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The software provides Ipopt optimization package an interface to the Re::Solve linear solver library. Re::Solve features GPU-resident direct and iterative linear solvers that could be used to accelerate optimization computations.
Integration of the Control Allocation technique to recover from Pilot Induced Oscillations (CAPIO) System into the control system of a Short Takeoff and Landing Mobility Concept Vehicle simulation presents a challenge because the CAPIO formulation requires that constrained optimization problems be solved at the controller operating frequency. We present a solution that utilizes a modified version of the well-known L-BFGS-B solver. Despite the iterative nature of the solver, the method is seen to converge in real time with sufficient reliability to support three weeks of piloted runs at the NASA Ames Vertical Motion Simulator (VMS) facility. The results of the optimization are seen to be excellent in the vast majority of real-time frames. Deficiencies in the quality of the results in some frames are shown to be improvable with simple termination criteria adjustments, though more real-time optimization iterations would be required.
AIRPLANE (Jameson/Baker) is a steady inviscid unstructured Euler flow solver. It has been validated on many HSR geometries. It is implemented as MESHPLANE, an unstructured mesh generator, and FLOPLANE, an iterative flow solver. The surface description from an Intergraph CAD system goes into MESHPLANE as collections of polygonal curves to generate the 3D mesh. The flow solver uses a multistage time stepping scheme with residual averaging to approach steady state, but R is not time accurate. The flow solver was ported from Cray to IBM SP2 by Wu-Sun Cheng (IBM); it could only be run on 4 CPUs at a time because of memory limitations. Meshes for the four cases had about 655,000 points in the flow field, about 3.9 million tetrahedra, about 77,500 points on the surface. The flow solver took about 23 wall seconds per iteration when using 4 CPUs. It took about eight and a half wall hours to run 1,300 iterations at a time (the queue limit is 10 hours). A revised version of FLOPLANE (Thomas) was used on up to 64 CPUs to finish up some calculations at the end. We had to turn on more communication when using more processors to eliminate noise that was contaminating the flow field; this added about 50% to the elapsed wall time per iteration when using 64 CPUs. This study involved computing lift and drag for a wing/body/nacelle configuration at Mach 0.9 and 4 degrees pitch. Four cases were considered, corresponding to four nacelle mass flow conditions.
A new open-source code for the simulation of the diffusion flamelet equations is proposed. Emphasis is placed on using an approximate Jacobian to reduce the computational cost of the matrix operations. Performance of the proposed solvers is tested by performing flamelet calculations with kinetic mechanisms of varying sizes. For the unity Lewis number equations, the present iterative Newton solver using an approximate Jacobian greatly outperforms direct Newton solvers using exact Jacobians. The computation cost scales linearly with the number of species, leading to a reduction in solution times by two orders of magnitude for mechanisms containing thousands of species. The applicability of the Jacobian approximations to the solution of the non-unity Lewis number flamelet equations is assessed. The approximations are generally inadequate to solve the full non-unity Lewis number equations but can be used in some applications depending on the balance of terms in the flamelet equations. As an example, the flamelet solver is applied to the study of sooting tendencies in laminar co-flow diffusion flames where modified non-unity Lewis number flamelet equations, previously shown to accurately reproduce experimentally-measured Yield Sooting Indices (YSI), are solved. Here, the accelerated flamelet solver is well suited for sensitivity analysis and uncertainty quantification with large detailed kinetic mechanisms, tasks for which the computational cost was previously prohibitive.
The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.
The objective of MULTI-LEADER is to cut design costs by 80% while generating more energy-efficient designs of multi-stage compressors by developing and implementing novel machine learning (ML) techniques, which enable faster and fewer design iterations, improved solver performance, and concurrent multi-disciplinary design. Current industrial practices for the design of multi-stage compressors involve simulation-based design optimization with successive levels of model fidelity, iteratively evaluated between distinct disciplines, one stage at a time to tackle the high dimensional design variations. This project addresses these key design challenges: (1) concurrent optimization of multiple stages under many non-linear constraints; (2) multitude of evaluation of high-fidelity and expensive solvers and their gradients during optimization convergence in high-dimensional design; (3) multi-disciplinary design to maximize aerodynamic performance while guaranteeing structural integrity and additive manufacturability; (4) utilization of multiple fidelity of solvers with disparate parameterization and modeling assumptions. MULTI-LEADER achieved more than 5x speed up in detailed design of more energy-efficient compressors via these machine learning (ML) innovations: (i) rapid design surrogates by multi-source learning from diverse fidelities across multiple disciplines, (ii) physics-constrained data-augmented modeling for improved empiricism, (iii) generative manifold embedding for high dimensional concurrent design without gradient information; (iv) budget-constrained fidelity-adaptive sampling towards fewer design iterations.
