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Stable Implementation of adaptive IGABEM in 2D in MATLAB

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COMPUTATIONAL METHODS IN APPLIED MATHEMATICS 2022年第3期22卷 563页

作者： Gantner, Gregor Praetorius, Dirk Schimanko, Stefan TU Wien Inst Anal & Sci Comp Wiedner Hauptstr 8-10-E101-4 A-1040 Vienna Austria

We report on the Matlab program package IGABEM2D which provides an easily accessible implementation of adaptive Galerkin boundary element methods in the frame of isogeometric analysis and which is available on the web for free download. Numerical experiments with IGABEM2D underline the particular importance of adaptive mesh refinement for high accuracy in isogeometric analysis.

关键词： Isogeometric Analysis Boundary Element Method adaptive algorithms Weakly Singular Integral Equation Hyper-singular Integral Equation

Recognition of Normalization Grounded adaptive Filtering Methods For Noise Cancellation In EEG Signal Recordings

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Recognition of Normalization Grounded Adaptive Filtering Met...

Innovations in High Speed Communication and Signal Processing (IHCSP), International Conference on

作者： Rishabh Bhardwaj Centre for Interdisciplinary Research in Business and Technology Chitkara University Institute of Engineering and Technology Chitkara University Punjab India

Electroencephalograms (EEGs) are promising tools for the diagnosis and treatment of neurological and mental disorders, and they are gaining ground as a measurement of brain activity. The electrical activity of the brain can be measured and recorded with an electroencephalogram (EEG). Electrodes are usually placed along the scalp and wired to a recorder to convey the data. The brain and spinal cord together make up the central nervous system, which controls every function in the human body. It receives data from the sensory organs, analyses and organizes it, and then decides what actions to direct the rest of the body to carry out based on that data. When a human brain is damaged, it can have catastrophic effects on every area of that person's existence. Accidents, assaults, concussions, lack of oxygen (near drowning), Alzheimer's disease and other degenerative diseases (dementia, Parkinson's disease), alcohol and other drugs, brain tumors, epilepsy, seizures, infections, and diseases (meningitis, encephalitis) are all examples of what are considered brain disorders. The goal is to design a variety of innovative ANC's for EEG signal denoising that address the challenges of computational complexity, Signal-to-Noise Ratio, Mis-regulation, and convergence. This is done by taking into account three types of adaptive algorithms: adaptive algorithms with normalization.

关键词： Finite impulse response filters adaptive filters adaptive algorithms IIR filters Filtering algorithms Noise cancellation Electroencephalography

The a posteriori error estimates and adaptive computation of nonconforming mixed finite elements for the Stokes eigenvalue problem

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APPLIED MATHEMATICS AND COMPUTATION 2022年 421卷 126951-126951页

作者： Sun, Lingling Yang, Yidu Guizhou Normal Univ Sch Math Sci Guiyang Peoples R China Guizhou Med Univ Sch Biol & Engn Guiyang Peoples R China

In this paper, we discuss the a posteriori error estimates and adaptive algorithm of non-conforming mixed finite elements including the Crouzeix-Raviart element and the enriched Crouzeix-Raviart element for the Stokes eigenvalue problem in Rd (d = 2 , 3) . We give the a posteriori error estimators and prove their reliability and efficiency. Based on the a posteriori error estimators we built two adaptive algorithms, the direct AFEM and the shifted-inverse AFEM. Numerical experiments and theoretical analysis are consistent, which indicates that the numerical eigenvalues obtained by the above two adaptive algo-rithms achieve the optimal convergence order O(dof -2d ) and approximate the exact ones from below. (c) 2022 The Author(s). Published by Elsevier Inc.

关键词： Stokes eigenvalue problem Nonconforming mixed finite element A posteriori error estimates adaptive algorithms

Goal-oriented error analysis of iterative Galerkin discretizations for nonlinear problems including linearization and algebraic errors

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arXiv 2023年

作者： Dolejší, Vít Congreve, Scott Charles University Faculty of Mathematics and Physics Sokolovská 83 Praha186 75 Czech Republic

We consider the goal-oriented error estimates for a linearized iterative solver for nonlinear partial differential equations. For the adjoint problem and iterative solver we consider, instead of the differentiation of the primal problem, a suitable linearization which guarantees the adjoint consistency of the numerical scheme. We derive error estimates and develop an efficient adaptive algorithm which balances the errors arising from the discretization and use of iterative solvers. Several numerical examples demonstrate the efficiency of this *** Codes 65N30, 65N15, 65N50 © 2023, CC BY-NC-ND.

关键词： adaptive algorithms

adaptive Experimentation at Scale: A Computational Framework for Flexible Batches

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arXiv 2023年

作者： Che, Ethan Namkoong, Hongseok Decision Risk and Operations Division Columbia Business School United States

Standard bandit algorithms that assume continual reallocation of measurement effort are challenging to implement due to delayed feedback and infrastructural/organizational difficulties. Motivated by practical instances involving a handful of reallocation opportunities in which outcomes are measured in batches, we develop a computation-driven adaptive experimentation framework that can flexibly handle batching. Our main observation is that normal approximations, which are universal in statistical inference, can also guide the design of adaptive algorithms. By deriving a Gaussian sequential experiment, we formulate a dynamic program that can leverage prior information on average rewards. Instead of the typical theory-driven paradigm, we leverage computational tools and empirical benchmarking for algorithm development. Our empirical analysis highlights a simple yet effective algorithm, Residual Horizon Optimization, which iteratively solves a planning problem using stochastic gradient descent. Our approach significantly improves power over standard methods, even when compared to Bayesian algorithms (e.g., Thompson sampling) that require full distributional knowledge of individual rewards. Overall, we expand the scope of adaptive experimentation to settings standard methods struggle with, involving limited adaptivity, low signal-to-noise ratio, and unknown reward distributions. Copyright © 2023, The Authors. All rights reserved.

