Adaptive radial basis function generated finite-difference (RBF-FD) on non-uniform nodes using pp-refinement

Radial basis functions-generated finite difference methods (RBF-FDs) have been gaining popularity recently. In particular, the RBF-FD based on polyharmonic splines (PHS) augmented with multivariate polynomials (PHS+poly) has been found significantly effective. For the approximation order of RBF-FDs' weights on scattered nodes, one can already find mathematical theories in the literature. Many practical problems in numerical analysis, however, do not require a uniform node-distribution. Instead, they would be better suited if specific areas of the domain, where complicated physics needed to be resolved, had a relatively higher node-density compared to the rest of the domain. In this work, we proposed a practical adaptive RBF-FD with a user-defined order of convergence with respect to the total number of (possibly scattered and non-uniform) data points $N$. Our algorithm outputs a sparse differentiation matrix with the desired approximation order. Numerical examples are provided to show that the proposed adaptive RBF-FD method yields the expected $N$-convergence even for highly non-uniform node-distributions. The proposed method also reduces the number of non-zero elements in the linear system without sacrificing accuracy.Comment: An updated version with seismic modeling will be included in version

A High-Order Kernel Method for Diffusion and Reaction-Diffusion Equations on Surfaces

In this paper we present a high-order kernel method for numerically solving diffusion and reaction-diffusion partial differential equations (PDEs) on smooth, closed surfaces embedded in $\mathbb{R}^d$. For two-dimensional surfaces embedded in $\mathbb{R}^3$, these types of problems have received growing interest in biology, chemistry, and computer graphics to model such things as diffusion of chemicals on biological cells or membranes, pattern formations in biology, nonlinear chemical oscillators in excitable media, and texture mappings. Our kernel method is based on radial basis functions (RBFs) and uses a semi-discrete approach (or the method-of-lines) in which the surface derivative operators that appear in the PDEs are approximated using collocation. The method only requires nodes at "scattered" locations on the surface and the corresponding normal vectors to the surface. Additionally, it does not rely on any surface-based metrics and avoids any intrinsic coordinate systems, and thus does not suffer from any coordinate distortions or singularities. We provide error estimates for the kernel-based approximate surface derivative operators and numerically study the accuracy and stability of the method. Applications to different non-linear systems of PDEs that arise in biology and chemistry are also presented

Applied Mathematics and Computational Physics

As faster and more efficient numerical algorithms become available, the understanding of the physics and the mathematical foundation behind these new methods will play an increasingly important role. This Special Issue provides a platform for researchers from both academia and industry to present their novel computational methods that have engineering and physics applications

時間周波数領域でのてんかん脳波識別に関する研究 ‐平均二乗根に基づく特徴抽出に着目して‐

Epilepsy affects over 50 million people on an average yearly world wide. Epileptic Seizure is a generalised term which has broad classification depending on the reasons behind its occurrence. Parvez et al. when applied feature instantaneous bandwidth B2AM and time averaged bandwidth B2FM for classification of interictal and ictal on Freiburg data base, the result dipped low to 77.90% for frontal lobe whereas it was 80.20% for temporal lobe compare to the 98.50% of classification accuracy achieved on Bonn dataset with same feature for classification of ictal against interictal. We found reasons behind such low results are, first Parvez et al. has used first IMF of EMD for feature computation which mostly noised induce. Secondly, they used same kernel parameters of SVM as Bajaj et al. which they must have optimised with different dataset. But the most important reason we found is that two signals s1 and s2 can have same instantaneous bandwidth. Therefore, the motivation of the dissertation is to address the drawback of feature instantaneous bandwidth by new feature with objective of achieving comparable classification accuracy. In this work, we have classified ictal from healthy nonseizure interictal successfully first by using RMS frequency and another feature from Hilbert marginal spectrum then with its parameters ratio. RMS frequency is the square root of sum of square bandwidth and square of center frequency. Its contributing parameters ratio is ratio of center frequency square to square bandwidth. We have also used dominant frequency and its parameters ratio for the same purpose. Dominant frequency have same physical relevance as RMS frequency but different by definition, i.e. square root of sum of square of instantaneous band- width and square of instantaneous frequency. Third feature that we have used is by exploiting the equivalence of RMS frequency and dominant frequency (DF) to define root mean instantaneous frequency square (RMIFS) as square root of sum of time averaged bandwidth square and center frequency square. These features are average measures which shows good discrimination power in classifying ictal from interictal using SVM. These features, fr and fd also have an advantage of overcoming the draw back of square bandwidth and instantaneous bandwidth. RMS frequency that we have used in this work is different from generic root mean square analysis. We have used an adaptive thresholding algorithm to address the issue of false positive. It was able to increase the specificity by average of 5.9% on average consequently increasing the accuracy. Then we have applied morphological component analysis (MCA) with the fractional contribution of dominant frequency and other rest of the features like band- width parameter’s contribution and RMIFS frequency and its parameters and their ratio. With the results from proposed features, we validated our claim to overcome the drawback of instantaneous bandwidth and square bandwidth.九州工業大学博士学位論文 学位記番号：生工博甲第323号 学位授与年月日：平成30年6月28日1 Introduction|2 Empirical Mode Decomposition|3 Root Mean Square Frequency|4 Root Mean Instantaneous Frequency Square|5 Morphological Component Analysis|6 Conclusion九州工業大学平成30年

