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At least 37 records · Page 2

Energy–Performance Trade-offs in Privacy-Preserving Federated Learning on SmartNIC-Enabled HPC Systems

Federated learning (FL) is increasingly deployed on accelerator-rich high-performance computing (HPC) systems, yet the system-level energy cost of privacy-aware FL remains poorly understood, particularly across heterogeneous networking and server-placement options. We present a measurement-driven study of energy–performance trade-offs for FL on GH200-class nodes across three deployment configurations: CPU-Ethernet, CPU-InfiniBand (RDMA-capable), and a DPU-hosted FL server over InfiniBand using a BlueField-3 SmartNIC/DPU. Using NVIDIA FLARE (NVFLARE), we align node-level power telemetry with per-round timing extracted from NVFLARE logs to quantify time-to-solution (TTS), energy-to-solution (ETS), energy-delay product (EDP), and synchronization behavior for three transformer models (ALBERT, DistilBERT, BERT), trained with and without differential privacy (DP). We find that interconnect choice is the dominant driver of runtime and energy: host-managed InfiniBand consistently reduces communication overhead versus Ethernet, yielding lower TTS/ETS/EDP. In contrast, in our NVFLARE deployment, placing the FL server on the DPU does not consistently match CPU-InfiniBand performance and can be slower—especially for larger models—highlighting that server placement alone is not sufficient to guarantee end-to-end gains. Finally, under our fixed-round protocol, DP increases per-round cost and runtime variance; ETS increases largely in proportion to TTS because average node power remains relatively stable across configurations.

Kotevska, Olivera [ORNL] (ORCID:0000000316772243)↗

Quantum Approximate Optimization Algorithm on Different Qubit Systems

Solving optimization problems is critical across many research domains, but the high dimensionality of parameter spaces often poses significant challenges. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising approach for accelerating optimization in the Noisy Intermediate-Scale Quantum (NISQ) era by leveraging both classical and quantum computational resources. However, its performance can vary depending on the underlying quantum hardware architecture. In this work, we evaluate the performance of QAOA on different quantum hardware platforms, specifically, superconducting transmon qubits and trapped-ion qubits, targetting real-world optimization problems formulated as fully connected Quadratic Unconstrained Binary Optimization (QUBO) instances. We evaluate both the solution quality and time-to-solution using dense QUBO matrices. Furthermore, we show that large-scale problems, such as a 100-bit QUBO instance, can be effectively tackled by integrating quantum computing with high-performance computing (HPC) resources. This study provides practical insights into the strengths and limitations of different qubit technologies and advances the application of quantum computing in solving real-world optimization problems.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗

Image Gradient Decomposition for Parallel and Memory-Efficient Ptychographic Reconstruction

Ptychography is a popular microscopic imaging modality for many scientific discoveries and sets the record for highest image resolution. Unfortunately, the high image resolution for ptychographic reconstruction requires significant amount of memory and computations, forcing many applications to compromise their image resolution in exchange for a smaller memory footprint and a shorter reconstruction time. In this paper, we propose a novel image gradient decomposition method that significantly reduces the memory footprint for ptychographic reconstruction by tessellating image gradients and diffraction measurements into tiles. In addition, we propose a parallel image gradient decomposition method that enables asynchronous point-to-point communications and parallel pipelining with minimal overhead on a large number of GPUs. Our experiments on a Titanate material dataset (PbTiO3) with 16632 probe locations show that our Gradient Decomposition algorithm reduces memory footprint by 51 times. In addition, it achieves time-to-solution within 2.2 minutes by scaling to 4158 GPUs with a super-linear strong scaling efficiency at 364% compared to runtimes at 6 GPUs. This performance is 2.7 times more memory efficient, 9 times more scalable and 86 times faster than the state-of-the-art algorithm.