关键词： adaptive algorithms

Near-Optimal algorithms for Private Online Optimization in the Realizable Regime

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arXiv 2023年

作者： Asi, Hilal Feldman, Vitaly Koren, Tomer Talwar, Kunal Apple United States Blavatnik School of Computer Science Tel Aviv University

We consider online learning problems in the realizable setting, where there is a zero-loss solution, and propose new Differentially Private (DP) algorithms that obtain near-optimal regret bounds. For the problem of online prediction from experts, we design new algorithms that obtain near-optimal regret Oe(Ε−1 log1.5 d) where d is the number of experts. This significantly improves over the best existing regret bounds for the DP non-realizable setting which are Oe(Ε−1 min {d, T 1/3 log d}). We also develop an adaptive algorithm for the small-loss setting with regret O(L★ log d + Ε−1 log1.5 d) where L★ is the total loss of the best expert. Additionally, we consider DP online convex optimization in the realizable setting and propose an algorithm with near-optimal regret Oe(Ε−1d1.5), as well as an algorithm for the smooth case with regret Oe(Ε−2/3(dT)1/3), both significantly improving over existing bounds in the non-realizable regime. Copyright © 2023, The Authors. All rights reserved.

关键词： adaptive algorithms

adaptive spectral proper orthogonal decomposition of tonal flows

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arXiv 2023年

作者： Yeung, Brandon C.Y. Schmidt, Oliver T. Department of Mechanical and Aerospace Engineering Jacobs School of Engineering University of California 9500 Gilman Drive La Jolla San DiegoCA92093-0411 United States

An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing bias of the spectrum. Smooth spectrum estimates of broadband regions are achieved by locally reducing variance of the spectrum. The method utilizes multitaper estimation with sine tapers. An iterative criterion based on modal convergence is introduced to enable the SPOD to adapt to spectral features. For tonal flows, the adaptivity is controlled by a single user input;for broadband flows, a constant number of sine tapers is recommended without adaptivity. The discrete version of Parseval’s theorem for SPOD is stated. Proper normalization of the tapers ensures that Parseval’s theorem is satisfied in expectation. Drastic savings in computational complexity and memory usage are facilitated by two aspects: (i) sine tapers, which permit post hoc windowing of a single Fourier transform;and (ii) time-domain lossless compression using a QR or eigenvalue decomposition. Sine-taper SPOD is demonstrated on time-resolved particle image velocimetry (TR-PIV) data from an open cavity flow [31] and high-fidelity large-eddy simulation (LES) data from a round jet [3], with and without adaptivity. For the tonal cavity flow, the adaptive algorithm outperforms Slepian-based multitaper SPOD in terms of variance and local bias of the spectrum, mode convergence, and memory usage. The tonal frequencies associated with the Rossiter instability are accurately identified. For both the tonal cavity and the broadband jet flows, results comparable to or better than those from standard SPOD based on Welch’s overlapped segment averaging are obtained with up to 75% fewer snapshots, including similar convergence of the Rossiter modes and Kelvin-Helmholtz wavepacket structures for the cavity and jet examples, respectively. Drawing from these examples, we establish best practices. Copyright © 2023, Th

关键词： adaptive algorithms

Mixed finite elements for Kirchhoff-Love plate bending

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arXiv 2023年

作者： Führer, Thomas Heuer, Norbert Facultad de Matemáticas Pontificia Universidad Católica de Chile Avenida Vicuña Mackenna 4860 Santiago Chile

We present a mixed finite element method with triangular and parallelogram meshes for the Kirchhoff–Love plate bending model. Critical ingredient is the construction of low-dimensional local spaces and appropriate degrees of freedom that provide conformity in terms of a sufficiently large tensor space and that allow for any kind of physically relevant Dirichlet and Neumann boundary conditions. For Dirichlet boundary conditions and polygonal plates, we prove quasi-optimal convergence of the mixed scheme. An a posteriori error estimator is derived for the special case of the biharmonic problem. Numerical results for regular and singular examples illustrate our findings. They confirm expected convergence rates and exemplify the performance of an adaptive algorithm steered by our error *** Codes 74S05, 35J35, 65N30, 65N30 Copyright © 2023, The Authors. All rights reserved.

关键词： adaptive algorithms

adaptive LOOCV-based kernel methods for solving time-dependent BVPs

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APPLIED MATHEMATICS AND COMPUTATION 2022年 429卷

作者： Cavoretto, Roberto Univ Torino Dept Math Giuseppe Peano Via Carlo Alberto 10 I-10123 Turin Italy INdAM Res Grp GNCS Turin Italy

In this article we propose an adaptive algorithm for the solution of time-dependent boundary value problems (BVPs). To solve numerically these problems, we consider the kernel- based method of lines that allows us to split the spatial and time derivatives, dealing with each separately. This adaptive scheme is based on a leave-one-out cross validation (LOOCV) procedure, which is employed as an error indicator. By this technique, we can first detect the domain areas where the error is estimated to be too large - generally due to steep variations or quick changes in the solution - and then accordingly enhance the numerical solution by applying a two-point refinement strategy. Numerical experiments show the efficacy and performance of our adaptive refinement method. (C) 2022 Elsevier Inc. All rights reserved.

关键词： Meshless approximation Kernel methods adaptive algorithms Refinement schemes Partial differential equations