effect of EGR on the laminar burning velocity of a EURO VI E10 specification gasoline (10% Ethanol content by volume) has been back calculated from engine pressure trace data, using the Leeds University Spark Ignition Engine Data Analysis (LUSIEDA) reverse thermodynamic code. The engine pressure data ranges from 5% to 25% EGR (by mass) with the running conditions, such as spark advance and pressure at intake valve closure, changed to maintain a constant engine load of 0.79 MPa gross mean effective pressure (GMEP). Based on the experimental data, a correlation is suggested on how the laminar burning velocity reduces with increasing EGR mass fraction. This correlation, together with existing models, was then implemented into the quasi-dimensional Leeds University Spark Ignition Engine (LUSIE) predictive engine code and resulting predictions are compared against measurements. It was found that the new correlation is in good agreement with experimental data for a diluent range of 5%-25%, providing the best fit for both engine loads investigated, whereas existing models tend to overpredict the reduction of burning velocity due to EGR.
Wed, 13 Oct 2021 06:45:51 GMThttp://hdl.handle.net/11420/105022021-10-13T06:45:51Z
- Wave propagation characteristics of Pararealhttp://hdl.handle.net/11420/10504Title: Wave propagation characteristics of Parareal
Authors: Ruprecht, Daniel
Abstract: The paper derives and analyses the (semi-)discrete dispersion relation of the Parareal parallel-in-time integration method. It investigates Parareal’s wave propagation characteristics with the aim to better understand what causes the well documented stability problems for hyperbolic equations. The analysis shows that the instability is caused by convergence of the amplification factor to the exact value from above for medium to high wave numbers. Phase errors in the coarse propagator are identified as the culprit, which suggests that specifically tailored coarse level methods could provide a remedy.
Wed, 13 Oct 2021 06:58:30 GMThttp://hdl.handle.net/11420/105042021-10-13T06:58:30Z
- Convergence of parareal for the Navier-Stokes equations depending on the Reynolds numberhttp://hdl.handle.net/11420/10538Title: Convergence of parareal for the Navier-Stokes equations depending on the Reynolds number
Authors: Steiner, Johannes; Ruprecht, Daniel; Speck, Robert; Krause, Rolf
Abstract: The paper presents first a linear stability analysis for the time-parallel Parareal method, using an IMEX Euler as coarse and a Runge-Kutta-3 method as fine propagator, confirming that dominant imaginary eigenvalues negatively affect Parareal’s convergence. This suggests that when Parareal is applied to the nonlinear Navier-Stokes equations, problems for small viscosities could arise. Numerical results for a driven cavity benchmark are presented, confirming that Parareal’s convergence can indeed deteriorate as viscosity decreases and the flow becomes increasingly dominated by convection. The effect is found to strongly depend on the spatial resolution.
Fri, 15 Oct 2021 07:43:25 GMThttp://hdl.handle.net/11420/105382021-10-15T07:43:25Z
- EWE : toward electro-mechanical cardiac simulations with MOOSEhttp://hdl.handle.net/11420/10533Title: EWE : toward electro-mechanical cardiac simulations with MOOSE
Authors: Ruprecht, Daniel; Winkel, Mathias; Krause, Rolf
Fri, 15 Oct 2021 06:43:38 GMThttp://hdl.handle.net/11420/105332021-10-15T06:43:38Z
- Does Boris-SDC conserve phase space volume?http://hdl.handle.net/11420/10534Title: Does Boris-SDC conserve phase space volume?
