241 research outputs found

    A Deep Learning algorithm to accelerate Algebraic Multigrid methods in Finite Element solvers of 3D elliptic PDEs

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    Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most severe limitation of AMG methods is the dependence on parameters that require to be fine-tuned. In particular, the strong threshold parameter is the most relevant since it stands at the basis of the construction of successively coarser grids needed by the AMG methods. We introduce a novel Deep Learning algorithm that minimizes the computational cost of the AMG method when used as a finite element solver. We show that our algorithm requires minimal changes to any existing code. The proposed Artificial Neural Network (ANN) tunes the value of the strong threshold parameter by interpreting the sparse matrix of the linear system as a black-and-white image and exploiting a pooling operator to transform it into a small multi-channel image. We experimentally prove that the pooling successfully reduces the computational cost of processing a large sparse matrix and preserves the features needed for the regression task at hand. We train the proposed algorithm on a large dataset containing problems with a highly heterogeneous diffusion coefficient defined in different three-dimensional geometries and discretized with unstructured grids and linear elasticity problems with a highly heterogeneous Young's modulus. When tested on problems with coefficients or geometries not present in the training dataset, our approach reduces the computational time by up to 30%

    Vortex motions in the solar atmosphere

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    Vortex flows, related to solar convective turbulent dynamics at granular scales and their interplay with magnetic fields within intergranular lanes, occur abundantly on the solar surface and in the atmosphere above. Their presence is revealed in high-resolution and high-cadence solar observations from the ground and from space and with state-of-the-art magnetoconvection simulations. Vortical flows exhibit complex characteristics and dynamics, excite a wide range of different waves, and couple different layers of the solar atmosphere, which facilitates the channeling and transfer of mass, momentum and energy from the solar surface up to the low corona. Here we provide a comprehensive review of documented research and new developments in theory, observations, and modelling of vortices over the past couple of decades after their observational discovery, including recent observations in Hα , innovative detection techniques, diverse hydrostatic modelling of waves and forefront magnetohydrodynamic simulations incorporating effects of a non-ideal plasma. It is the first systematic overview of solar vortex flows at granular scales, a field with a plethora of names for phenomena that exhibit similarities and differences and often interconnect and rely on the same physics. With the advent of the 4-m Daniel K. Inouye Solar Telescope and the forthcoming European Solar Telescope, the ongoing Solar Orbiter mission, and the development of cutting-edge simulations, this review timely addresses the state-of-the-art on vortex flows and outlines both theoretical and observational future research directions

    Vortex Motions in the Solar Atmosphere: Definitions, Theory, Observations, and Modelling

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    Vortex flows, related to solar convective turbulent dynamics at granular scales and their interplay with magnetic fields within intergranular lanes, occur abundantly on the solar surface and in the atmosphere above. Their presence is revealed in high-resolution and high-cadence solar observations from the ground and from space and with state-of-the-art magnetoconvection simulations. Vortical flows exhibit complex characteristics and dynamics, excite a wide range of different waves, and couple different layers of the solar atmosphere, which facilitates the channeling and transfer of mass, momentum and energy from the solar surface up to the low corona. Here we provide a comprehensive review of documented research and new developments in theory, observations, and modelling of vortices over the past couple of decades after their observational discovery, including recent observations in Hα, innovative detection techniques, diverse hydrostatic modelling of waves and forefront magnetohydrodynamic simulations incorporating effects of a non-ideal plasma. It is the first systematic overview of solar vortex flows at granular scales, a field with a plethora of names for phenomena that exhibit similarities and differences and often interconnect and rely on the same physics. With the advent of the 4-m Daniel K. Inouye Solar Telescope and the forthcoming European Solar Telescope, the ongoing Solar Orbiter mission, and the development of cutting-edge simulations, this review timely addresses the state-of-the-art on vortex flows and outlines both theoretical and observational future research directions

    Space-Time Block Preconditioning for Incompressible Resistive Magnetohydrodynamics