Iterative memory-bound solvers commonly occur in HPC codes. Typical GPU implementations have a loop on the host side that invokes the GPU kernel as much as time/algorithm steps there are. The termination of each kernel implicitly acts the barrier required after advancing the solution every time step. We propose an execution model for running memory-bound iterative GPU kernels: PERsistent KernelS (PERKS). In this model, the time loop is moved inside persistent kernel, and device-wide barriers are used for synchronization. We then reduce the traffic to device memory by caching subset of the output in each time step in the unused registers and shared memory. PERKS can be generalized to any iterative solver: they largely independent of the solver's implementation. We explain the design principle of PERKS and demonstrate effectiveness of PERKS for a wide range of iterative 2D/3D stencil benchmarks (geomean speedup of 2.12x for 2D stencils and 1.24x for 3D stencils over state-of-art libraries), and a Krylov subspace conjugate gradient solver (geomean speedup of 4.86x in smaller SpMV datasets from SuiteSparse and 1.43x in larger SpMV datasets over a state-of-art library). All PERKS-based implementations available at: https://github.com/neozhang307/PERKS.
Abstract Low precision arithmetic, in particular half precision (16‐bit) floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings in energy. Motivated by this, there has been a renewed interest in mixed precision iterative refinement schemes for solving linear systems , and new variants of GMRES‐based iterative refinement have been developed. Each particular variant with a given combination of precisions leads to different condition number‐based constraints for convergence of the backward and forward errors, and each has different performance costs. The constraints for convergence given in the literature are, as an artifact of the analyses, often overly strict in practice, and thus could lead a user to select a more expensive variant when a less expensive one would have sufficed. In this work, we develop a multistage mixed precision iterative refinement solver which aims to combine existing mixed precision approaches to balance performance and accuracy and improve usability. For a user‐specified initial combination of precisions, the algorithm begins with the least expensive approach and convergence is monitored via inexpensive computations with quantities produced during the iteration. If slow convergence or divergence is detected using particular stopping criteria, the algorithm switches to use a more expensive, but more reliable variant. A novel aspect of our approach is that, unlike existing implementations, our algorithm first attempts to use “stronger” GMRES‐based solvers for the solution update before resorting to increasing the precision(s). In some scenarios, this can avoid the need to refactorize the matrix in higher precision. We perform extensive numerical experiments on a variety of random dense problems and problems from real applications which confirm the benefits of the multistage approach.
The talk will discuss current work in developing and applying the INS2D and INS3D flow solvers to problems in high-lift aerodynamics, primarily multi-element airfoils. These flow solvers solve the incompressible Navier-Stokes equations using the method of artificial compressibility. High-lift system flowfields are perhaps the most challenging aeronautical configurations for CFD. Difficulties with convergence for multi-element configurations using fine-grid overset meshes has led to research in using Krylov-space iterative matrix solvers. In particular, a Generalized Minimum Residual (GMRES) solver has found to be a dramatic improvement over a previously used Gauss-Seidal line-relaxation solver.
RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.
A digital adaptive controller is applied to the active flutter suppression problem of a wing under time varying flight conditions in subsonic and transonic flow. Linear quadratic controller gain at each time step is obtained using an iterative Riccati solver. The digital adaptive optimal controller is robust with respect to the unknown external loads. Flutter and divergence instabilities are simultaneously suppressed using a trailing-edge control surface and displacement sensing. A new transonic unsteady aerodynamic approximation methodology is developed which enables one to carry out the rapid calculation required for transonic aeroservoelastic applications. This approximation is based on a combination of unsteady subsonic aerodynamics combined with a transonic correction procedure. Aeroservoelastic transient time response is obtained using Roger's approximation, state transition matrices and an iterative time marching algorithm. The aeroservoelastic system in the time domain is modeled using a deterministic ARMA model together with a parameter estimator. Transonic flutter boundaries of a wing structure are computed, in the time domain, using an estimated aeroelastic system matrix and are in good agreement with experimental data for the low transonic Mach number range.