Multi-layer Utilization of Beamforming in Millimeter Wave MIMO Systems

mmWave frequencies ranging between (30-300GHz) have been considered the perfect solution to the scarcity of bandwidth in the traditional sub-6GHz band and to the ever increasing demand of many emerging applications in today\u27s era. 5G and beyond standards are all considering the mmWave as an essential part of there networks. Beamforming is one of the most important enabling technologies for the mmWave to compensate for the huge propagation lose of these frequencies compared to the sub-6GHz frequencies and to ensure better spatial and spectral utilization of the mmWave channel space. In this work, we tried to develop different techniques to improve the performance of the systems that use mmWave. In the physical layer, we suggested several hybrid beamforming architectures that both are relatively simple and spectrally efficient by achieving fully digital like spectral efficiency (bits/sec/Hz). For the mobility management, we derived the expected degradation that can affect the performance of a special type of beamforming that is called the Random Beamforming (RBF) and optimized the tunable parameters for such systems when working in different environments. Finally, in the networking layer, we first studied the effect of using mmWave frequencies on the routing performance comparing to the performance achieved when using sub-6 GHz frequencies. Then we developed a novel opportunistic routing protocol for Mobile Ad-Hoc Networks (MANET) that uses a modified version of the Random Beamforming (RBF) to achieve better end to end performance and to reduce the overall delay in delivering data from transmitting nodes to the intended receiving nodes. From all these designs and studies, we conclude that mmWave frequencies and their enabling technologies (i.e. Beamforming, massive MIMO, ...etc.) are indeed the future of wireless communicatons in a high demanding world of Internet of Things (IoT), Augmented Reality (AR), Virtual Reality (VR), and self driving cars

Detached Eddy Simulation for Aerospace Applications

With the continuous growth in air traffic that we see nowadays, comes an increase in the requirements needed to be satisfied in order to certify an aircraft for operation. These stricter regulations affect aspects such as CO2 emissions, sound pollution and so on, pushing manufacturers to aim for lighter, more efficient, more robust designs. These improvements might be achieved in two different ways; by improving/optimizing existing technology, or by developing new technological concepts. In either of the two scenarios, numerical tools, such as optimization methods or reliable fluid flow simulations play a paramount role. In this thesis, new functionalities implemented into the in-house compressible Computational Fluid Dynamics (CFD) solver, G3D::Flow, are described. These new additions have been put in place with the objective of performing turbomachinery simulations using hybrid RANS/LES methods as well as nozzle flow simulations. Some of the additions to G3D::Flow include: phase-lagged pitch-wise and rotor-stator interfaces based on the chorochronic method as well as a method based on Proper Orthogonal Decomposition (POD), sliding grid interface and synthetic turbulence injection. The added capabilities, enable G3D::Flow to perform high-fidelity turbomachinery CFD simulations, which were not affordable before due to their high computational cost, since truncated domains can be used.A hybrid RANS/LES simulation of the VOLVO S6 nozzle contour operating under overexpanded conditions is performed. This same geometry, under the same conditions, was previously simulated and reported using a different hybrid RANS/LES methodology. A reduction of over $50\%$ in the difference between the predicted standard deviation of the side loads and those measured in a previous experimental is observed in the current simulation.In this work, an optimization framework called HAMON is also presented, which is based on evolutionary algorithms. In cases where the optimization is based on computationally heavy tasks, such as 3D CFD simulations, meta-modeling techniques can be used to speed up the optimization processes. HAMON can be used to fine tune an existing design, or as it has been used here, as black-box approach. It has been able to design counter rotating open rotors with more than acceptable performance where no knowledge about propeller aerodynamics was assumed, giving all the design variables more freedom than probably needed. This black-box approach might be specially useful when optimizing new technologies for which no prior knowledge exist, allowing not only to, hopefully, find good designs but also to show the trends of what a good design should be like

Prompt sky localization of compact binary sources using meshfree approximation

The number of gravitational wave signals from the merger of compact binary systems detected in the network of advanced LIGO and Virgo detectors is expected to increase considerably in the upcoming science runs. Once a confident detection is made, it is crucial to reconstruct the source's properties rapidly, particularly the sky position and chirp mass, to follow up on these transient sources with telescopes operating at different electromagnetic bands for multi-messenger astronomy. In this context, we present a rapid parameter estimation (PE) method aided by mesh-free approximations to accurately reconstruct properties of compact binary sources from data gathered by a network of gravitational wave detectors. This approach builds upon our previous algorithm (Pathak et al.\cite{pathak2022rapid}) to expedite the evaluation of the likelihood function and extend it to enable coherent network PE in a ten-dimensional parameter space, including sky position and polarization angle. Additionally, we propose an optimized interpolation node placement strategy during the start-up stage to enhance the accuracy of the marginalized posterior distributions. With this updated method, we can estimate the properties of binary neutron star (BNS) sources in approximately 2.4~(2.7) minutes for the \TaylorF~(\texttt{IMRPhenomD}) signal model by utilizing 64 CPU cores on a shared memory architecture. Furthermore, our approach can be integrated into existing parameter estimation pipelines, providing a valuable tool for the broader scientific community.Comment: 20 pages, 10 figure