arXiv subjects

Stephan C. Kramer

Publications and source records attributed to Stephan C. Kramer.

10 recordsLinked to original sources

arXiv2026

Machine Learning Based Mesh Movement for Non-Hydrostatic Tsunami Simulation

This study investigates the use of machine learning based mesh movement method, specifically the Universal Mesh Movement Network (UM2N), with depth integrated non-hydrostatic shallow water models. Motivation for this comes from the need for models which balance efficiency and accuracy for use in probabilistic coastal hazard assessment. Implementations are built on the discontinuous Galerkin finite-element (DG-FE) based software, Thetis, which leverages the partial differential equation (PDE) framework Firedrake for automated code generation. Verification on benchmark test cases and validation against laboratory measurements of coastal hazards, focusing on tsunami propagation, run-up, and inundation is performed. In these tests, the UM2N-driven meshes help resolve key non-hydrostatic dynamics including wave refraction over a conical shoal, run-up with wetting-drying on a conical island, and tsunami inundation in the Monai Valley laboratory benchmark, and yield numerical solutions in close agreement with reference fine-mesh computations and measured data. Notably, in the Monai Valley case, UM2N achieves a ~91% reduction in wave-peak error at the nearshore gauge compared with ~74% for the conventional Monge--Amp\`ere (MA) mesh movement, both relative to the coarse fixed mesh. The UM2N surrogate based approach accelerates the conventional mesh movement step, achieving a ~32% reduction in total runtime and ~2 times speed-up in mesh movement step time over the MA solver on GPU, while offering a significant improvement in robustness over long integration periods and under strongly nonlinear wave conditions.

physics.ao-ph↗

arXiv2022

Efficient optimization of a regional water elevation model with an automatically generated adjoint

Calibration of unknown model parameters is a common task in many ocean model applications. We present an adjoint-based optimization of an unstructured mesh shallow water model for the Baltic Sea. Spatially varying bottom friction parameter is tuned to minimize the misfit with respect to tide gauge sea surface height (SSH) observations. A key benefit of adjoint-based optimization is that computational cost does not depend on the number of unknown variables. Adjoint models are, however, typically very laborious to implement. In this work, we leverage a domain specific language framework in which the discrete adjoint model can be obtained automatically. The adjoint model is both exactly compatible with the discrete forward model and computationally efficient. A gradient-based quasi-Newton method is used to minimize the misfit. Optimizing spatially-variable parameters is typically an under-determined problem and can lead to over-fitting. We employ Hessian-based regularization to penalize the spatial curvature of the friction field to overcome this problem. The SSH dynamics in the Baltic Sea are simulated for a 3-month period. Optimization of the bottom friction parameter results in significant improvement of the model performance. The results are especially encouraging in the complex Danish Straits region, highlighting the benefit of unstructured meshes. Domain specific language frameworks enable automated model analysis and provide easy access to adjoint modeling. Our application shows that this capability can be enabled with few efforts, and the optimization procedure is robust and computationally efficient.

physics.ao-ph↗

arXiv2018

An investigation into the accuracy of the depth-averaging used in tidal turbine array optimisation

Depth-averaged shallow water models are widely used for the large-scale simulation of tidal turbine arrays. The relatively low computational complexity of this approach allows for layout optimisations aimed at improving the total array power output as well as an assessment of large-scale environmental impacts. In order to assess the suitability of using depth-averaged models to optimise array configurations, a comprehensive comparison between the wake profiles and power outputs predicted by a 2D shallow water model and a 3D actuator disc momentum (ADM) model is presented. Initially, a viscosity sensitivity analysis is presented to outline the limitations associated with using a constant eddy viscosity in the depth-averaged model and to outline the importance of correctly calibrating this value in line with the freestream velocity magnitude. Thereafter, the depth-averaged OpenTidalFarm (OTF) tool is used to optimise the positions of an array of 32 turbines in an ideal channel and the 3D Fluidity ADM-RANS model is used to assess the accuracy of the OTF predictions for the first time. It is shown that with the help of corrected power calculations a good agreement between the two models can be achieved, thus demonstrating the value of the eddy viscosity calibration implemented in the depth-averaged model.

physics.flu-dyn↗

arXiv2018

Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to real life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability preserving time integration method and slope limiters. Compared to previous DG models advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.

physics.ao-ph↗

arXiv2018

Relaxation of photoexcitations in polaron-induced magnetic microstructures

We investigate the evolution of a photoexcitation in correlated materials over a wide range of time scales. The system studied is a one-dimensional model of a manganite with correlated electron, spin, orbital, and lattice degrees of freedom, which we relate to the three-dimensional material Pr$_{1-x}$Ca$_{x}$MnO$_3$. The ground-state phases for the entire composition range are determined and rationalized by a coarse-grained polaron model. At half-doping a pattern of antiferromagnetically coupled Zener polarons is realized. Using time-dependent density-matrix renormalization group (tDMRG), we treat the electronic quantum dynamics following the excitation. The emergence of quasiparticles is addressed, and the relaxation of the nonequilibrium quasiparticle distribution is investigated via a linearized quantum-Boltzmann equation. Our approach shows that the magnetic microstructure caused by the Zener polarons leads to an increase of the relaxation times of the excitation.