This paper studies the shallow Ritz method for solving the one-dimensional diffusion problem. It is shown that the shallow Ritz method improves the order of approximation dramatically for non-smooth problems. To realize this optimal or nearly optimal order of the shallow Ritz approximation, we develop a damped block Newton (dBN) method that alternates between updates of the linear and non-linear parameters. Per each iteration, the linear and the non-linear parameters are updated by exact inversion and one step of a modified, damped Newton method applied to a reduced non-linear system, respectively. The computational cost of each dBN iteration is $\mathcal{O}$(n). Starting with the non-linear parameters as a uniform partition of the interval, numerical experiments show that the dBN is capable of efficiently moving mesh points to nearly optimal locations. In conclusion, to improve the efficiency of the dBN further, we propose an adaptive damped block Newton (AdBN) method by combining the dBN with the adaptive neuron enhancement (ANE) method [28].
The original Tepla (TEnsile PLAsticity) ductile damage model, based on the Gurson yield surface, has long been used to model damage evolution and material failure under dynamic loading. Unfortunately, Tepla suffered from mesh sensitivity, numerical instability, and limited predictive capability. Here, we theoretically reformulate Tepla to address these issues. We especially focus on the prediction of porosity, which is the key state variable used for modeling ductile damage, as compared to more easily measured surface velocities, which are at best an indirect measure of damage. Key model changes include separating the viscosity during volumetric void growth from underlying shear strength behavior and switching to an iterative bisection solver. The new Tepla is then calibrated on incipient spall experiments on half-hard copper and tantalum, which demonstrate its ability to simultaneously fit the model to recovered porosity distributions and measured surface velocities, a stringent test. Improved numerical behavior, such as greatly reduced mesh sensitivity, is also shown in those simulations. Finally, the new Tepla model is applied to several high-explosive loaded, sweeping wave experiments, showing the ability of the model to predict behavior on tests with significantly different loading conditions and histories than the calibration data.
Mitigation of failure modes in the continuous synthesis (CS) of a drug substance (DS) has the potential to widen the adoption of continuous manufacturing (CM) technologies by the pharmaceutical industry. Here, this work demonstrates the development of a robust continuous process for the synthesis of carbamazepine (CBZ), an essential medicine as per the World Health Organization (WHO), facilitated by kinetic modelling and monitored by in-line Raman spectroscopy. Accurate kinetic modelling and the use of validated process analytical technology (PAT) models for quantitative measurement were found to play an important role in developing CS of drug substances. Kinetic data for the formation of CBZ from iminostilbene (ISB) were collected by batch reaction sampling and high-performance liquid chromatography (HPLC) analysis. A non-linear solver and iterative method was applied to determine two sets of Arrhenius parameters simultaneously for the reaction system by minimizing the standard error of the model fit. The start-up and dynamic equilibrium stages for the CS of CBZ using a continuous stirred tank reactor (CSTR) were modelled based on the batch kinetic data and employed to optimize conversion and simulate process disturbances. An in-line Raman spectroscopy method was successfully developed, validated, and integrated to determine the concentrations of CBZ and ISB within the operating range for the CS. The CS kinetic model was evaluated experimentally from startup to dynamic equilibrium over 10 residence times with monitoring by HPLC and in-line Raman spectroscopy. The developed kinetic model in tandem with in-line Raman spectroscopy successfully predicted disturbances due to changes in process variables and can serve as a useful tool in the future design of advanced process control strategies for the continuous synthesis of CBZ.
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We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly-bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. Here, these methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.
In this paper, we present spectral equivalence results for high-order tensor product edge- and face-based finite elements for the H(curl) and H(div) function spaces. Specifically, we show for certain choices of shape functions that the mass and stiffness matrices of the high-order elements are spectrally equivalent to those for an assembly of low-order elements on the associated Gauss--Lobatto--Legendre mesh. Based on this equivalence, efficient preconditioners can be designed with favorable computational complexity. Numerical results are presented which confirm the theory and demonstrate the benefits of the equivalence results for overlapping Schwarz preconditioners.
GCAM assumptions typically generate scenarios that are designed to be internally consistent and globally coherent. The gcamdata tool which facilitates the compilation of data sets and user assumptions is not well suited to tailoring to specific country or regional realities, sponsor requirements, or perform harmonization for model intercomparison needs. As described in this report, the GCAM Regional Tuning project develops a computational framework that enables users to adjust GCAM parameters, so model outputs match targeted outcomes at user-defined spatial, temporal, and sectoral resolutions. The framework integrates GCAM, gcamdata, and gcamwrapper with a set of flexible “tuning directives” and an iterative numerical solver. Users can define targets (e.g., technology shares in power generation, BEV uptake, sectoral service demands), select tuners that manipulate relevant GCAM parameters (e.g., share weights, cost adders, elasticities), and export tuned parameters as reusable GCAM XML inputs for future runs. We demonstrate the approach and document usage, diagnostics, and known limitations, and we outline potential future directions.