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    This work develops a novel all-at-once space-time preconditioning approach for resistive magnetohydrodynamics (MHD), with a focus on model problems targeting fusion reactor design. We consider parallel-in-time due to the long time domains required to capture the physics of interest, as well as the complexity of the underlying system and thereby computational cost of long-time integration. To ameliorate this cost by using many processors, we thus develop a novel approach to solving the whole space-time system that is parallelizable in both space and time. We develop a space-time block preconditioning for resistive MHD, following the space-time block preconditioning concept first introduced by Danieli et al. in 2022 for incompressible flow, where an effective preconditioner for classic sequential time-stepping is extended to the space-time setting. The starting point for our derivation is the continuous Schur complement preconditioner by Cyr et al. in 2021, which we proceed to generalise in order to produce, to our knowledge, the first space-time block preconditioning approach for the challenging equations governing incompressible resistive MHD. The numerical results are promising for the model problems of island coalescence and tearing mode, with the overhead computational cost associated with space-time preconditioning versus sequential time-stepping being modest and primarily in the range of 2x-5x, which is low for parallel-in-time schemes in general. Additionally, the scaling results for inner (linear) and outer (nonlinear) iterations are flat in the case of fixed time-step size and only grow very slowly in the case of time-step refinement.Comment: 25 pages, 4 figures, 3 table

    Monolithic multigrid methods for high-order discretizations of time-dependent PDEs

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    A currently growing interest is seen in developing solvers that couple high-fidelity and higher-order spatial discretization schemes with higher-order time stepping methods for various time-dependent fluid plasma models. These problems are famously known to be stiff, thus only implicit time-stepping schemes with certain stability properties can be used. Of the most powerful choices are the implicit Runge-Kutta methods (IRK). However, they are multi-stage, often producing a very large and nonsymmetric system of equations that needs to be solved at each time step. There have been recent efforts on developing efficient and robust solvers for these systems. We have accomplished this by using a Newton-Krylov-multigrid approach that applies a multigrid preconditioner monolithically, preserving the system couplings, and uses Newton’s method for linearization wherever necessary. We show robustness of our solver on the single-fluid magnetohydrodynamic (MHD) model, along with the (Navier-)Stokes and Maxwell’s equations. For all these, we couple IRK with higher-order (mixed) finiteelement (FEM) spatial discretizations. In the Navier-Stokes problem, we further explore achieving more higher-order approximations by using nonconforming mixed FEM spaces with added penalty terms for stability. While in the Maxwell problem, we focus on the rarely used E-B form, where both electric and magnetic fields are differentiated in time, and overcome the difficulty of using FEM on curved domains by using an elasticity solve on each level in the non-nested hierarchy of meshes in the multigrid method

    The Fifteenth Marcel Grossmann Meeting

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    The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

    Hermes-3: Multi-component plasma simulations with BOUT++

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    A new open source tool for fluid simulation of multi-component plasmas is presented, based on a flexible software design that is applicable to scientific simulations in a wide range of fields. This design enables the same code to be configured at run-time to solve systems of partial differential equations in 1D, 2D or 3D, either for transport (steady-state) or turbulent (time-evolving) problems, with an arbitrary number of ion and neutral species. To demonstrate the capabilities of this tool, applications relevant to the boundary of tokamak plasmas are presented: 1D simulations of diveror plasmas evolving equations for all charge states of neon and deuterium; 2D transport simulations of tokamak equilibria in single-null X-point geometry with plasma ion and neutral atom species; and simulations of the time-dependent propagation of plasma filaments (blobs). Hermes-3 is publicly available on Github under the GPL-3 open source license. The repository includes documentation and a suite of unit, integrated and convergence tests.Comment: Submitted to Computer Physics Communication