Wang, Xiao↗

Scalable Deep Learning-Based Microarchitecture Simulation on GPUs

Cycle-accurate microarchitecture simulators are essential tools for designers to architect, estimate, optimize, and manufacture new processors that meet specific design expectations. However, conventional simulators based on discrete-event methods often require an exceedingly long time-to-solution for the simulation of applications and architectures at full complexity and scale. Given the excitement around wielding the machine learning (ML) hammer to tackle various architecture problems, there have been attempts to employ ML to perform architecture simulations, such as Ithemal and SimNet. However, the direct application of existing ML approaches to architecture simulation may be even slower due to overwhelming memory traffic and stringent sequential computation logic. This work proposes the first graphics processing unit (GPU)-based microarchitecture simulator that fully unleashes the potential of GPUs to accelerate state-of-the-art ML-based simulators. First, considering the application traces are loaded from central processing unit (CPU) to GPU for simulation, we introduce various designs to reduce the data movement cost between CPUs and GPUs. Second, we propose a parallel simulation paradigm that partitions the application trace into sub-traces to simulate them in parallel with rigorous error analysis and effective error correction mechanisms. Combined, this scalable GPU-based simulator outperforms by orders of magnitude the traditional CPU-based simulators and the state-of-the-art ML-based simulators, i.e., SimNet and Ithemal.

97 MATHEMATICS AND COMPUTING↗

Active Learning Surrogates for Integrating Electron Microscopy and Computational Insights from Simulations in Autonomous Experiments

Artificial Intelligence (AI) combined with simulations and experiments has great potential to accelerate scientific discovery across technology and pharmaceuticals. However, the gap between simulations and experiments is challenging due to disparities in time and scale, making it difficult to estimate properties like energy and electronic states from experiments, and to provide feedback based on theoretical insights.Our research addresses the challenge by developing unique deep kernel based surrogate models that learns from microscopic images, mapping structural features to energy differences from defect formation. We start with full-training using simulated images to determine optimal settings, establishing a baseline for active learning. Using these settings from the baseline, active learning is trained, and predicts structures along simulation trajectories based on uncertainty and energetic stability, thus reducing data requirements, simulation time and computational costs. The results demonstrate that the model achieves a low average error margin of approximately 0.03 meV, indicating good performance. To enhance feature extraction and reconstruction capabilities, we developed an autoencoder-decoder as additional surrogate to create latent space to capture essential features, enabling precise comparisons between simulations and experiments. The results from this model achieved a reconstruction loss of around 0.2 and accurately reconstructed molecular structures.Overall, this work advances the steering of experiments through computational simulations by employing a surrogate models that actively predicts the trajectories of structural evolution, achieving time-to-solution comparable to experimental measurements.

Saranathan, Gayathri [Hewlett-Packard]↗

MACHINE LEARNING-ENABLED PREDICTION OF TRANSIENT INJECTION MAP IN AUTOMOTIVE INJECTORS WITH UNCERTAINTY QUANTIFICATION

Accurate prediction of injection profiles is a critical aspect of linking injector operation with engine performance and emissions. However, highly resolved injector simulations can take one to two weeks of wall-clock time, which is incompatible with engine design cycles with desired turnaround times of less than a day. Hence, it is important to reduce the time-to-solution of the internal flow simulations by several orders of magnitude to make it compatible with engine simulations. This work demonstrates a data-driven approach for tackling the computational overhead of injector simulations, whereby the transient injection profiles are emulated for a side-oriented, single-hole diesel injector using a Bayesian machine-learning framework. First, an interpretable Bayesian learning strategy was employed to understand the effect of design parameters on the total void fraction field. Then, autoencoders are utilized for efficient dimensionality reduction of the flowfields. Gaussian process models are finally used to predict the spatiotemporal void fraction field at the injector exit for unknown operating conditions. The Gaussian process models produce principled uncertainty estimates associated with the emulated flowfields, which provide the engine designer with valuable information of where the data-driven predictions can be trusted in the design space. The Bayesian flowfield predictions are compared with the corresponding predictions from a deep neural network, which has been transfer-learned from static needle simulations from a previous work by the authors. The emulation framework can predict the void fraction field at the exit of the orifice within a few seconds, thus achieving a speed-up factor of up to 38 x 10(6) over the traditional simulation-based approach of generating transient injection maps.

machine learning↗

Two-Level Sketching Alternating Anderson Acceleration for Complex Physics Applications