cond-mat.str-el↗

arXiv2016

Design optimisation and resource assessment for tidal-stream renewable energy farms using a new continuous turbine approach

This paper presents a new approach for optimising the design of tidal stream turbine farms. In this approach, the turbine farm is represented by a turbine density function that specifies the number of turbines per unit area and an associated continuous locally-enhanced bottom friction field. The farm design question is formulated as a mathematical optimisation problem constrained by the shallow water equations and solved with efficient, gradient-based optimisation methods. The resulting method is accurate, computationally efficient, allows complex installation constraints, and supports different goal quantities such as to maximise power or profit. The outputs of the optimisation are the optimal number of turbines, their location within the farm, the overall farm profit, the farm's power extraction, and the installation cost. We demonstrate the capabilities of the method on a validated numerical model of the Pentland Firth, Scotland. We optimise the design of four tidal farms simultaneously, as well as individually, and study how farms in close proximity may impact upon one another.

cs.CE↗

arXiv2016

On the validity of tidal turbine array configurations obtained from steady-state adjoint optimisation

Extracting the optimal amount of power from an array of tidal turbines requires an intricate understanding of tidal dynamics and the effects of turbine placement on the local and regional scale flow. Numerical models have contributed significantly towards this understanding, and more recently, adjoint-based modelling has been employed to optimise the positioning of the turbines in an array in an automated way and improve on simple, regular man-made configurations. Adjoint-based optimisation of high-resolution and ideally 3D transient models is generally a very computationally expensive problem. As a result, existing work on the adjoint optimisation of tidal turbine placement has been mostly limited to steady-state simulations in which very high, non-physical values of the background viscosity are required to ensure that a steady-state solution exists. However, such compromises may affect the reliability of the modelled turbines, their wakes and interactions, and thus bring into question the validity of the computed optimal turbine positions. This work considers a suite of idealised simulations of flow past tidal turbine arrays in a 2D channel. It compares four regular array configurations, detailed by Divett et al. (2013), with the configuration found through adjoint optimisation in a steady-state, high-viscosity setup. The optimised configuration produces considerably more power. The same configurations are then used to produce a suite of transient simulations that do not use constant high-viscosity, and instead use large eddy simulation (LES) to parameterise the resulting turbulent structures. It is shown that the LES simulations produce less power than that predicted by the constant high-viscosity runs. Nevertheless, they still follow the same trends in the power curve throughout time, with optimised layouts continuing to perform significantly better than simplified configurations.

physics.flu-dyn↗

arXiv2015

Parallel Statistical Multi-resolution Estimation

We discuss several strategies to implement Dykstra's projection algorithm on NVIDIA's compute unified device architecture (CUDA). Dykstra's algorithm is the central step in and the computationally most expensive part of statistical multi-resolution methods. It projects a given vector onto the intersection of convex sets. Compared with a CPU implementation our CUDA implementation is one order of magnitude faster. For a further speed up and to reduce memory consumption we have developed a new variant, which we call incomplete Dykstra's algorithm. Implemented in CUDA it is one order of magnitude faster than the CUDA implementation of the standard Dykstra algorithm. As sample application we discuss using the incomplete Dykstra's algorithm as preprocessor for the recently developed super-resolution optical fluctuation imaging (SOFI) method (Dertinger et al. 2009). We show that statistical multi-resolution estimation can enhance the resolution improvement of the plain SOFI algorithm just as the Fourier-reweighting of SOFI. The results are compared in terms of their power spectrum and their Fourier ring correlation (Saxton and Baumeister 1982). The Fourier ring correlation indicates that the resolution for typical second order SOFI images can be improved by about 30 per cent. Our results show that a careful parallelization of Dykstra's algorithm enables its use in large-scale statistical multi-resolution analyses.

physics.comp-ph↗

arXiv2013

Real-Time Phase Masks for Interactive Stimulation of Optogenetic Neurons

Experiments with networks of optogenetically altered neurons require stimulation with high spatio-temporal selectivity. Computer-assisted holography is an energy-efficient method for robust and reliable addressing of single neurons on the millisecond-timescale inherent to biologial information processing. We show that real-time control of neurons can be achieved by a CUDA-based hologram computation.

math.OC↗

arXiv2001

Pattern Formation of Ion Channels with State Dependent Electrophoretic Charges and Diffusion Constants in Fluid Membranes

A model of mobile, charged ion channels in a fluid membrane is studied. The channels may switch between an open and a closed state according to a simple two-state kinetics with constant rates. The effective electrophoretic charge and the diffusion constant of the channels may be different in the closed and in the open state. The system is modeled by densities of channel species, obeying simple equations of electro-diffusion. The lateral transmembrane voltage profile is determined from a cable-type equation. Bifurcations from the homogeneous, stationary state appear as hard-mode, soft-mode or hard-mode oscillatory transitions within physiologically reasonable ranges of model parameters. We study the dynamics beyond linear stability analysis and derive non-linear evolution equations near the transitions to stationary patterns.

cond-mat.soft↗