Authors: Winkel, Mathias; Speck, Robert; Ruprecht, Daniel
Fri, 15 Oct 2021 06:51:16 GMThttp://hdl.handle.net/11420/105342021-10-15T06:51:16Z
- Optimal parameter choice for the pole conditionhttp://hdl.handle.net/11420/10536Title: Optimal parameter choice for the pole condition
Authors: Ruprecht, Daniel; Schädle, Achim; Schmidt, Frank
Fri, 15 Oct 2021 07:13:18 GMThttp://hdl.handle.net/11420/105362021-10-15T07:13:18Z
- Convergence of Parareal with spatial coarseninghttp://hdl.handle.net/11420/10535Title: Convergence of Parareal with spatial coarsening
Authors: Ruprecht, Daniel
Fri, 15 Oct 2021 06:58:21 GMThttp://hdl.handle.net/11420/105352021-10-15T06:58:21Z
- Parallel-in-space-and-time simulation of the three-dimensional, unsteady Navier-Stokes equations for incompressible flowhttp://hdl.handle.net/11420/10540Title: Parallel-in-space-and-time simulation of the three-dimensional, unsteady Navier-Stokes equations for incompressible flow
Authors: Croce, Roberto; Ruprecht, Daniel; Krause, Rolf
Fri, 15 Oct 2021 08:11:13 GMThttp://hdl.handle.net/11420/105402021-10-15T08:11:13Z
- Hybrid space-time parallel solution of Burgers’ equationhttp://hdl.handle.net/11420/10541Title: Hybrid space-time parallel solution of Burgers’ equation
Authors: Krause, Rolf; Ruprecht, Daniel
Fri, 15 Oct 2021 08:31:43 GMThttp://hdl.handle.net/11420/105412021-10-15T08:31:43Z
- A massively space-time parallel N-body solverhttp://hdl.handle.net/11420/10557Title: A massively space-time parallel N-body solver
Authors: Speck, Robert; Ruprecht, Daniel; Krause, Rolf; Emmett, Matthew; Minion, Michael; Winkel, Mathias; Gibbon, Paul
Abstract: We present a novel space-time parallel version of the Barnes-Hut tree code PEPC using PFASST, the Parallel Full Approximation Scheme in Space and Time. The naive use of increasingly more processors for a fixed-size N-body problem is prone to saturate as soon as the number of unknowns per core becomes too small. To overcome this intrinsic strong-scaling limit, we introduce temporal parallelism on top of PEPC's existing hybrid MPI/PThreads spatial decomposition. Here, we use PFASST which is based on a combination of the iterations of the parallel-in-time algorithm parareal with the sweeps of spectral deferred correction (SDC) schemes. By combining these sweeps with multiple space-time discretization levels, PFASST relaxes the theoretical bound on parallel efficiency in parareal. We present results from runs on up to 262,144 cores on the IBM Blue Gene/P installation JUGENE, demonstrating that the spacetime parallel code provides speedup beyond the saturation of the purely space-parallel approach. © 2012 IEEE.
Tue, 19 Oct 2021 12:35:28 GMThttp://hdl.handle.net/11420/105572021-10-19T12:35:28Z
- A space-time parallel solver for the three-dimensional heat equationhttp://hdl.handle.net/11420/10556Title: A space-time parallel solver for the three-dimensional heat equation
Authors: Speck, Robert; Ruprecht, Daniel; Emmett, Matthew; Bolten, Matthias; Krause, Rolf
Abstract: The paper presents a combination of the time-parallel "parallel full approximation scheme in space and time" (PFASST) with a parallel multigrid method (PMG) in space, resulting in a mesh-based solver for the three-dimensional heat equation with a uniquely high degree of efficient concurrency. Parallel scaling tests are reported on the Cray XE6 machine "Monte Rosa" on up to 16,384 cores and on the IBM Blue Gene/Q system "JUQUEEN" on up to 65,536 cores. The efficacy of the combined spatial-and temporal parallelization is shown by demonstrating that using PFASST in addition to PMG significantly extends the strong-scaling limit. Implications of using spatial coarsening strategies in PFASST's multi-level hierarchy in large-scale parallel simulations are discussed. © 2014 The authors and IOS Press.
Tue, 19 Oct 2021 12:28:45 GMThttp://hdl.handle.net/11420/105562021-10-19T12:28:45Z
- Holistic data centres : next generation data and thermal energy infrastructureshttp://hdl.handle.net/11420/10559Title: Holistic data centres : next generation data and thermal energy infrastructures
Authors: Townend, Paul; Xu, Jie; Summers, Jon; Ruprecht, Daniel; Thompson, Harvey
Abstract: Digital infrastructure is becoming more distributed and requiring more power for operation. At the same time, many countries are working to de-carbonise their energy, which will require electrical generation of heat for populated areas. What if this heat generation was combined with digital processing?
Tue, 19 Oct 2021 14:02:29 GMThttp://hdl.handle.net/11420/105592021-10-19T14:02:29Z
- Integrating an N-body problem with SDC and PFASSThttp://hdl.handle.net/11420/10542Title: Integrating an N-body problem with SDC and PFASST
Authors: Speck, Robert; Ruprecht, Daniel; Krause, Rolf; Emmett, Matthew; Minion, Michael; Winkel, Mathias; Gibbon, Paul
Fri, 15 Oct 2021 09:12:13 GMThttp://hdl.handle.net/11420/105422021-10-15T09:12:13Z
- Parareal for diffusion problems with spaceand time-dependent coefficientshttp://hdl.handle.net/11420/10539Title: Parareal for diffusion problems with spaceand time-dependent coefficients
Authors: Ruprecht, Daniel; Speck, Robert; Krause, Rolf
Fri, 15 Oct 2021 07:57:00 GMThttp://hdl.handle.net/11420/105392021-10-15T07:57:00Z
- Multiple scales methods in meteorologyhttp://hdl.handle.net/11420/10558Title: Multiple scales methods in meteorology
Authors: Klein, Rupert; Vater, Stefan; Päschke, Eileen; Ruprecht, Daniel
Abstract: With emphasis on meteorological applications, we discuss here the fluid dynamical fundamental governing equations, their nondimensionalization including the identification of key nondimensional parameters, and a general approach to meteorological modelling based on multiple scales asymptotics.