We present a novel two-level sketching extension of the Alternating Anderson–Picard (AAP) method for accelerating fixed-point iterations in challenging single- and multiphysics simulations governed by discretized PDEs. Our approach combines a static, physics-based projection that reduces the least-squares (LS) problem to the most informative field (e.g., via Schur-complement insight) with a dynamic, algebraic sketching stage driven by a backward stability analysis under Lipschitz continuity. We introduce inexpensive estimators for stability thresholds and cache-aware randomized selection strategies to balance computational cost against memory access overhead. The resulting algorithm solves reduced LS systems in place, minimizes memory footprints, and seamlessly alternates between low-cost Picard updates and Anderson mixing. Implemented in Julia, our two-level sketching AAP achieves up to 50% time-to-solution reductions compared to standard Anderson acceleration—without degrading convergence rates—on benchmark problems including Stokes, 𝑝-Laplacian, bidomain, and Navier–Stokes formulations at varying problem sizes. These results demonstrate the method’s robustness, scalability, and potential for integration into high-performance scientific computing frameworks. Our implementation is available open source in the AAP.jl library.

Barnafi, Nicolas [University of Chile, Santiago]↗

Analog Computing for Science

Conventional digital computing faces fundamental physical limits: large scale computing systems already con sume tens of Megawatts of power, Dennard scaling has ended, and data movement costs dominate application performance. Next generation experimental facilities generate data at rates that overwhelm conventional pro cessing and demand real-time analysis at the source. Analog computing, which exploits the continuous dynamics of physical systems to perform computation, promises a transformative path toward orders-of-magnitude gains in energy efficiency and time-to-solution for scientific workloads.

97 MATHEMATICS AND COMPUTING↗

A Comparison of GPU-Accelerated Multiphase CFD Solvers on the Polaris Supercomputer: Part 1

This report is in support of the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program sponsored by the U.S. Department of Energy (USDOE). With INCITE-level resources, one project, titled BubblyFlow, was granted computational resources for the 2025 calendar year on the Polaris supercomputer at the Argonne Leadership Computing Facility (ALCF). The project aims to conduct simulations to understand the fundamental characteristics of turbulent bubbly flow phenomena in nature. Staff at the ALCF and Argonne’s Computational Science division, along with collaborators at the City College of New York and University of Illinois at Chicago, helped a summer student to assess the accuracy and performance of two high performance computing (HPC) codes. Both codes, ImExLBM and FluTAS, are fundamentally different in their mathematical and numerical modeling. However, both may be used to solve the same physical problem. The collaboration sought to better understand the differences between both codes in terms of accuracy and efficiency. This would ultimately help the BubblyFlow project better utilize resources and establish a knowledge-base of code capabilities in future simulation campaigns. We compare ImExLBM and FluTAS, two high-performance multiphase computational fluid dynamics (CFD) solvers, in terms of physical fidelity, time-to-solution, and parallel efficiency. We validate ImExLBM (Implicit-Explicit Lattice Boltzmann Method) against a canonical benchmark and assess it’s performance relative to FluTAS (Fluid Transport Accelerated Solver), a well-established open-source CFD code.

97 MATHEMATICS AND COMPUTING↗

Nek5000/RS performance on advanced GPU architectures

The authors explore performance scalability of the open-source thermal-fluids code, NekRS, on the U.S. Department of Energy's leadership computers, Crusher, Frontier, Summit, Perlmutter, and Polaris. Particular attention is given to analyzing performance and time-to-solution at the strong-scale limit for a target efficiency of 80%, which is typical for production runs on the DOE's high-performance computing systems. Several examples of anomalous behavior are also discussed and analyzed.

97 MATHEMATICS AND COMPUTING↗

FEOTS v0.0.0: a new offline code for the fast equilibration of tracers in the ocean

Abstract. In this paper we introduce a new software framework for the offline calculation of tracer transport in the ocean. The Fast Equilibration of Ocean Tracers Software (FEOTS) is an end-to-end set of tools to efficiently calculate tracer distributions on a global or regional sub-domain using transport operators diagnosed from a comprehensive ocean model. To the best of our knowledge, this is the first application of a transport matrix model to an eddying ocean state. While a Newton–Krylov-based equilibration capability is still under development and not presented here, we demonstrate in this paper the transient modeling capabilities of FEOTS in an application focused on the Argentine Basin, where intense eddy activity and the Zapiola Anticyclone lead to strong mixing of water masses. The demonstration illustrates progress in developing offline passive tracer simulation capabilities, while highlighting the challenges of the impulse response functions approach in capturing tracer transports by a non-linear advection scheme. Our future work will focus on improving the computational efficiency of the code to reduce time-to-solution, using different basis functions to better represent non-linear advection operators, applying FEOTS to a parent model with unstructured grids (Ocean Model for Prediction Across Scales, MPAS-Ocean), and fully implementing a Newton–Krylov steady-state solver.

