arXiv subjects

Stefan Henneking

Publications and source records attributed to Stefan Henneking.

16 recordsLinked to original sources

arXiv2026

Sensor Placement for Tsunami Early Warning via Large-Scale Bayesian Optimal Experimental Design

Real-time tsunami early warning relies on distributed sensor networks to infer seismic sources and seafloor motion. Optimizing these networks via Bayesian optimal experimental design (OED) is exceptionally challenging for systems governed by hyperbolic partial differential equations, which lack the spectral decay required by standard low-rank approximations. We present a scalable Bayesian OED framework for linear time-invariant systems. By reformulating the inverse problem in the data space, we transform OED into dense matrix subset selection. We propose a multi-GPU, Schur-complement-update-based, greedy algorithm that solves the OED problem using a pipelined approach that fully overlaps I/O with GPU computations. Our framework achieves near-perfect weak and strong scaling across hundreds of GPUs on Perlmutter and Frontier. Applied to the 2025 Gordon Bell Prize-winning digital twin for tsunami forecasting in the Cascadia Subduction Zone, we optimize a 175-sensor network, minimizing the uncertainty of a parameter field with over one billion degrees of freedom.

cs.DC↗

arXiv2026

Bessel Functions and Analysis of Circular Waveguides

The paper is devoted to the study of circularly coiled optical slab waveguides, which is also applicable to acoustical waveguides. We use a change of variables and the classical Frobenius method to compute Bessel functions of complex order and complex argument, and combine it with a perfectly matched layer technique to solve the relevant Bessel eigenvalue problem and deliver accurate loss factors for eigensolutions to the three-layer optical slab waveguide problem. The solutions provide a benchmark for verifying model implementations of this problem and allow for a numerical verification of the Glazman criterion that provides a foundation for the well-posedness and stability analysis of homogeneous circular waveguides with impedance boundary conditions.

physics.comp-ph↗

arXiv2026

Rapid Earthquake-to-Tsunami Waveform Generation via Large-Scale Multi-GPU FFT Convolution Applied to the Cascadia Subduction Zone

Data-driven methods for earthquake and tsunami early warning rely on large ensembles of rupture scenarios and their resulting waveforms, but generating such datasets with repeated high-fidelity seismic and tsunami simulations is prohibitively expensive. We exploit the linear time-invariant structure of both dynamics to precompute elastic Green's functions and acoustic-gravity adjoint responses, reducing the source-to-waveform map to two consecutive convolution operators. We evaluate these convolutions with a distributed, FFT-accelerated GPU pipeline that partitions the large seafloor grid across GPUs and directly generates the final observation waveforms. We demonstrate the scalability of this pipeline for the Cascadia Subduction Zone with 963 subfaults, 2,416,530 seafloor grid points, 64 observation locations, and 256 timesteps, requiring 9.45 TiB of aggregate GPU memory. On 64 GB200 GPUs within one NVL72 domain, the pipeline generates waveforms in 24 ms per rupture once the response operators are resident, enabling large rupture ensembles to be evaluated within minutes.

cs.DC↗

arXiv2026

Bent optical waveguide finite element analysis with a 3D envelope Maxwell model

With the goal of accurately extracting the optical field losses in a three-dimensional (3D), circularly coiled waveguide (e.g., bent optical fiber), this effort presents the numerical methodologies that are implemented for an envelope Maxwell model that propagates electromagnetic fields as an entirely boundary value problem. Our unique modeling approach includes an ultraweak variational formulation of the envelope Maxwell model in the curved geometry of the bending, which is discretized by the discontinuous Petrov-Galerkin (DPG) method, which permits residual-driven mesh and polynomial-order adaptivity. This also, then, requires a unique approach for constructing perfectly matched layers (PMLs) as absorbing boundary conditions in both the direction of optical field propagation and in the tangential directions, where unguided energy escapes the waveguide. Our coiled waveguide modeling technology extracts the mode confinement losses from the propagation of the coherent optical field through the bent waveguide. We verify our simulations against the semi-analytical results from the analogous bent slab waveguide problem, and we successfully demonstrate stable convergence to loss values for the 3D coiled optical fiber problem, which has never been done previously for our specific modeling approach.

physics.optics↗

arXiv2026

Real-time probabilistic tsunami forecasting in Cascadia from sparse offshore pressure observations

Near-field tsunami early warning in the Cascadia Subduction Zone is limited by sparse offshore observations. We investigate whether a hypothetical network of 175 ocean-bottom pressure sensors can support real-time Bayesian inference of the full spatiotemporal seafloor velocity field and probabilistic tsunami forecasting for a margin-wide and a partial fully-coupled Cascadia earthquake dynamic rupture-tsunami scenario. The simulated oceanic acoustic, Rayleigh, and tsunami wavefields are similar during the first two minutes after nucleation but diverge thereafter, enabling rapid earthquake scenario discrimination. Using an acoustic-gravity inversion with assimilation of pressure data, tsunami wave height forecasts are obtained in less than a second. We leverage a Bayesian inversion-based framework that splits the computations into an offline precomputation phase performed with large-scale computing facilities, and an online phase that computes forecasts and can be executed on a laptop. Forecast errors remain low at 22.1% for the margin-wide and 19.6% for the partial rupture.

