Article
Mathematics, Applied
Bin He
Summary: The main goal of this paper is to develop a fast and effective meshless method using radial basis function (RBF) for the time domain model equations of an electromagnetic wave concentration device. The paper introduces the use of perfect matching layer technology to transform an unbounded domain problem into a bounded domain problem and presents the development of a leap-frog RBF meshless method based on the leap-frog finite-difference time-domain scheme to solve the coupled complex modeling equations.
Article
Computer Science, Interdisciplinary Applications
A. Hajiollow, Y. Lotfi, K. Parand, A. H. Hadian, K. Rashedi, J. A. Rad
Summary: This paper explores the dynamics modeling and behavior analysis of the inverse boundary Stefan problem, proposing the use of radial basis functions in conjunction with a linearization algorithm to overcome difficulties like non-linearity and free boundary property. Numerical examples demonstrate the accuracy and stability of the method.
ENGINEERING WITH COMPUTERS
(2021)
Article
Computer Science, Interdisciplinary Applications
Cheng-Yu Ku, Li-Dan Hong, Chih-Yu Liu, Jing-En Xiao
Summary: This paper proposes a novel meshless approach using space-time polyharmonic radial polynomial basis functions to model saturated and unsaturated flows in porous media. By investigating saturated and unsaturated flow problems, the robustness and high accuracy of the proposed method are demonstrated. The proposed space-time polyharmonic radial polynomial basis functions provide highly accurate solutions and higher accuracy and stability compared to conventional time-marching schemes in solving saturated and unsaturated flow problems.
ENGINEERING WITH COMPUTERS
(2021)
Review
Mechanics
Roberto Verzicco
Summary: Immersed boundary methods (IBMs) are computational techniques that solve flow problems in complex geometric configurations using Cartesian structured meshes. Despite their implementation in the 1970s, IBMs gained credibility only in the new millennium. These methods have advantages and disadvantages, and the choice of the most suitable IBM implementation depends on careful analysis of each problem. High-Reynolds number flows pose a limitation to IBMs due to the resolution of thin wall shear layers, but researchers have developed strategies to alleviate this weakness.
ANNUAL REVIEW OF FLUID MECHANICS
(2023)
Article
Mathematics, Applied
Zhiying Ma, Xinxiang Li, C. S. Chen
Summary: A new Kansa method with fictitious center approach is proposed in this paper, where the radial basis function (RBF) approximation is augmented by polynomial basis functions. The proposed approach significantly improves the accuracy and stability of the previously proposed ghost point method using radial basis functions, eliminating the difficulty of selecting a good RBF shape parameter. Two numerical examples are presented to demonstrate the effectiveness and improvement of the proposed method over previous methods.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Hongbo Guan, Zhimin Zhang, Huiqing Zhu
Summary: This paper explores the structure of basis functions in the bilinear immersed finite element space for two dimensional elliptic interface problems, demonstrating that each immersed basis function on a rectangular interface element can be broken down into a standard bilinear basis function and a corresponding bubble function. By providing detailed expressions of these bubble functions on the reference element, it reveals another perspective on the nature of immersed basis functions, which can be extended to other immersed finite element spaces in a similar manner.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Engineering, Marine
Baiwei Feng, Chengsheng Zhan, Zuyuan Liu, Xide Cheng, Haichao Chang
Summary: The Wendland psi 3,1 (W) function was selected for hull surface modification based on radial basis functions (RBF) interpolation. A case study validated the advantages of this method, resulting in optimized hull form with reduced wave-making resistance and total resistance. The findings support the feasibility and value of RBF interpolation-based surface modification in engineering practice.
JOURNAL OF MARINE SCIENCE AND ENGINEERING
(2021)
Article
Engineering, Aerospace
Liang Xie, Zhicong Kang, Haifeng Hong, Zhihua Qiu, Biao Jiang
Summary: A new mesh deformation method, namely the dual-restricted RBF algorithm, is proposed in this study. This algorithm improves the efficiency of the mesh deformation process by introducing a constraint function for stationary wall preservation.
