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AnisWave2D is a 2D finite-difference code for simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.
Modernizing SW4 for massively parallel time-domain simulations of earthquake ground motions in 3D earth models increases resolution and provides ground motion estimates for critical infrastructure risk evaluations. Simulations of ground motions from large (M ≥ 7.0) earthquakes require domains on the order of 100 to500 km and spatial granularity on the order of 1 to5 m resulting in hundreds of billions of grid points. Surface-focused structured mesh refinement (SMR) allows for more constant grid point per wavelength scaling in typical Earth models, where wavespeeds increase with depth. In fact, MR allows for simulations to double the frequency content relative to a fixed grid calculation on a given resource. The authors report improvements to the SW4 algorithm developed while porting the code to the Cori Phase 2 (Intel Xeon Phi) systems at the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory. As a result, investigations of the performance of the innermost loop of the calculations found that reorganizing the order of operations can improve performance for massive problems.
Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfiability modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.
Multigrid methods are optimal; that is, their rate of convergence is independent of the number of grid points, because they use a nested sequence of coarse grids to represent different scales of the solution. This nesting does, however, usually lead to certain restrictions of the permissible size of the discretised problem. In cases where the modeler is free to specify the whole problem, such constraints are of little importance because they can be taken into consideration from the outset. We consider the situation in which there are other competing constraints on the resolution. These restrictions may stem from the physical problem (e.g., if the discretised operator contains experimental data measured on a fixed grid) or from the need to avoid limitations set by the hardware. In this paper we discuss a modification to the cell-centered multigrid algorithm, so that it can be used br problems with any resolution. We discuss in particular a coarsening strategy and choice of intergrid transfer operators that can handle grids with both an even or odd number of cells. The method is described and applied to linear equations obtained by discretization of two- and three-dimensional second-order elliptic PDEs.
Knowledge of the plasma fluxes at geosynchronous orbit is important to both scientific and operational investigations. We present a new empirical model of the ion flux and the electron flux at geosynchronous orbit (GEO) in the energy range ~1 eV to ~40 keV. The model is based on a total of 82 satellite-years of observations from the Magnetospheric Plasma Analyzer instruments on Los Alamos National Laboratory satellites at GEO. These data are assigned to a fixed grid of 24 local-times and 40 energies, at all possible values of Kp. Bi-linear interpolation is used between grid points to provide the ion flux and the electron flux values at any energy and local-time, and for given values of geomagnetic activity (proxied by the 3-hour Kp index), and also for given values of solar activity (proxied by the daily F10.7 index). Initial comparison of the electron flux from the model with data from a Compact Environmental Anomaly Sensor II (CEASE-II), also located at geosynchronous orbit, indicate a good match during both quiet and disturbed periods. The model is available for distribution as a FORTRAN code that can be modified to suit user-requirements.
Here, the breakup of a periodic jet is examined computationally, using a front-tracking/finite-volume method, where the interface is represented by connected marker points moving with the fluid, while the governing equations are solved on a fixed grid. Tracking the interface allows control of whether topology changes take place or not. The Reynolds and Capillary numbers are kept relatively low ($Re = 150$ and $Ca = 2$) so most of the flow is well resolved. The effect of topology changes is examined by following the jet until it has mostly disintegrated, for different “coalescence criterion,” based on the thickness of thin films and threads. The evolution of both two-dimensional and fully three-dimensional flows is examined. It is found that although there is a significant difference between the evolution when no breakup takes place and when it does, once breakup takes place the evolution is relatively insensitive to exactly how it is triggered for a range of coalescence criterion, and any differences are mostly confined to the smallest scales.
A well-established numerical approach to solve the Navier-Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved, which is used to orthogonally project the velocity field to maintain the incompressibility constraint. In this paper, we develop a mathematical correspondence between Newtonian fluids in the incompressible limit and hypo-elastoplastic solids in the slow, quasi-static limit. Using this correspondence, we formulate a new fixed-grid, Eulerian numerical method for simulating quasi-static hypo-elastoplastic solids, whereby the stress is explicitly updated, and then an elliptic problem for the velocity is solved, which is used to orthogonally project the stress to maintain the quasi-staticity constraint. We develop a finite-difference implementation of the method and apply it to an elasto-viscoplastic model of a bulk metallic glass based on the shear transformation zone theory. We show that in a two-dimensional plane strain simple shear simulation, the method is in quantitative agreement with an explicit method. Like the fluid projection method, it is efficient and numerically robust, making it practical for a wide variety of applications. We also demonstrate that the method can be extended to simulate objects with evolving boundaries. Here, we highlight a number of correspondences between incompressible fluid mechanics and quasi-static elastoplasticity, creating possibilities for translating other numerical methods between the two classes of physical problems.