physics.geo-ph↗

arXiv2026

Accelerating High-Order Finite Element Simulations at Extreme Scale with FP64 Tensor Cores

Finite element simulations play a critical role in a wide range of applications, from automotive design to tsunami modeling and computational electromagnetics. Performing these simulations efficiently at the high resolutions needed for practical applications and scientific insights necessitates the use of high-order methods and large-scale supercomputing. While much progress has been made in porting finite element codes to GPU systems in recent years, additional improvements in the efficiency and computational speed of GPU-accelerated high-order finite element simulations are in constant demand. In this paper, we demonstrate that the FP64 tensor cores on NVIDIA GPUs can be used to further accelerate such simulations, achieving significant speedups in key kernels of MFEM, a scalable open-source finite element library widely used in HPC applications. By integrating FP64 tensor cores with kernel fusion optimizations, we were able to achieve up to 2$\times$ performance gains and up to 83% energy efficiency gains on NVIDIA's Grace Hopper GH200 and Grace Blackwell GB200 architectures. To the best of our knowledge, this is the first time that FP64 tensor cores have been directly programmed to accelerate large-scale finite element scientific computing applications. We demonstrate the performance of the optimized kernels at exascale by showing near-perfect weak scaling efficiency and 90% strong scaling efficiency across nearly 10,000 GPUs on the Alps system. The new algorithms and MFEM enhancements directly benefit complex production codes, including the 2025 Gordon Bell Prize-winning application for real-time tsunami forecasting.

cs.DC↗

arXiv2026

Goal-Oriented Real-Time Bayesian Inference for Linear Autonomous Dynamical Systems With Application to Digital Twins for Tsunami Early Warning

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity PDE models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into an offline phase in which the PDE model is solved a limited number of times, and an online phase that computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our goal is to apply this framework to construct digital twins for subduction zones to provide early warning for tsunamis. To this end, we show how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic-gravity wave equations, to infer the earthquake-induced seafloor motion (discretized with 10^9 parameters) and forecast the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with 10^8 inversion parameters for which goal-oriented Bayesian inference is accomplished in real time.

math.NA↗

arXiv2025

Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides

In a time-harmonic setting, we show for heterogeneous acoustic and homogeneous electromagnetic wavesguides stability estimates with the stability constant depending linearly on the length $L$ of the waveguide. These stability estimates are used for the analysis of the (ideal) ultraweak (UW) variant of the Discontinuous Petrov Galerkin (DPG) method. For this UW DPG, we show that the stability deterioration with $L$ can be countered by suitably scaling the test norm of the method. We present the ``full envelope approximation'', a UW DPG method based on non-polynomial ansatz functions that allows for treating long waveguides.

math.NA↗

arXiv2025

Real-time Bayesian inference at extreme scale: A digital twin for tsunami early warning applied to the Cascadia subduction zone

We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic-gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline-online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.

cs.DC↗

arXiv2025

Fast And Scalable FFT-Based GPU-Accelerated Algorithms for Block-Triangular Toeplitz Matrices With Application to Linear Inverse Problems Governed by Autonomous Dynamical Systems

We present an efficient and scalable algorithm for performing matrix-vector multiplications ("matvecs") for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving inverse problems governed by autonomous systems, and time-invariant systems in particular. In this article, we consider inverse problems that infer unknown parameters from observational data of a linear time-invariant dynamical system given in the form of partial differential equations (PDEs). Matrix-free Newton-conjugate-gradient methods are often the gold standard for solving these inverse problems, but they require numerous actions of the Hessian on a vector. Matrix-free adjoint-based Hessian matvecs require solution of a pair of linearized forward/adjoint PDE solves per Hessian action, which may be prohibitive for large-scale inverse problems. Time invariance of the forward PDE problem leads to a block Toeplitz structure of the discretized parameter-to-observable (p2o) map defining the mapping from inputs (parameters) to outputs (observables) of the PDEs. This block Toeplitz structure enables us to exploit two key properties: (1) compact storage of the p2o map and its adjoint; and (2) efficient fast Fourier transform (FFT)-based Hessian matvecs. The proposed algorithm is mapped onto large multi-GPU clusters and achieves more than 80 percent of peak bandwidth on NVIDIA A100 GPUs. Excellent weak scaling is shown for up to 48 A100 GPUs. For the targeted problems, the implementation executes Hessian matvecs within fractions of a second, which is orders of magnitude faster than can be achieved by conventional matrix-free Hessian matvecs via forward/adjoint PDE solves.

math.NA↗

arXiv2024

A Vectorial Envelope Maxwell Formulation for Electromagnetic Waveguides with Application to Nonlinear Fiber Optics