AEROSPACE SCIENCE AND TECHNOLOGY
(2022)
Article
Engineering, Multidisciplinary
Shuangqiang Wang, Guiyong Zhang, Yunan Cai, Boqian Yan, Qian Tang
Summary: Immersed methods are powerful numerical measures for simulating fluid-structure interactions using non-conforming meshes. They can be classified into immersed boundary methods and immersed domain methods, with representative methods being IBLBM-SPIM and IS-PIM. The study compares their performances, showing that IS-PIM allows independent mesh sizes for fluid and solid domains, while IBLBM-SPIM ensures numerical stability across a range of density ratios and directly influences solid deformation and motion. The study also provides insights for developing novel methods for different FSI problems.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Engineering, Multidisciplinary
Mohamed Boujoudar, Abdelaziz Beljadid, Ahmed Taik
Summary: We propose a new approach to solve the nonlinear Richards equation using the Kirchhoff transformation and localized radial basis function (LRBF) techniques. This method reduces nonlinearity and models unsaturated flow through heterogeneous soils. We introduce special techniques to handle medium heterogeneity and apply the Kirchhoff transformation with the Brooks and Corey model and a power-law relation. The resulting equation is solved using LRBF methods, which are computationally efficient and avoid mesh generation.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Engineering, Aerospace
Massoud Tatar
Summary: This study presents a novel global reduced-order modeling and parameter estimation of a maneuvering aircraft using radial basis functions. A computational fluid dynamics approach accurately predicts the flow field, a neural network constructs a nonlinear aerodynamic model, and stability derivatives are analyzed for their dependency on reduced frequency and angle of attack, as well as the influence of angle of attack on moment coefficients.
JOURNAL OF AEROSPACE ENGINEERING
(2021)
Article
Chemistry, Multidisciplinary
S. K. Safdar Hossain, Bamidele Victor Ayodele, Zaid Abdulhamid Alhulaybi, Muhammad Mudassir Ahmad Alwi
Summary: This study explores the feasibility of using machine learning to model biohydrogen production from waste glycerol. The findings show that the multilayer perceptron neural network has better predictive performance, and the combination of activation functions in the hidden and outer layers and the optimization algorithm type significantly affect the model's performance. Waste glycerol is the most significant input variable in predicting biohydrogen production.
APPLIED SCIENCES-BASEL
(2022)
Article
Engineering, Multidisciplinary
Mohammad Fazli, Murray Rudman, Shibo Kuang, Andrew Chryss
Summary: This paper describes the numerical methodology of several versions of immersed boundary methods (such as Volume Penalization IBM, Indirect Imposition of Discrete Forcing IBM, and Direct Imposition of Discrete Forcing IBM) and their applications in Newtonian and yield-pseudoplastic flows. The investigation shows that explicit forcing methods are incompatible with flows with non-Newtonian yield-pseudoplastic rheology, while the implicit forcing method is reliable for modeling non-Newtonian flows.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Engineering, Multidisciplinary
Bryce D. Wilkins, Theodore V. Hromadka
Summary: This paper discusses the technical aspects of using the digamma function as a basis function for the CVBEM, and demonstrates its utility by applying it to a mixed boundary value problem of the Laplace type.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Multidisciplinary Sciences
Deyun Zhong, Ju Zhang, Liguan Wang, Lin Bi
Summary: This paper presents an automatic modeling method for narrow vein type ore bodies based on Boolean combination constraints. By constructing implicit functions and performing Boolean operations, the method can effectively model narrow vein type ore bodies, which is of practical value.
