# Top PDF Multi-Domain Spectral Methods for Data Reduction in Numerical Relativity Simulations

### Multi-Domain Spectral Methods for Data Reduction in Numerical Relativity Simulations

refinement using a sequence of nested, logically rectangular meshes on which the partial differential equation is discretized [4]. This technique allows for the adaptation of precision for areas of the model that exhibit dynamic and/or multi-scale behavior. For our work on initial data, we use Carpet, an adaptive mesh refinement and multi-patch driver [14], via code found at http://einsteintoolkit.org/ [10]. These types of problems have extreme data storage requirements since each level of refinement is often quite large, potentially including millions of grid cells, with up to 15 levels of refinement being called upon for the highest resolution simulations [11]. To combat this we look for methods to store data more efficiently, preserving the vast majority of the information content from a simulation while reducing the overall storage requirements.

### Topics in Numerical Relativity: Solving the Initial Value Problem Using Adaptive Mesh Refinement, Examining Evolution Stability Using Spectral Methods, and Finding Apparent Horizons using a Mean Curvature--Level Set Method

This dissertation touches on a representative sampling of the issues in numerical relativity. Chapter 2 describes some of the necessary theoretical background including the Einstein equations and the 3+1 decomposition of the Einstein equations known as the ADM decomposition. Chapter 3 explains the initial value problem of general relativity. To evolve any physical system, one must start with valid initial data. The initial data must obey the laws of physics; in our case, it must satisfy constraint equations. Chapter 4 will describe our initial value solver using multigrid and adaptive mesh refinement called AMRMG (Adaptive Mesh Refinement MultiGrid). The initial data for one of the first successful binary black hole simulations was provided by AMRMG . Chapter 5 details a new class of initial data made feasible by AMRMG : distorted black holes using the puncture method. Chapter 6 describes the evolution equations as they written in the ADM formalism. It explains the inherent stabilities encountered with this form, and it illustrates exponentially growing instabilities with some numerical examples. This chapter also contains an introduction to controlling constraint violations during an evolution. We use spectral methods to implement a constrained evolution. Spectral methods are well established computational tools, but they are somewhat novel to the numerical relativity community. Chapter 7 explains spectral methods as they are most commonly used in relativity and describes the

### A Tale of Two Dust Storms: analysis of a complex dust event in the Middle East

Abstract. Lofted mineral dust over data-sparse regions presents considerable challenges to satellite-based remote sensing methods and numerical weather prediction alike. The southwest Asia domain is replete with such examples, with its diverse array of dust sources, dust mineralogy, and meteo- rologically driven lofting mechanisms on multiple spatial and temporal scales. A microcosm of these challenges occurred over 3–4 August 2016 when two dust plumes, one lofted within an inland dry air mass and another embedded within a moist air mass, met over the southern Arabian Peninsula. Whereas conventional infrared-based techniques readily de- tected the dry air mass dust plume, they experienced marked difficulties in detecting the moist air mass dust plume, be- coming apparent when visible reflectance revealed the plume crossing over an adjacent dark water background. In com- bining information from numerical modeling, multi-satellite and multi-sensor observations of lofted dust and moisture profiles, and idealized radiative transfer simulations, we de- velop a better understanding of the environmental controls of this event, characterizing the sensitivity of infrared-based dust detection to column water vapor, dust vertical extent, and dust optical properties. Differences in assumptions of dust complex refractive index translate to variations in the sign and magnitude of the split-window brightness temper- ature difference commonly used for detecting mineral dust. A multi-sensor technique for mitigating the radiative mask- ing effects of water vapor via modulation of the split-window

### Surrogate Models of Gravitational Waves from Numerical Relativity Simulations of Binary Black Hole Mergers

The Spectral Einstein Code (SpEC) [123] is a numerical relativity code that can perform BBH simulations. It presently can handle mass ratios up to 10, dimensionless spin magnitudes of almost 1 [55], and is typically used for simulations lasting dozens of orbits, although it is capable of performing hundreds of orbits given enough computing time [16]. The singularities inside the BHs are excised from the computational domain. The excised regions are chosen to lie within the BH apparent horizons, which are gauge-dependent null surfaces guaranteed to lie inside the event horizons. This ensures the outside physics are not a ff ected. The remaining domain, which extends out to some outer boundary, is decomposed into many subdomains. Each subdomain is treated spectrally [124, 125] – all quantities are decomposed into basis functions, and the basis function expansions are truncated at some finite number of terms which determines the resolution. The advantage of spectral methods is that for problems with smooth solutions, the numerical truncation error decays exponentially with the number of basis functions. Subdomains are split and merged, and their resolution is controlled automatically using adaptive mesh refinement. The computational grid is fixed but mapped onto the physical domain using rotations, translations, scalings and other maps. These maps are controlled to ensure the excised regions remain inside the BH apparent horizons [126]. SpEC uses a generalized harmonic evolution system [127] which chooses coordinates x µ to satisfy an inhomogeneous wave equation,