54 ENVIRONMENTAL SCIENCES↗

Optimization of Car Body under Constraints of Noise, Vibration, and Harshness (NVH), and Crash

To be competitive on the today's market, cars have to be as light as possible while meeting the Noise, Vibration, and Harshness (NVH) requirements and conforming to Government-man dated crash survival regulations. The latter are difficult to meet because they involve very compute-intensive, nonlinear analysis, e.g., the code RADIOSS capable of simulation of the dynamics, and the geometrical and material nonlinearities of a thin-walled car structure in crash, would require over 12 days of elapsed time for a single design of a 390K elastic degrees of freedom model, if executed on a single processor of the state-of-the-art SGI Origin2000 computer. Of course, in optimization that crash analysis would have to be invoked many times. Needless to say, that has rendered such optimization intractable until now. The car finite element model is shown. The advent of computers that comprise large numbers of concurrently operating processors has created a new environment wherein the above optimization, and other engineering problems heretofore regarded as intractable may be solved. The procedure, shown, is a piecewise approximation based method and involves using a sensitivity based Taylor series approximation model for NVH and a polynomial response surface model for Crash. In that method the NVH constraints are evaluated using a finite element code (MSC/NASTRAN) that yields the constraint values and their derivatives with respect to design variables. The crash constraints are evaluated using the explicit code RADIOSS on the Origin 2000 operating on 256 processors simultaneously to generate data for a polynomial response surface in the design variable domain. The NVH constraints and their derivatives combined with the response surface for the crash constraints form an approximation to the system analysis (surrogate analysis) that enables a cycle of multidisciplinary optimization within move limits. In the inner loop, the NVH sensitivities are recomputed to update the NVH approximation model while keeping the Crash response surface constant. In every outer loop, the Crash response surface approximation is updated, including a gradual increase in the order of the response surface and the response surface extension in the direction of the search. In this optimization task, the NVH discipline has 30 design variables while the crash discipline has 20 design variables. A subset of these design variables (10) are common to both the NVH and crash disciplines. In order to construct a linear response surface for the Crash discipline constraints, a minimum of 21 design points would have to be analyzed using the RADIOSS code. On a single processor in Origin 2000 that amount of computing would require over 9 months! In this work, these runs were carried out concurrently on the Origin 2000 using multiple processors, ranging from 8 to 16, for each crash (RADIOSS) analysis. Another figure shows the wall time required for a single RADIOSS analysis using varying number of processors, as well as provides a comparison of 2 different common data placement procedures within the allotted memories for each analysis. The initial design is an infeasible design with NVH discipline Static Torsion constraint violations of over 10%. The final optimized design is a feasible design with a weight reduction of 15 kg compared to the initial design. This work demonstrates how advanced methodology for optimization combined with the technology of concurrent processing enables applications that until now were out of reach because of very long time-to-solution.

Kodiyalam, Srinivas↗

An Analysis of Performance Enhancement Techniques for Overset Grid Applications

The overset grid methodology has significantly reduced time-to-solution of high-fidelity computational fluid dynamics (CFD) simulations about complex aerospace configurations. The solution process resolves the geometrical complexity of the problem domain by using separately generated but overlapping structured discretization grids that periodically exchange information through interpolation. However, high performance computations of such large-scale realistic applications must be handled efficiently on state-of-the-art parallel supercomputers. This paper analyzes the effects of various performance enhancement techniques on the parallel efficiency of an overset grid Navier-Stokes CFD application running on an SGI Origin2000 machine. Specifically, the role of asynchronous communication, grid splitting, and grid grouping strategies are presented and discussed. Results indicate that performance depends critically on the level of latency hiding and the quality of load balancing across the processors.