Tue, 19 Oct 2021 13:55:23 GMThttp://hdl.handle.net/11420/105582021-10-19T13:55:23Z
- Numerical simulation of skin transport using Pararealhttp://hdl.handle.net/11420/10526Title: Numerical simulation of skin transport using Parareal
Authors: Kreienbuehl, Andreas; Naegel, Arne; Ruprecht, Daniel; Speck, Robert; Wittum, Gabriel; Krause, Rolf
Abstract: In silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms. This article investigates the applicability of the time-parallel Parareal algorithm to a brick and mortar setup, a precursory problem to skin permeation. The C++ library Lib4PrM implementing Parareal is combined with the UG4 simulation framework, which provides the spatial discretization and parallelization. The combination’s performance is studied with respect to convergence and speedup. It is confirmed that anisotropies in the domain and jumps in diffusion coefficients only have a minor impact on Parareal’s convergence. The influence of load imbalances in time due to differences in number of iterations required by the spatial solver as well as spatio-temporal weak scaling is discussed.
Thu, 14 Oct 2021 10:26:54 GMThttp://hdl.handle.net/11420/105262021-10-14T10:26:54Z
- Interweaving PFASST and Parallel Multigridhttp://hdl.handle.net/11420/10524Title: Interweaving PFASST and Parallel Multigrid
Authors: Minion, Michael; Speck, Robert; Bolten, Matthias; Emmett, Matthew; Ruprecht, Daniel
Abstract: The parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and discretized PDEs. As the name suggests, PFASST is similar in spirit to a space-time FAS multigrid method performed over multiple time-steps in parallel. However, since the original focus of PFASST has been on the performance of the method in terms of time parallelism, the solution of any spatial system arising from the use of implicit or semi-implicit temporal methods within PFASST have simply been assumed to be solved to some desired accuracy completely at each sub-step and each iteration by some unspecified procedure. It hence is natural to investigate how iterative solvers in the spatial dimensions can be interwoven with the PFASST iterations and whether this strategy leads to a more efficient overall approach. This paper presents an initial investigation on the relative performance of different strategies for coupling PFASST iterations with multigrid methods for the implicit treatment of diffusion terms in PDEs. In particular, we compare full accuracy multigrid solves at each sub-step with a small fixed number of multigrid V-cycles. This reduces the cost of each PFASST iteration at the possible expense of a corresponding increase in the number of PFASST iterations needed for convergence. Parallel efficiency of the resulting methods is explored through numerical examples.
Thu, 14 Oct 2021 10:16:19 GMThttp://hdl.handle.net/11420/105242021-10-14T10:16:19Z
- Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problemshttp://hdl.handle.net/11420/10528Title: Transparent boundary conditions based on the Pole Condition for time-dependent, two-dimensional problems
Authors: Ruprecht, Daniel; Schädle, Achim; Schmidt, Frank
Abstract: The pole condition approach for deriving transparent boundary conditions is extended to the time-dependent, two-dimensional case. Non-physical modes of the solution are identified by the position of poles of the solution's spatial Laplace transform in the complex plane. By requiring the Laplace transform to be analytic on some problem dependent complex half-plane, these modes can be suppressed. The resulting algorithm computes a finite number of coefficients of a series expansion of the Laplace transform, thereby providing an approximation to the exact boundary condition. The resulting error decays super-algebraically with the number of coefficients, so relatively few additional degrees of freedom are sufficient to reduce the error to the level of the discretization error in the interior of the computational domain. The approach shows good results for the Schrödinger and the drift-diffusion equation but, in contrast to the one-dimensional case, exhibits instabilities for the wave and Klein-Gordon equation. Numerical examples are shown that demonstrate the good performance in the former and the instabilities in the latter case.
Thu, 14 Oct 2021 10:31:56 GMThttp://hdl.handle.net/11420/105282021-10-14T10:31:56Z