47 research outputs found
A Scalable Two-Level Domain Decomposition Eigensolver for Periodic Schr\"odinger Eigenstates in Anisotropically Expanding Domains
Accelerating iterative eigenvalue algorithms is often achieved by employing a
spectral shifting strategy. Unfortunately, improved shifting typically leads to
a smaller eigenvalue for the resulting shifted operator, which in turn results
in a high condition number of the underlying solution matrix, posing a major
challenge for iterative linear solvers. This paper introduces a two-level
domain decomposition preconditioner that addresses this issue for the linear
Schr\"odinger eigenvalue problem, even in the presence of a vanishing
eigenvalue gap in non-uniform, expanding domains. Since the quasi-optimal
shift, which is already available as the solution to a spectral cell problem,
is required for the eigenvalue solver, it is logical to also use its associated
eigenfunction as a generator to construct a coarse space. We analyze the
resulting two-level additive Schwarz preconditioner and obtain a condition
number bound that is independent of the domain's anisotropy, despite the need
for only one basis function per subdomain for the coarse solver. Several
numerical examples are presented to illustrate its flexibility and efficiency.Comment: 30 pages, 7 figures, 2 table
Bosonic fields in strong-field gravity
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
EQUADIFF 15
Equadiff 15 – Conference on Differential Equations and Their Applications – is an international conference in the world famous series Equadiff running since 70 years ago. This booklet contains conference materials related with the 15th Equadiff conference in the Czech and Slovak series, which was held in Brno in July 2022. It includes also a brief history of the East and West branches of Equadiff, abstracts of the plenary and invited talks, a detailed program of the conference, the list of participants, and portraits of four Czech and Slovak outstanding mathematicians
Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
Quantum computers offer an intriguing path for a paradigmatic change of
computing in the natural sciences and beyond, with the potential for achieving
a so-called quantum advantage, namely a significant (in some cases exponential)
speed-up of numerical simulations. The rapid development of hardware devices
with various realizations of qubits enables the execution of small scale but
representative applications on quantum computers. In particular, the
high-energy physics community plays a pivotal role in accessing the power of
quantum computing, since the field is a driving source for challenging
computational problems. This concerns, on the theoretical side, the exploration
of models which are very hard or even impossible to address with classical
techniques and, on the experimental side, the enormous data challenge of newly
emerging experiments, such as the upgrade of the Large Hadron Collider. In this
roadmap paper, led by CERN, DESY and IBM, we provide the status of high-energy
physics quantum computations and give examples for theoretical and experimental
target benchmark applications, which can be addressed in the near future.
Having the IBM 100 x 100 challenge in mind, where possible, we also provide
resource estimates for the examples given using error mitigated quantum
computing
BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and Gross-Pitaevskii equations. Stationary states computation
International audienceWe present BEC2HPC which is a parallel HPC spectral solver for computing the ground states of the nonlinear Schrödinger equation and the Gross-Pitaevskii equation (GPE) modeling rotating Bose-Einstein condensates (BEC). Considering a standard pseudo-spectral discretization based on Fast Fourier Transforms (FFTs), the method consists in finding the numerical solution of the energy functional minimization problem under normalization constraint by using a preconditioned nonlinear conjugate gradient method. We present some numerical simulations and scalability results for the 2D and 3D problems to obtain the stationary states of BEC with fast rotation and large nonlinearities. The code takes advantage of existing HPC libraries and can itself be leveraged to implement other numerical methods like e.g. for the dynamics of BECs
Model Order Reduction for Nonlinear and Time-Dependent Parametric Optimal Flow Control Problems
The goal of this thesis is to provide an overview of the latest advances on reduced order methods for parametric optimal control governed by partial differential equations. Historically, parametric optimal control problems are a powerful and elegant mathematical framework to fill the gap between collected data and model equations to make numerical simulations more reliable and accurate for forecasting purposes. For this reason, parametric optimal control problems are widespread in many research and industrial fields. However, their computational complexity limits their actual applicability, most of all in a parametric nonlinear and time-dependent framework. Moreover, in the forecasting setting, many simulations are required to have a more comprehensive knowledge of very complex systems and this should happen in a small amount of time. In this context, reduced order methods might represent an asset to tackle this issue. Thus, we employed space-time reduced techniques to deal with a wide range of equations. We propose a space-time proper orthogonal decomposition for nonlinear (and linear) time-dependent (and steady) problems and a space-time Greedy with a new error estimation for parabolic governing equations. First of all, we validate the proposed techniques through many examples, from
the more academic ones to a test case of interest in coastal management exploiting the Shallow Waters Equations model.
Then, we will focus on the great potential of optimal control techniques in several advanced applications. As a first example, we will show some deterministic and stochastic environmental applications, adapting the reduced model to the latter case to reach even faster numerical simulations. Another application concerns the role of optimal control in steering bifurcating phenomena arising in nonlinear governing equations. Finally, we propose a neural network-based paradigm to deal with the optimality system for parametric prediction