Djomehri, J. J.↗

Progress Toward Generation of a Navier-Stokes Database for a Harrier in Ground Effect

The Harrier YAV-8B aircraft is capable of vertical and short-field take-off and landing (V/STOL) by directing its four exhaust nozzles toward the ground, or conventional flight by rotating its nozzles into a horizontal position. The British Royal Air Force and the United States Marine Corps have used this aircraft for more than 30 years to provide a quick reaction time for troop support, and reduce the need for long runways. The success of this powered-lift (PL) vehicle has also prompted the more recent design of the Joint Strike Fighter (JSF). However there are significant safety issues that must be addressed when operating a PL vehicle in close proximity to the ground. Hot Gas Ingestion (HGI) by the inlets can result in a rapid loss of powered lift; and high-speed jet flows along the ground plane can induce low pressures underneath the vehicle, causing a 'suck-down' effect. Under these conditions, departure from controlled flight may occur. Moreover, unsteady ground vortices and jet fountains can affect the aircraft,s controllability and its proximity to ground troops. The viscous, time-dependent flow fields of PL vehicles are difficult to accurately and efficiently predict using Computational Fluid Dynamics (CFD). A number of researchers have used the time-dependent Reynolds-averaged Navier-Stokes (RANS) equations to compute flows for single and multiple jets in a cross-flow. A few have added some geometric complexity to the problem by computing flows for jet-augmented delta wings near a ground plane. Smith et.al. computed for the first time a single RANS solution about a simplified Harrier. This geometry included a fuselage, wing, leading edge root extension (LERX), inlets, and exhaust nozzles. All of these investigations cite two practical problems with computing these flows: 1) the need for improved solution accuracy; and, 2) the need for faster solution methods. We view the need for faster solution methods as key to improving the solution accuracy and making this class of computation more routine. One can hardly refine grids, explore the use of advanced turbulence models, and generate databases when it takes weeks of dedicated computer time for a single solution. Chaderjian, Ahmad, Pandya, and Murman have focused on reducing the time-to-solution for this very difficult and complex problem through process automation and exploitation of parallel computing. They began with the Harrier geometry reported, and added a deflected wing flap and empennage for greater realism. To date more than 80 solutions have been carried out. This paper will describe this process and progress made in reducing the time required to generate a simple longitudinal force and moment database for a Harrier in ground effect. It shows a typical snap-shot from an unsteady streakline animation, where fluid particles are colored by temperature. The ground vortex and a jet-fountain vortex are highlighted. It also shows a similar streakline image, where HGI occurs due to the vehicle in close proximity to the ground. It is show the mean lift coefficient as a function of angle of attack and height. The angle of attack range was 4 deg less than or = alpha less than or = 10 deg with an increment of 1 degree, and the height range was 10 ft less than or = h less than or = 30ft with an increment of 5 feet. This 35 solution database was extended to over 2500 cases using a monotone cubic-spline interpolation procedure. The suck-down effect (reduction of lift near the ground) is highlighted in the figure. The "cushion effect," the conventional reduction of lift as the vehicle moves out of ground effect, is also indicated. All 35 RANS solutions were obtained using 952 Silicon Graphics Origin 2000 and 3000 processors in dedicated mode for one week. Typically, 112 processors were assigned to each case. Some other cases used fewer processors to utilize all available CPUS. The final paper will report on the automation of the solution process, including: grid generation, job monitoring, solution completion criteria, and post processing. Moreover, improvements in parallel efficiency for a dual time-step algorithm for the RANS equations will also be presented. Results will be discussed in detail using unsteady streakline flow visualization to correlate unsteady flow structures with dominant aerodynamic frequencies. The stability derivatives, CL, and CL, will also be presented.

Chaderjian, Neal M.↗

Performance Enhancement Strategies for Multi-Block Overset Grid CFD Applications

The overset grid methodology has significantly reduced time-to-solution of highfidelity computational fluid dynamics (CFD) simulations about complex aerospace configurations. The solution process resolves the geometrical complexity of the problem domain by using separately generated but overlapping structured discretization grids that periodically exchange information through interpolation. However, high performance computations of such large-scale realistic applications must be handled efficiently on state-of-the-art parallel supercomputers. This paper analyzes the effects of various performance enhancement strategies on the parallel efficiency of an overset grid Navier-Stokes CFD application running on an SGI Origin2000 machinc. Specifically, the role of asynchronous communication, grid splitting, and grid grouping strategies are presented and discussed. Details of a sophisticated graph partitioning technique for grid grouping are also provided. Results indicate that performance depends critically on the level of latency hiding and the quality of load balancing across the processors.

