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An Efficient Numerical algorithm for the Model Describing the Competition Between Super- and Sub-diffusions Driven by Fractional Brownian Sheet Noise

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JOURNAL OF SCIENTIFIC COMPUTING 2023年第1期96卷 1-24页

作者： Sun, Jing Nie, Daxin Deng, Weihua Lanzhou Univ Sch Math & Stat Gansu Key Lab Appl Math & Complex Syst Lanzhou 730000 Peoples R China

Super- and sub-diffusions are two typical types of anomalous diffusions in the natural world. In this work, we discuss the numerical scheme for the model describing the competition between super- and sub-diffusions driven by fractional Brownian sheet noise. Based on the obtained regularization result of the solution by using the properties of Mittag-Leffler function and the regularized noise by Wong-Zakai approximation, we make full use of the regularity of the solution operators to achieve optimal convergence of the regularized solution. The spectral Galerkin method and the Mittag-Leffler Euler integrator are respectively used to deal with the space and time operators. In particular, by contour integral, the fast evaluation of the Mittag-Leffler Euler integrator is realized. We provide complete error analyses, which are verified by the numerical experiments.

关键词： Model for anomalous diffusion Fractional Brownian sheet Wong-Zakai approximation Mittag-Leffler Euler integrator Spectral Galerkin method fast algorithm Error analyses

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fast algorithms for integral formulations of steady-state radiative transfer equation

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JOURNAL OF COMPUTATIONAL PHYSICS 2019年 380卷 191-211页

作者： Fan, Yuwei An, Jing Ying, Lexing Stanford Univ Dept Math Stanford CA 94305 USA Stanford Univ Inst Computat & Math Engn Stanford CA 94305 USA

We investigate integral formulations and fast algorithms for the steady-state radiative transfer equation with isotropic and anisotropic scattering. When the scattering term is a smooth convolution on the unit sphere, a model reduction step in the angular domain using the Fourier transformation in 2D and the spherical harmonic transformation in 3D significantly reduces the number of degrees of freedoms. The resulting Fourier coefficients or spherical harmonic coefficients satisfy a Fredholm integral equation of the second kind. We study the uniqueness of the equation and proved an a priori estimate. For a homogeneous medium, the integral equation can be solved efficiently using the FFT and iterative methods. For an inhomogeneous medium, the recursive skeletonization factorization method is applied instead. Numerical simulations demonstrate the efficiency of the proposed algorithms in both homogeneous and inhomogeneous cases and for both transport and diffusion regimes. (C) 2018 Elsevier Inc. All rights reserved.

关键词： fast algorithm Radiative transfer Fredholm integral equation Recursive skeletonization FFT Anisotropic scattering

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Sonography in Pre-clinical Care

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DEUTSCHE MEDIZINISCHE WOCHENSCHRIFT 2024年第15期149卷 912-924页

作者： Knott, Dominik Siegl, Lutz Siegl, Katharina Bundeswehrkrankenhauses Berlin Zent Interdisziplinaren Notaufnahme Berlin Germany Bundeswehrkrankenhaus Zentrums Notfall & Rettungsmed Berlin Germany Bundeswehrkrankenhaus Klin Anasthesiol Intens Med Schmerztherapie & Notf Berlin Germany

"Have you had a sonogram yet?" is a question that is asked several times a day in clinical emergency medicine. Sonography is a quick and non-invasive way of looking into a person. It is now not only a valuable diagnostic tool, but in times of a lack of resources it is also a way of sensibly controlling and accelerating treatment paths for patients.

关键词： Notfallmedizin Point-of-Care-Ultraschall Notfallsonografie fast-algorithmus Polytrauma Reanimation emergency medicine point-of-care ultrasound emergency sonography fast algorithm polytrauma resuscitation

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Sonography in the preclinical setting

NOTARZT

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NOTARZT 2024年第1期40卷 31-43页

作者： Knott, Dominik Siegl, Lutz Siegl, Katharina Bundeswehr Hosp Berlin Gen Med Responsible Training Cent interdisciplinary emerge Berlin Germany Bundeswehr Hosp Berlin Ctr Emergency Rescue Med Berlin Germany Bundeswehr Hosp Berlin Clin Anesthesiol Intens Care Med Pain Therapy & Em Berlin Germany Bundeswehrkrankenhaus Berlin Klin X Scharnhorststr 13 D-10557 Berlin Germany