SCIENTIFIC REPORTS
(2022)
Article
Engineering, Electrical & Electronic
Santosh Pokhrel, Varun Shankar, Jamesina J. Simpson
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION
(2018)
Article
Computer Science, Interdisciplinary Applications
Varun Shankar, Aaron L. Fogelson
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Computer Science, Interdisciplinary Applications
Varun Shankar, Grady B. Wright
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Computer Science, Interdisciplinary Applications
Varun Shankar, Akil Narayan, Robert M. Kirby
JOURNAL OF COMPUTATIONAL PHYSICS
(2018)
Article
Computer Science, Interdisciplinary Applications
Kathryn P. Drake, Grady B. Wright
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Computer Science, Interdisciplinary Applications
Kathryn P. Drake, Grady B. Wright
JOURNAL OF COMPUTATIONAL PHYSICS
(2020)
Article
Computer Science, Interdisciplinary Applications
Varun Shankar, Grady B. Wright, Aaron L. Fogelson
Summary: The study introduces a high-order radial basis function finite difference method for solving advection-diffusion equations on time-varying domains. The framework eliminates overlap parameters, enables tuning-free assembly of differentiation matrices on moving domains, and demonstrates high performance with high convergence rates.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright
Summary: This paper presents a new method for surface reconstruction from a point cloud by utilizing the approximate normals to the surface. By using curl-free radial basis function interpolation of the normals, an implicit surface approximation for the point cloud can be obtained. The method is combined with a partition of unity technique to better represent local features and handle noise in both the normals and the point positions.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Applied
Grady B. Wright, Andrew Jones, Varun Shankar
Summary: We propose a new meshfree geometric multilevel (MGM) method for solving linear systems arising from discretizing elliptic PDEs on point cloud surfaces. The method utilizes Poisson disk sampling for coarsening point clouds and uses polyharmonic splines for transferring information. It is applicable to various localized meshfree methods and has been tested on different problems, showing efficient convergence rates and scalability. The effectiveness of MGM is further demonstrated on challenging applications involving complicated surfaces.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Andrew M. Jones, Peter A. Bosler, Paul A. Kuberry, Grady B. Wright
Summary: Approximating differential operators on two-dimensional surfaces is a crucial problem in various fields. Localized meshfree methods, such as generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD), have been proven effective and efficient in achieving high accuracy at low computational cost for this task. However, a direct comparison of these methods for approximating surface differential operators (SDOs) has not been conducted yet. This study aims to fill this gap and compare the performance of GMLS with an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly). Furthermore, we investigate the relationship between the tangent plane formulation of SDOs and the local coordinate formulation used in GMLS, and propose a new RBF-FD method for approximating the tangent space of an unknown point cloud surface using ideas from the GMLS SDO formulation. Evaluation: 8/10.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Applied
Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright
Summary: The paper introduces a technique for constructing global approximants of divergence-free or curl-free vector fields by combining div/curl-free radial basis functions in a partition of unity framework, applicable to vector fields in 2D space and on surfaces, and providing approximations for scalar potentials. The method effectively bypasses the computational expense issue caused by the global nature of the problem.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
Varun Shankar, Grady B. Wright, Akil Narayan
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2020)
Article
Mathematics, Interdisciplinary Applications
Sean D. Lawley, Varun Shankar
MULTISCALE MODELING & SIMULATION
(2020)
Article
Computer Science, Interdisciplinary Applications
Ashish Bhole, Herve Guillard, Boniface Nkonga, Francesca Rapetti
Summary: Finite elements of class C-1 are used for computing magnetohydrodynamics instabilities in tokamak plasmas, and isoparametric approximations are employed to align the mesh with the magnetic field line. This numerical framework helps in understanding the operation of existing devices and predicting optimal strategies for the international ITER tokamak. However, a mesh-aligned isoparametric representation encounters issues near critical points of the magnetic field, which can be addressed by combining aligned and unaligned meshes.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Federico Vismara, Tommaso Benacchio
Summary: This paper introduces a method for solving hyperbolic-parabolic problems on multidimensional semi-infinite domains. By dividing the computational domain into bounded and unbounded subdomains and coupling them using numerical fluxes at the interface, accurate numerical solutions are obtained. In addition, computational cost can be reduced by tuning the parameters of the basis functions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
Article
Computer Science, Interdisciplinary Applications
Keigo Enomoto, Takato Ishida, Yuya Doi, Takashi Uneyama, Yuichi Masubuchi
Summary: We have developed a novel Moving Particle Simulation (MPS) method to accurately reproduce the motion of fibers in sheared liquids. By introducing the micropolar fluid model, we address the issue of fibers being aligned with the flow direction in conventional MPS simulations. Our method is capable of accurately reproducing the fiber motion predicted by Jeffery's theory.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
(2024)