### Towards implicit subgrid-scale modeling by particle methods

where x p ,α p ,ω p and v p denote the location, circulation, vorticity and volume of the respective particle. The Lagrangian formulation of particle methods avoids the explicit discretization of the convective term in the governing transport equations and the associated stability constraints. The particle positions are modiﬁed according to the local ﬂow. Large velocity gradients lead to local accumulation or spreading of particles, which result in a loss of accuracy of the computation. Non-linear stability implies that particle paths are not allowed to cross, which results in the time-step constraint dt ≤ C||∇u|| −1 ∞ . This condition is often less demanding than classical CFL conditions. However, it implies that maintaining a regular particle distribution is an important issue. Therefore rather irregular particle positions are projected onto a regular mesh by interpolating the particle data onto the grid. Thereafter new particles are created at regularly distributed positions. Solving the diﬀusion part of the equations uses explicit solvers that are stable under the condition νdt ≤ Ch −2 , which is generally not a severe limitation for 3D computations with moderate to high Reynolds numbers.

### Design of Multi Stage Axial Flow Compressor and Validation using Numerical Simulations

and 50 0 from the base profile [1]. The engineered blades were screened, as working fluid in a simple smoke tunnel of wooden smoke with white smoke. The research indicated that the blade curvature controls the degree of flow deviation from the blade surface, and it is also apparent from the research that shallow angles hold superior promise in the compressor unit's efficiency. Ujjawal and Joshi [2] designed the five-stage axial-flow compressor utilizing the mean line technique and using NACA 65410 profiles blade coordinates were generated. Solid work modeling was used for first stage creation and to corroborate the results, CFD simulation was performed using ANSYS CFX. Comparing the results of the theoretical layout with the analytical results, it was observed that the findings of the computational fluid dynamics analysis are consistent within the acceptable range of theoretical results. Ahmed et al. [3] studied design and optimization of multistage axial compressors. The objective of the work was to define a methodology for the design and analysis of multistage axial-flow compressors. At the conception stage of a fifteen-stage compressor with inlet guide vanes (IGV), a numerical methodology was implemented to optimize effectiveness. Two computer programs were produced using "Visual Basic" for the design and optimization of the compressor through a southern flow analysis of the compressor with the premise of axisymmetric flow properties. Findings show that this modeling approach is much easier than the regular computational methods which involve much more modeling/programming work and runtime of the machine. Zhang et al. [4] explored an aerodynamic design based on the surface hypothesis of the S1/S2 stream that includes the design of the S2 stream surface through-flow, blade profile design, stack blade models

### Survey on data mining methods and applications in healthcare domain sector

What heightens this difference in approach is the fact that most standard data mining is concerned mostly with describing but not explaining the patterns and trends. In contrast, medicine needs those explanations because a slight difference could change the balance between life or death. For example, anthrax and influenza share the same symptoms of respiratory problems. Lowering the threshold signal in a data mining experiment may either raise an anthrax alarm when there is only a flu outbreak. The converse is even more fatal: a perceived flu outbreak turns out to be an anthrax epidemic (Wong et al 2005). It is no coincidence that we found that, in most of the data mining papers on disease and treatment, the conclusions were almost-always vague and cautious. Many would report encouraging results but recommend further study. This failure to be conclusive indicates the current lack of credibility of data mining in these particular niches of healthcare.

### Spatio-Frequential Characterization of Turbulence Excitations From Vibratory Responses Using Inverse Techniques : Part 2 - Extraction of the physical excitation field from the modal responses

To tackle the final part of the identification problem, in order to find the features of the physical flow excitation from the modal excitation results of Figure 3, these may be worked in various manners. Any identification approach used will obviously depend on what is hypothesized about the unknown excitation field under investigation. Here we will assume that the flow turbulence excitations to be identified actually behave as modeled through the general formulation developed in Part 1. For identification of the unknown excitation field, the space-domain [0, ] L will be decomposed in

### Multi scale numerical simulations on piezoresistivity of CNT/polymer nanocomposites

is very time-consuming for high CNT loading cases since there may be multiple contact points for one CNT with other neighboring CNTs. However, for low CNT loading cases discussed here, this operation is comparatively simple. The shortest distance (0.47 nm) is determined by matching the numerical predicted conductivity and piezoresistivity with the experimental ones. It is reasonable to set up this shortest distance (0.47 nm) since, in general, the equilibrium distance between two independent carbon atomistic structures under Lennard-Jones potential or van der Waals force ranges approximately from 0.3 to 0.5 nm. Furthermore, it is interesting to find that the shortest distance is much lower than the average diameter of the CNTs in the nu- merical simulations (i.e., 50 nm). Therefore, the range of distance d between two central lines of two cylindrical CNTs to introduce the tunneling effect should be [D + d min , D + d max ], where d min and d max are 0.47 nm and

### The Embedded System Integrated ECG Monitoring and Low Energy Led Light Stimulation

A system with ECG monitoring and low energy LED light stimulation is proposed. In the study, ECG signal is calculated to get time-domain and frequency domain HRV and ANS was analyzed. When the calculated values are out of the self-defined criteria, the system will remind the user to turn on LED to stimulate specific body site (ex. Neiguan point (PC6)) to balance ANS. In additional, the operating frequency and the dosage are adjustable, the default setting is 10 Hz and the duty cycle is 50%. The data and control parameter can be sent and received between the embedded system and the computer by UART for storage, display, calculation and analysis. In the future, more physiological signals such as electroencephalogram, photoplethysmography etc. would be included into the system for the judgment reference.