This article presents an ultraweak discontinuous Petrov-Galerkin (DPG) formulation of the time-harmonic Maxwell equations for the vectorial envelope of the electromagnetic field in a weakly-guiding multi-mode fiber waveguide. This formulation is derived using an envelope ansatz for the vector-valued electric and magnetic field components, factoring out an oscillatory term of $exp(-i \mathsf{k}z)$ with a user-defined wavenumber $\mathsf{k}$, where $z$ is the longitudinal fiber axis and field propagation direction. The resulting formulation is a modified system of the time-harmonic Maxwell equations for the vectorial envelope of the propagating field. This envelope is less oscillatory in the $z$-direction than the original field, so that it can be more efficiently discretized and computed, enabling solution of the vectorial DPG Maxwell system for $1000\times$ longer fibers than previously possible. Different approaches for incorporating a perfectly matched layer for absorbing the outgoing wave modes at the fiber end are derived and compared numerically. The resulting formulation is used to solve a 3D Maxwell model of an ytterbium-doped active gain fiber amplifier, coupled with the heat equation for including thermal effects. The nonlinear model is then used to simulate thermally-induced transverse mode instability (TMI). The numerical experiments demonstrate that it is computationally feasible to perform simulations and analysis of real-length optical fiber laser amplifiers using discretizations of the full vectorial time-harmonic Maxwell equations. The approach promises a new high-fidelity methodology for analyzing TMI in high-power fiber laser systems and is extendable to including other nonlinearities.

math.NA↗

arXiv2023

Scalable DPG Multigrid Solver for Helmholtz Problems: A Study on Convergence

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov-Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12-26) and extends the convergence results from $\mathcal{O}(10^7)$ degrees of freedom (DOFs) to $\mathcal{O}(10^9)$ DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear dependence with respect to the wave frequency. The paper concludes with numerical results on hp-adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.

math.NA↗

arXiv2023

hp3D User Manual

User Manual for the hp3D Finite Element Software, available on GitHub at https://github.com/Oden-EAG/hp3d

math.NA↗

arXiv2023

An Anisotropic $hp$-Adaptation Framework for Ultraweak Discontinuous Petrov-Galerkin Formulations

In this article, we present a three-dimensional anisotropic $hp$-mesh refinement strategy for ultraweak discontinuous Petrov--Galerkin (DPG) formulations with optimal test functions. The refinement strategy utilizes the built-in residual-based error estimator accompanying the DPG discretization. The refinement strategy is a two-step process: (a) use the built-in error estimator to mark and isotropically $hp$-refine elements of the (coarse) mesh to generate a finer mesh; (b) use the reference solution on the finer mesh to compute optimal $h$- and $p$-refinements of the selected elements in the coarse mesh. The process is repeated with coarse and fine mesh being generated in every adaptation cycle, until a prescribed error tolerance is achieved. We demonstrate the performance of the proposed refinement strategy using several numerical examples on hexahedral meshes.

cs.CE↗

arXiv2020

A numerical study of the pollution error and DPG adaptivity for long waveguide simulations

High-frequency wave propagation has many important applications in acoustics, elastodynamics, and electromagnetics. Unfortunately, the finite element discretization for these problems suffers from significant numerical pollution errors that increase with the wavenumber. It is critical to control these errors to obtain a stable and accurate method. We study the effect of pollution for very long waveguide problems in the context of robust discontinuous Petrov-Galerkin (DPG) finite element discretizations. Our numerical experiments show that the pollution primarily has a diffusive effect causing energy loss in the DPG method while phase errors appear less significant. We report results for 3D vectorial time-harmonic Maxwell problems in waveguides with more than 8000 wavelengths. Our results corroborate previous analysis for the Galerkin discretization of the Helmholtz operator by Melenk and Sauter (2011). Additionally, we discuss adaptive refinement strategies for multi-mode fiber waveguides where the propagating transverse modes must be resolved sufficiently. Our study shows the applicability of the DPG error indicator to this class of problems. Finally, we illustrate the importance of load balancing in these simulations for distributed-memory parallel computing.

math.NA↗

arXiv2020

Model and computational advancements to full vectorial Maxwell model for studying fiber amplifiers

We present both modeling and computational advancements to a unique three-dimensional discontinuous Petrov-Galerkin finite element model for the simulation of laser amplification in a fiber amplifier. Our model is based on the time-harmonic Maxwell equations, and it incorporates both amplification via an active dopant and thermal effects via coupling with the heat equation. As a full vectorial finite element simulation, this model distinguishes itself from other fiber amplifier models that are typically posed as an initial value problem and make significantly more approximations. Our model supports co-, counter-, and bi-directional pumping configurations, as well as inhomogeneous and anisotropic material properties. The longer-term goal of this modeling effort is to study nonlinear phenomena that prohibit achieving unprecedented power levels in fiber amplifiers, along with validating typical approximations used in lower-fidelity models. The high-fidelity simulation comes at the cost of a high-order finite element discretization with many degrees of freedom per wavelength. This is necessary to counter the effect of numerical pollution due to the high-frequency nature of the wave simulation. To make the computation more feasible, we have developed a novel longitudinal model rescaling, using artificial material parameters with the goal of preserving certain quantities of interest. Our numerical tests demonstrate the applicability and utility of this scaled model in the simulation of an ytterbium-doped, step-index fiber amplifier that experiences laser amplification and heating. We present numerical results for the nonlinear coupled Maxwell/heat model with up to 240 wavelengths.

math.NA↗