We use a suite of cosmological hydrodynamical simulations, run by two fixed grid codes, to investigate the properties of solenoidal and dilatational motions of the intergalactic medium (IGM) and the impact of numerical viscosity on turbulence in an ΛCDM universe. The codes differ only in the spatial difference discretization. We find that (1) The vortical motion grows rapidly since z = 2 and reaches ∼10 km s{sup –1}-90 km s{sup –1} at z = 0. Meanwhile, the small-scale compressive ratio r{sub CS} drops from 0.84 to 0.47, indicating comparable vortical and compressive motions at z = 0. (2) Power spectra of the solenoidal velocity possess two regimes, ∝k {sup –0.89} and ∝k {sup –2.02}, while the total and dilatational velocity follow the scaling k {sup –1.88} and k {sup –2.20}, respectively, in the turbulent range. The IGM turbulence may contain two distinct phases, the supersonic and post-supersonic phases. (3) The non-thermal pressure support, measured by the vortical kinetic energy, is comparable with the thermal pressure for ρ{sub b} ≅ 10-100, or T < 10{sup 5.5} K at z = 0.0. The deviation of the baryon fraction from the cosmic mean shows a preliminary positive correlation with the turbulence pressure support. (4) A relatively higher numerical viscosity would dissipate both the compressive and vortical motions of the IGM into thermal energy more effectively, resulting in less developed vorticity, remarkably shortened inertial range, and leading to a non-negligible uncertainty in the thermal history of gas accretion. Shocks in regions outside of clusters are significantly suppressed by numerical viscosity since z = 2, which may directly cause the different levels of turbulence between the two codes.
We present the results of two-dimensional (2D) hydrodynamical simulations of circumbinary disk accretion using the finite-volume code DISCO. This code solves the 2D viscous Navier-Stokes equations on a high-resolution moving mesh which shears with the fluid flow, greatly reducing advection errors in comparison with a fixed grid. We perform a series of simulations for binary mass ratios in the range 0.026 ≤ q ≤ 1.0, each lasting longer than a viscous time so that we reach a quasi-steady accretion state. In each case, we find that gas is efficiently stripped from the inner edge of the circumbinary disk and enters the cavity along accretion streams, which feed persistent 'mini disks' surrounding each black hole. We find that for q ≳ 0.1, the binary excites eccentricity in the inner region of the circumbinary disk, creating an overdense lump which gives rise to enhanced periodicity in the accretion rate. The dependence of the periodicity on mass ratio may provide a method for observationally inferring mass ratios from measurements of the accretion rate. We also find that for all mass ratios studied, the magnitude of the accretion onto the secondary is sufficient to drive the binary toward larger mass ratio. This suggests a mechanism for biasing mass-ratio distributions toward equal mass.
We provide an explicit recursive divide-and-conquer approach for simulating quantum dynamics and derive a discrete first-quantized nonrelativistic QED Hamiltonian based on the many-particle Pauli-Fierz Hamiltonian. We apply this recursive divide-and-conquer algorithm to this Hamiltonian and compare it to a concrete simulation algorithm that uses qubitization. Our divide-and-conquer algorithm, using lowest-order Trotterization, scales for fixed grid spacing as O ~ ( Λ N 2 η 2 t 2 / ϵ ) for grid size N , η particles, simulation time t , field cutoff Λ , and error ϵ . Our qubitization algorithm scales as O ~ ( N ( η + N ) ( η + Λ 2 ) t log ( 1 / ϵ ) ) . This shows that even a naive partitioning and low-order splitting formula can yield, through our divide-and-conquer formalism, superior scaling to qubitization for large Λ . We compare the relative costs of these two algorithms on systems that are relevant for applications such as the spontaneous emission of photons and the photoionization of electrons. We observe that for different parameter regimes, one method can be favored over the other. Finally, we give new algorithmic and circuit-level techniques for gate optimization, including a new way of implementing a group of multicontrolled- X gates that can be used for better analysis of circuit cost. Published by the American Physical Society 2024
The automotive industry’s pursuit of Level 5 autonomy is constrained by substantial perception-compute power requirements, often reaching 1, 000 + watts in full autonomy stacks. Reducing this energy burden requires rethinking perception not only at the high-end autonomy level, but also at the foundational Advanced Driver Assistance Systems (ADAS) level where low-power, safety-critical sensing can have broad impact. Neuromorphic vision provides a promising starting point: HD Dynamic Vision Sensors (DVS) can operate below 100 mW at the sensor level by reporting only asynchronous brightness changes. However, low-power sensing alone is insufficient if downstream perception reintroduces dense, energy-intensive computation. In particular, many event-driven object-detection pipelines still rely on CNN backbones, while purely spiking alternatives often trade away accuracy or ignore deployment constraints. We introduce ObstacleSense, a highly compact, CNN-free hybrid ANN–SNN framework for Level 0–1 forward-corridor obstacle awareness. Instead of performing full-scene object detection with a convolutional feature backbone, ObstacleSense targets the safety-critical question of whether the ego corridor is occupied and how far the nearest obstacle is. The architecture combines polarity-conditioned event encoding, lightweight temporal spiking dynamics, axial spatial mixing, and coarse-to-fine range estimation within a regular fixed-grid compute pattern. This design avoids the dense CNN backbone commonly used in event-based detection while maintaining a small state footprint suitable for eventual small-FPGA deployment. Before hardware mapping, we evaluate the software implementation using a model-side power proxy derived from MACs, weight and activation traffic, and spiking state updates under shared FP16 assumptions. On simulated CARLA event corpora, the deployment-oriented model achieves 0.9464 objectness F1, 0.9978 grid-level mAP, and 0.8987 m distance Mean Absolute Error at an estimated 1.92 mW proxy cost, while maintaining performance on unseen generalization test sequences.