### What’s in a Domain? Multi Domain Learning for Multi Attribute Data

Multi-Domain learning assumes that a sin- gle metadata attribute is used in order to di- vide the data into so-called domains. How- ever, real-world datasets often have multi- ple metadata attributes that can divide the data into domains. It is not always apparent which single attribute will lead to the best do- mains, and more than one attribute might im- pact classification. We propose extensions to two multi-domain learning techniques for our multi-attribute setting, enabling them to si- multaneously learn from several metadata at- tributes. Experimentally, they outperform the multi-domain learning baseline, even when it selects the single “best” attribute.

### Online Methods for Multi Domain Learning and Adaptation

So far we have considered settings with a small number of similar domains. While this is typical of multi-task problems, real world settings present many domains which do not all share the same be- haviors. Online algorithms scale to numerous ex- amples and we desire the same behavior for numer- ous domains. Consider a spam filter used by a large email provider, which filters billions of emails for millions of users. Suppose that spammers control many accounts and maliciously label spam as legiti- mate. Alternatively, subsets of users may share pref- erences. Since behaviors are not consistent across domains, shared parameters cannot be learned. We seek algorithms robust to this behavior.

### Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator

this paper, we examine the rising phenomena found in a two-degree of freedom vibro- impact system as a system parameter is varied, and find similar results to [14] regarding the drop in sticking time. We demonstrate using numerical simulations that rising and multi-sliding are qualitatively equivalent bifurcations events by observing that the stick- ing solutions become tangent to the boundary of the sticking region at a rising event — analogous to results for sliding orbits shown by [18].

### Spectral-spatial classification of hyperspectral data using spectral-domain local binary patterns

15 Li, Wei, et al. "Local Binary Patterns and Extreme Learning Machine for Hyperspectral Imagery Classification." IEEE Transactions on Geoscience & Remote Sensing 53.7(2015):1-13. 16 Huang, Xin, and L. Zhang. "An SVM Ensemble Approach Combining Spectral, Structural, and Semantic Features for the Classification of High-Resolution Remotely Sensed Imagery." IEEE Transactions on Geoscience & Remote Sensing 51.1(2013):257-272.

### A high accuracy numerical method based on spectral theory of compact operator for biharmonic eigenvalue equations

The rest of this paper is organized as follows. Section  provides some preliminaries. In Section , by employing the orthogonal spherical polynomials approximation and the spectral theory of compact operator, we derive the error estimates of approximate eigen- values and eigenfunctions. In Section , by adopting orthogonal spherical base functions, we establish the discrete model with sparse mass and stiﬀ matrices which is very eﬃcient for ﬁnding the numerical solutions of biharmonic eigenvalue equations on the spherical domain. In Section , we provide some numerical examples to validate that the theoretical results are correct. Finally, we provide some conclusions in Section .

### Application of spectral methods in economic data analysis

If APPLICATION OF SPECTRAL METHODS IN ECONOMIC DATA ANALYSIS by Richard Deane Terrell A Thesis presented to the Australian National University for the Degree of Doctor of Philosophy The results presen[.]

### The seasonal adjustment of economic data by spectral methods

If this smoothed periodogram is to produce good estimates of the average spectral density in each hand, the true function f(A) must not vary too much within each hand; or if it does vary it should vary about the centre of the band in such a way that the biases on either side cancel out. This is the most vital consideration in the estimation of spectra. The whole problem of seasonal adjustment can he viewed as one of spectral estimation and the smoothness requirement is the reason why we firstly remove the trend and seasonal components since we have prior knowledge of the location of these spectral peaks. We will then estimate the spectrum of the residuals, which we expect to he relatively smooth and which, as we

### Generalization Propagator Method for DOA Estimation

In this paper, a GPM is proposed to estimate the DOA of narrow-band incident signals in uniform linear array. The method is an expansion of traditional PM. It uses different block structures of array manifold to get a new spectral function without EVD, by which the array received date can be utilized more effectually. Simulation results show that GPM is much better than PM at low SNR and snapshots. Corresponding GRPM is also obtained from GPM like root-MUSIC. Its performance is very close to root-MUSIC, but much better than RPM and ESPRIT. So this study can provide a good reference for associated problem estimation of DOA.