Djomehri, M. Jahed↗

GEOS Atmospheric Model: Challenges at Exascale

The Goddard Earth Observing System (GEOS) model at NASA's Global Modeling and Assimilation Office (GMAO) is used to simulate the multi-scale variability of the Earth's weather and climate, and is used primarily to assimilate conventional and satellite-based observations for weather forecasting and reanalysis. In addition, assimilations coupled to an ocean model are used for longer-term forecasting (e.g., El Nino) on seasonal to interannual times-scales. The GMAO's research activities, including system development, focus on numerous time and space scales, as detailed on the GMAO website, where they are tabbed under five major themes: Weather Analysis and Prediction; Seasonal-Decadal Analysis and Prediction; Reanalysis; Global Mesoscale Modeling, and Observing System Science. A brief description of the GEOS systems can also be found at the GMAO website. GEOS executes as a collection of earth system components connected through the Earth System Modeling Framework (ESMF). The ESMF layer is supplemented with the MAPL (Modeling, Analysis, and Prediction Layer) software toolkit developed at the GMAO, which facilitates the organization of the computational components into a hierarchical architecture. GEOS systems run in parallel using a horizontal decomposition of the Earth's sphere into processing elements (PEs). Communication between PEs is primarily through a message passing framework, using the message passing interface (MPI), and through explicit use of node-level shared memory access via the SHMEM (Symmetric Hierarchical Memory access) protocol. Production GEOS weather prediction systems currently run at 12.5-kilometer horizontal resolution with 72 vertical levels decomposed into PEs associated with 5,400 MPI processes. Research GEOS systems run at resolutions as fine as 1.5 kilometers globally using as many as 30,000 MPI processes. Looking forward, these systems can be expected to see a 2 times increase in horizontal resolution every two to three years, as well as less frequent increases in vertical resolution. Coupling these resolution changes with increases in complexity, the computational demands on the GEOS production and research systems should easily increase 100-fold over the next five years. Currently, our 12.5 kilometer weather prediction system narrowly meets the time-to-solution demands of a near-real-time production system. Work is now in progress to take advantage of a hybrid MPI-OpenMP parallelism strategy, in an attempt to achieve a modest two-fold speed-up to accommodate an immediate demand due to increased scientific complexity and an increase in vertical resolution. Pursuing demands that require a 10- to 100-fold increases or more, however, would require a detailed exploration of the computational profile of GEOS, as well as targeted solutions using more advanced high-performance computing technologies. Increased computing demands of 100-fold will be required within five years based on anticipated changes in the GEOS production systems, increases of 1000-fold can be anticipated over the next ten years.

ESMF↗

Lattice Boltzmann and Navier-Stokes Cartesian CFD Approaches for Airframe Noise Predictions

Lattice Boltzmann (LB) and compressible Navier-Stokes (NS) equations based computational fluid dynamics (CFD) approaches are compared for simulating airframe noise. Both LB and NS CFD approaches are implemented within the Launch Ascent and Vehicle Aerodynamics (LAVA) framework. Both schemes utilize the same underlying Cartesian structured mesh paradigm with provision for local adaptive grid refinement and sub-cycling in time. We choose a prototypical massively separated, wake-dominated flow ideally suited for Cartesian-grid based approaches in this study - The partially-dressed, cavity-closed nose landing gear (PDCC-NLG) noise problem from AIAA's Benchmark problems for Airframe Noise Computations (BANC) series of workshops. The relative accuracy and computational efficiency of the two approaches are systematically compared. Detailed comments are made on the potential held by LB to significantly reduce time-to-solution for a desired level of accuracy within the context of modeling airframes noise from first principles.

Airframe Noise Prediction↗

Efficient Preconditioning of a High-Order Solver for Multiple Physics

This work addresses preconditioning approaches for an implicit high-order solver frame-work applied to multiple physics. The solver is based on a space-time spectral element method and matrix-free Newton-Krylov solver developed at NASA over the recent years. Within this context, most preconditioning methods are impractical, as the computational time and memory requirements scale poorly with increasing polynomial orders. To improve computational efficiency, we first describe a novel entity-based Block Jacobi preconditioner for the continuous-Galerkin solution of the linear-elasticity and linear-shell equations. Second, we introduce a multigrid algorithm to further reduce time-to-solution on stiff cases arising from continuous-and discontinuous-Galerkin discretizations. Results obtained on relevant single-physics reference solutions, demonstrate the feasibility of the methods, paving the way for high-order solutions of fully coupled multi-physics problems.

STMD↗