Preclinical ultrasound is another valuable tool in the repertoire of emergency medical and rescue service personnel. If the question is clear, it can quickly narrow down differential diagnoses and guide further treatment as well as optimise the choice and preparation of the target hospital. With the devices currently available, it is possible to generate technically high-quality ultrasound images, even if image storage assigned to patients is still a challenge. Thanks to the wide availability of sonography, learning formats and expertise, it is possible to achieve a good level of competence in this procedure. Actually, the biggest obstacles are remembering to use it and incorporating it sensibly into the operational procedure, as it is often necessary to modify the approach that has been established for years. Before introducing prehospital ultrasound, staff should be trained and procedures should be jointly defined to make ultrasound a valuable addition to prehospital treatment and patient disposition.

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A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrodinger equations

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JOURNAL OF COMPUTATIONAL PHYSICS 2021年 425卷 109869-109869页

作者： Yin, Baoli Wang, Jinfeng Liu, Yang Li, Hong Inner Mongolia Univ Sch Math Sci Hohhot 010021 Peoples R China Inner Mongolia Univ Finance & Econ Sch Stat & Math Hohhot 010070 Peoples R China

We aim at analyzing a novel structure preserving difference scheme for the high dimensional nonlinear space-fractional Schrodinger equation. The temporal direction is discretized by the modified Crank-Nicolson scheme, while the spacial variable is approximated by formulas from the shifted convolution quadrature. The energy and mass preserving properties are proved rigorously for the scheme based on the newly developed properties of the coefficients matrix. Further, the optimal convergence rate O(h(2) + tau(2)) is derived in detail where h, tau denote the spacial and temporal mesh sizes, respectively. To save the computing cost, we consider the preconditioned fast BiCG (PF-BiCG) algorithm for the resulting complex systems, with the computing complexity of O(N log N) at each time step and the memory requirement of O(N). Numerical experiments are conducted to confirm our theoretical conclusions and the efficiency of the fast algorithm. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Structure preserving scheme Nonlinear space-fractional Schrodinger equation fast algorithm The shifted convolution quadrature

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Convergence and superconvergence analysis of finite element methods for nonlinear Ginzburg-Landau equation with Caputo derivative

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COMPUTATIONAL & APPLIED MATHEMATICS 2023年第6期42卷 1-32页

作者： Chen, Fang Li, Meng Zhao, Yanmin Tang, Yifa Zhengzhou Univ Sch Math & Stat Zhengzhou 450001 Peoples R China Xuchang Univ Sch Sci Henan Joint Int Res Lab High Performance Computat Xuchang 461000 Peoples R China Chinese Acad Sci Acad Math & Syst Sci LSEC ICMSEC Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China

In this paper, we study and analyze the time fractional Ginzburg-Landau equation (FGLE) using finite element methods (FEMs) in space and L1 scheme in time. The unconditional optimal L-2-norm error estimates are obtained based on the time-space error splitting technique. Using the relation between interpolation operator and Ritz projection operator, we obtain the superclose results in H-1-norm. Furthermore, the global superconvergence results are established through the interpolation postprocessing technique. To overcome the weak singularity of the solution at the initial time and improve the computational efficiency, we adopt the nonuniform L1 scheme in the time direction and built corresponding fast algorithm based on sum-of-exponential technique. Finally, we provide several numerical experiments to verify the theoretical results and demonstrate the advantages of the fast algorithm.

关键词： Nonlinear time FGLE Convergence and superconvergence FEM Time-space error splitting technique fast algorithm

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A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system

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NUMERICAL algorithmS 2022年第4期90卷 1437-1463页

作者： Pang, Gang Ji, Songsong Beihang Univ Sch Math Sci Beijing 102206 Peoples R China Peking Univ Coll Engn HEDPS CAPT & LTCS Beijing 100871 Peoples R China

In this paper, we use a fully discrete Crank-Nicolson scheme to solve the Cauchy problem for one-dimensional linearized Green-Naghdi system with fast convolution boundary condition which is derived through the Pade approximation for the square root function. We also introduce a constant damping term to guarantee the stability. While the damping term meets certain conditions, the stability is proved for the numerical solutions with the fast convolution boundary condition. Therefore, the difficulty of numerical instability which rises in Kazakova and Noble (SIAM J. Num. Anal. 1, 657-683, 2020) is overcome. The computational cost of the convolution integral is reduced from O(N-2) to O(N ln(N)) for the total number of time steps N. Numerical examples verify the theoretical results and demonstrate the performance for the fast numerical method.