This program provides a fixed-grid quadrature algorithm to compute integrals in the self-energy of the quark propagator within the Maris-Tandy model. The quark propagator both on t he spacelike real axis and at complex-valued momenta is determined from its Schwinger-Dyson equation (SDE). We first apply an iterative solver to find the quark propagator on the spacelike real axis. The propagator at complex-valued momenta is then computed from its self-energy based on this solution, where demanding integrals are encountered. In order to compute of these integrals, we apply customized variable transformations for the radial integral after subtracting the asymptotics. We subsequently apply an optional compound of quadrature rules for the angular integral.
This report will discuss new capabilities that have been added to the sample.py and uniform_sampler.py codes. The codes have been updated to allow for both log-uniform sampling and categorical variables. The categorical variables do not have to be numeric. The different values for a categorical variable are specified in a limits file by having spaces between them. The difference between sample.py and uniform_sampler.py is that sample.py is for generating random samples and uniform_sampler.py is for generating samples or points on a fixed grid. After sourcing a file to set the environment, execute the codes with the commands: sample.py and uniform sampler.py .
In this paper, evidence is presented for the existence of multiple solutions of Reynolds-averaged Navier–Stokes equations with the one-equation Spalart–Allmaras and two-equation Wilcox $k-ω$ turbulence models on fixed grids in three dimensions and how they were obtained is described. The two major configurations considered are an “academic” extruded two-dimensional airfoil geometry and the trap wing test case. The observed appearance of the multiple solutions seems to be closely related to smooth body separation (sometimes massive) routinely observed in flows over high-lift configurations, especially near stall angles of attack. The results are obtained and cross-verified with two stabilized finite-element codes (streamwise upwind Petrov–Galerkin), which provide residual converged results for complex flows with second-order discretizations. In the paper, the ways multiple solutions have been obtained are described, including such obvious ones as providing a different initial guess to the steady-state solver as well as somewhat unexpected (in this context) techniques of using implicit residual smoothing while time marching to steady state. The phenomenon of the so-called pseudosolutions is also discussed, which is loosely defined as solutions to the discrete system of equations having “sharp” convergence behavior (sometimes up to six to seven orders of the relative residual reduction), which fail to achieve the stronger, machine-zero convergence criterion. Some numerical observations are also presented on the sensitivity of the obtained multiple solutions to the discretization and grid perturbations.
An experimental cockpit mounted head-up type display system was developed and evaluated by LaRC pilots during the landing phase of light aircraft operations. The Landing Site Indicator (LASI) system display consists of angle of attack, angle of sideslip, and indicated airspeed images superimposed on the pilot's view through the windshield. The information is made visible to the pilot by means of a partially reflective viewing screen which is suspended directly in frot of the pilot's eyes. Synchro transmitters are operated by vanes, located at the left wing tip, which sense angle of attack and sideslip angle. Information is presented near the center of the display in the form of a moving index on a fixed grid. The airspeed is sensed by a pitot-static pressure transducer and is presented in numerical form at the top center of the display.
Numerical techniques for assessing and certifying the accuracy of the modeling of partial differential equations (PDE) to the user's specifications are analyzed. Examples of the certification process with conventional techniques are summarized for the three dimensional steady state full potential and the two dimensional steady Navier-Stokes equations using fixed grid methods (FG). The advantages of the Full Approximation Storage (FAS) scheme of the multigrid technique of A. Brandt compared with the conventional certification process of modeling PDE are illustrated in one dimension with the transformed potential equation. Inferences are drawn for how MG will improve the certification process of the numerical modeling of two and three dimensional PDE systems. Elements of the error assessment process that are common to FG and MG are analyzed.
A numerical procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by using better approximations of the truncation error computed from local subdomain grid refinements. This technique is used to obtain refined solutions of steady, inviscid, transonic flow past a wedge. The effects of truncation error on the pressure distribution, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and wave drag due to the shocks, a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.