    Bosonic fields in strong-field gravity

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    In this thesis, we investigate bosonic fields in the strong-field and highly dynamical regime of general relativity focusing specifically on the black hole superradiance process of scalar and vector fields, as well as on the nonlinear dynamics of isolated and binary scalar boson stars. In the first part of this thesis, we lay the foundation to use boson stars as a particularly simple model to explore the dynamical behavior of inspiraling and merging ultra compact and black hole mimicking objects. To that end, we construct self-consistent initial data describing isolated and binary star configurations and subsequently utilizing numerical evolutions of the full Einstein-Klein-Gordon system of equations to explore this dynamical behavior. We investigate the linear stability properties of families of rotating stars in scalar theories with various types of self-interactions. Using numerical evolutions, we find that a linear instability present in rotating boson star solutions within linear scalar theories is quenched by nonlinear scalar interactions in a subset of stars. Furthermore, utilizing the conformal thin-sandwich formalism, we numerically construct generic binary boson star initial data satisfying the constraints of the Einstein equations. We adapt existing and introduce new methods, to initial data quality, as well as reduce residual orbital eccentricity. With these methods, we were able to generate self-consistent inspiral-merger-ringdown gravitational waveforms of eccentricity-reduced binary boson stars, for the first time. Lastly, scalar self-interactions may delay the merger time of identical inspiraling binary star configurations, or drive the system to an entirely different end state. In particular, we show explicitly that rotating boson stars can form during the merger of two non-spinning stars. In the second part of this thesis, we focus on how well-motivated ultralight scalar and vector bosons, extending the Standard Model of particle physics, can be probed through the observable signatures of the black hole superradiance process. Energy and angular momentum are extracted from a black hole via this mechanism, are deposited in an oscillating bosonic cloud, and finally dissipated through gravitational wave emission from the system. Here, we introduce the gravitational waveform model, SuperRad, modeling the cloud’s oscillation frequency, growth and decay timescales, as well as the amplitude and phase evolution of the emitted gravitational radiation, for both scalar and vector boson clouds. This model combines state of the art analytical results with numerical computations to provide the most accurate predictions across the relevant parameter space. Moreover, we investigate the impact of a non-vanishing kinetic mixing between an ultralight vector boson forming a superradiant cloud and the Standard Model photon. Such mixing robustly results in the formation of a highly turbulent pair plasma within the bosonic cloud. We characterize the associated electromagnetic signatures and devise strategies to observe such signatures through multi-messenger observation campaigns

    Investigation of ultra-intense laser interactions with long scale length pre-plasmas and nanowire targets via escaped fast electrons

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    In this thesis the results of two experimental campaigns investigating the performance of novel nanowire targets via escaping fast electrons at the target rear surface are presented. An initial experiment was carried out to diagnose the efficiency of laser interactions with nanowire coated and planar targets using imaging of coherent transition radiation (CTR) emission induced by exiting fast electrons. This experiment was subject to an intense pre- pulse of intensity I ∼ 10 17 W/cm^2 irradiating the targets prior to the arrival of the main laser pulse. Hydrodynamic simulations demonstrate the pre-pulse irradiation launched a shock-wave into the target, disrupting the rear surface of the thinner targets. CTR emission was still observed experimentally from these thinner targets, despite the significant target expansion. Particle-in-cell simulations are used to show the scale length of the density disruption was short enough to retain the efficient production of CTR emission in the optical regime. In addition, the hydrodynamic simulations revealed the formation of an extended pre-plasma at the front surface of the targets. This is predicted to facilitate the generation of super-ponderomotive electrons, beneficial towards the production of CTR. Remarkably, under these non-ideal conditions an increase in CTR emission was observed for a subset of shots on the nanowire coated targets compared to planar targets. This result is explained by proposing a less dense, longer scale length pre-plasma is produced from the nanowires, expediting the production of fast electrons with a greater hot electron temperature. A subsequent experiment aimed to realise a high contrast laser interaction with nanowires through the use of a frequency doubled laser pulse. In this campaign a pepper-pot diagnostic was employed to measure the emittance of the exiting fast electron beam, a novel measurement for nanowire targets. The results indicate fast electrons with a greater emittance are obtained from the nanowire targets relative to planar targets. Particle-in-cell simulations are carried out that predict a greater transverse momenta of fast electrons from the nanowire targets, supporting this conclusion
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