关键词： Green-Naghdi system Pade approximation Convolution quadrature Artificial boundary condition fast algorithm Stability

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A fast Temporal Second Order Difference Scheme for the Fractional Sub-diffusion Equations on One Dimensional Space Unbounded Domain

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数学研究（英文） 2023年第2期56卷 173-205页

作者： Ren-Jun Qi Zhi-Zhong Sun School of Mathematics Southeast UniversityNanjing 210096China

The numerical solution of the fractional sub-diffusion equations on one di-mensional space unbounded domain is *** on the high-order local artificial boundary conditions proposed in[Zhang W.,et al.,***.,2017,50(1):28-53],the original space unbounded problem can be reformulated to an initial-boundary value problem on a bounded computational *** Alikhanov's L2-1σformula and sum-of-exponentials approximation,a fast temporal second order differ-ence scheme for the reduced problem is *** unique solvability,stability and convergence order O(τ2+h2)of the proposed method are proved by means of en-ergy method,where τ and h denote the time and space step sizes,*** numerical examples are included to validate the theoretical *** the best of our knowledge,this is the first work that combines the high order numerical method with the artificial boundary method for the time fractional diffusion problems on spatial unbounded domains.

关键词： difference scheme energy method fast algorithm Fractional sub-diffusion equations high-order local artificial boundary conditions space unbounded domain

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fast algorithm on Parameter Estimation of Wideband LFM Signal Based on Down-chirp and CS

Fast Algorithm on Parameter Estimation of Wideband LFM Signa...

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IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC)

作者： Wang Kang Ye Wei Lao Guochao Wang Yong Equipment Acad Beijing Peoples R China

ISBN: (纸本)9781479952748

Compressed Sensing (CS) has been successfully applied to the parameter estimation of Linear Frequency Modulation (LFM) signal. Compared to the Nyquist sampling method, far less samples are needed to estimate the frequency parameter. However, the super-resolution estimation of frequency parameter can greatly increase the number of atoms in the over-complete dictionary and it will brings a huge amount of computation. This paper proposes resolutions to this problem. Taking the feature of CS into account that the sampling and compression are completed at the same time, we structure a measurement matrix which can complete the compressive sampling and down-chirp simultaneously. Furthermore, we propose a down-chirp based method and improve it with fast computing strategy to solve the above problem. Simulation results have proved that the frequency parameter can be accurate estimated under a low SNR and sampling condition. Meanwhile, compared with the proposed method, the improved algorithm greatly reduces the scale of over-complete dictionary and the amount of computation, and the estimation time has been cut down significantly.

关键词： Compressed Sensing parameter estimation LFM fast algorithm down-chirp

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TrendRank method for evaluating the importance of power grid nodes considering information network

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IET GENERATION TRANSMISSION & DISTRIBUTION 2023年第3期17卷 539-550页

作者： Su, Qingyu Chen, Cong Li, Jian Northeast Elect Power Univ Sch Automat Engn Jilin Jilin Peoples R China

To ensure the stable operation of power systems, critical nodes need to be identified for key protection. The LeaderRank algorithm is a fast and accurate algorithm for identifying key nodes, but it has obvious inappropriateness when targeting the power system. For this reason, this paper considers the scheduling function of the information network and the power flow betweenness of the power grid. A TrendRank algorithm is proposed to identify key nodes in complex power grids. TrendRank values can be computed iteratively by a weighted distribution strategy of internally linked nodes and then ranked. The performance of the TrendRank method has been fully tested and benchmarked on IEEE39 and IEEE118. The comparison of four performance metrics fully validates the effectiveness and superiority of the method. The TrendRank algorithm provides an idea in protecting the power system, which makes the economic cost of protecting the power system lower.

关键词： power grid power system Optimisation techniques TrendRank values Power system management, operation and economics TrendRank algorithm social networking (online) TrendRank method Power transmission, distribution and supply critical nodes key nodes LeaderRank algorithm data mining Information networks fast algorithm Data handling techniques Power system control complex power grids power grids load flow information network Power engineering computing key protection internally linked nodes power flow betweenness

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