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Relevant bibliographies by topics / Kernel-independent fast solvers

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Academic literature on the topic 'Kernel-independent fast solvers'

Author: Grafiati

Published: 6 September 2023

Last updated: 31 July 2025

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Journal articles on the topic "Kernel-independent fast solvers"

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Guo, Han, Jun Hu, Hanru Shao, and Zaiping Nie. "Hierarchical Matrices Method and Its Application in Electromagnetic Integral Equations." International Journal of Antennas and Propagation 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/756259.

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Hierarchical (H-) matrices method is a general mathematical framework providing a highly compact representation and efficient numerical arithmetic. When applied in integral-equation- (IE-) based computational electromagnetics,H-matrices can be regarded as a fast algorithm; therefore, both the CPU time and memory requirement are reduced significantly. Its kernel independent feature also makes it suitable for any kind of integral equation. To solveH-matrices system, Krylov iteration methods can be employed with appropriate preconditioners, and direct solvers based on the hierarchical structure o

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Su, Jianxun, Zengrui Li, Xujin Yuan, Yaoqing (Lamar) Yang, and Junhong Wang. "Integral Equation Analysis of EM Scattering from Multilayered Metallic Photonic Crystal Accelerated with Adaptive Cross Approximation." International Journal of Antennas and Propagation 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/274307.

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A space-domain integral equation method accelerated with adaptive cross approximation (ACA) is presented for the fast and accurate analysis of electromagnetic (EM) scattering from multilayered metallic photonic crystal (MPC). The method directly solves for the electric field in order to easily enable the periodic boundary condition (PBC) in the spatial domain. The ACA is a purely algebraic method allowing the compression of fully populated matrices; hence, its formulation and implementation are independent of integral equation kernel (Green’s function). Therefore, the ACA is very well suited f

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Kaarnioja, Vesa, Yoshihito Kazashi, Frances Y. Kuo, Fabio Nobile, and Ian H. Sloan. "Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification." Numerische Mathematik 150, no. 1 (2021): 33–77. http://dx.doi.org/10.1007/s00211-021-01242-3.

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AbstractThis paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice—a setting that, as pointed out by Zeng et al. (Monte Carlo and Quasi-Monte Carlo Methods 2004, Springer, New York, 2006) and Zeng et al. (Constr. Approx. 30: 529–555, 2009), allows fast evaluation by fast Fourier transform, so avoiding the need for a linear solver. The main contribution of the paper is the application to the approximation problem for uncertainty quantification of elliptic partial differential equations, with the diffusion coe

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Mirrazavi Salehian, Seyed Sina, Nadia Figueroa, and Aude Billard. "A unified framework for coordinated multi-arm motion planning." International Journal of Robotics Research 37, no. 10 (2018): 1205–32. http://dx.doi.org/10.1177/0278364918765952.

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Coordination is essential in the design of dynamic control strategies for multi-arm robotic systems. Given the complexity of the task and dexterity of the system, coordination constraints can emerge from different levels of planning and control. Primarily, one must consider task-space coordination, where the robots must coordinate with each other, with an object or with a target of interest. Coordination is also necessary in joint space, as the robots should avoid self-collisions at any time. We provide such joint-space coordination by introducing a centralized inverse kinematics (IK) solver u

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Han, Yaochuang, Peipei Guo, Yufeng Nie, and Lan Zhang. "Kernel-Independent Fast Multipole Boundary Element Solver for Coupled Conduction–Radiation Heat Transfer Problem." Journal of Thermophysics and Heat Transfer, February 11, 2022, 1–6. http://dx.doi.org/10.2514/1.t6546.

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Monteiro, Henrique B. N., and Daniel M. Tartakovsky. "A meshless stochastic method for Poisson–Nernst–Planck equations." Journal of Chemical Physics 161, no. 5 (2024). http://dx.doi.org/10.1063/5.0223018.

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A plethora of biological, physical, and chemical phenomena involve transport of charged particles (ions). Its continuum-scale description relies on the Poisson–Nernst–Planck (PNP) system, which encapsulates the conservation of mass and charge. The numerical solution of these coupled partial differential equations is challenging and suffers from both the curse of dimensionality and difficulty in efficiently parallelizing. We present a novel particle-based framework to solve the full PNP system by simulating a drift–diffusion process with time- and space-varying drift. We leverage Green’s functi

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Wang, L., Y. Fournier, J. F. Wald, and Y. Mesri. "A graph neural network-based framework to identify flow phenomena on unstructured meshes." Physics of Fluids 35, no. 7 (2023). http://dx.doi.org/10.1063/5.0156975.

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Driven by the abundant data generated from computational fluid dynamics (CFD) simulations, machine learning (ML) methods surpass the deterministic criteria on flow phenomena identification in the way that they are independent of a case-by-case threshold by combining the flow field properties and the topological distribution of the phenomena. The current most popular and successful ML models based on convolutional neural networks are limited to structured meshes and unable to directly digest the data generated from unstructured meshes, which are more widely used in real industrial CFD simulatio

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Dissertations / Theses on the topic "Kernel-independent fast solvers"

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Negi, Yoginder Kumar. "Fast Solvers and Preconditioning Methods in Computational Electromagnetics." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4509.

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Method of Moments (MoM) is an integral equation based solver and is one of the most popular computational techniques to solve complex 3D Electromagnetic problems efficiently and accurately. Compared to the conventional differential equation solvers, MoM does not require a volumetric discretization of the entire bounding box containing the structure or imposes absorbing boundary condition or perfect match layer. However, due to Green's function interactions, the MoM matrix is dense leading to quadratic matrix fill time and cubic solve time complexity. As the scale and the complexity of the prob

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Conference papers on the topic "Kernel-independent fast solvers"

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Ahmad Altounji, Nizar, Mohammad Anwar Assaad, and Ahmad Younso. "A Study on Flexible Bayes Classifier Using K-Nearest Neighbor Density Estimator." In 5TH INTERNATIONAL CONFERENCE ON COMMUNICATION ENGINEERING AND COMPUTER SCIENCE (CIC-COCOS'24). Cihan University-Erbil, 2024. http://dx.doi.org/10.24086/cocos2024/paper.1478.

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Naïve Bayes (NB) Classifier is considered one of the most widely used algorithms to solve classification problems due to its simplicity, high performance and fast computational process, which assumes that feature variables are independent and continuous variables follow gaussian distribution. Due to that most real-life applications may have feature variables that can’t be modeled by gaussian distribution, or may violate the independence assumption, Flexible Naïve Bayes (FNB) Classifier becomes more suitable, which estimates the densities using a non-parametric Kernel Density Estimator (KDE). I

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