Electromagnetic modelling using unstructured grid Finite Difference Method and Radial Basis Functions

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

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On a high-order Gaussian radial basis function generated Hermite finite difference method and its application

CALCOLO ◽

10.1007/s10092-021-00443-4 ◽

2021 ◽

Vol 58 (4) ◽

Author(s):

Fazlollah Soleymani ◽

Shengfeng Zhu

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Radial Basis Function ◽

Basis Function ◽

Difference Method ◽

High Order ◽

Radial Basis

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A NUMERICAL METHOD FOR 1D TIME-DEPENDENT SCHRÖDINGER EQUATION USING RADIAL BASIS FUNCTIONS

International Journal of Computational Methods ◽

10.1142/s0219876213410107 ◽

2013 ◽

Vol 10 (02) ◽

pp. 1341010 ◽

Cited By ~ 2

Author(s):

TONGSONG JIANG ◽

ZHAOLIN JIANG ◽

JOSEPH KOLIBAL

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Numerical Method ◽

Radial Basis Functions ◽

Finite Difference Scheme ◽

Good Accuracy ◽

Basis Functions ◽

Time Dependent ◽

Numerical Examples ◽

Radial Basis

This paper proposes a new numerical method to solve the 1D time-dependent Schrödinger equations based on the finite difference scheme by means of multiquadrics (MQ) and inverse multiquadrics (IMQ) radial basis functions. The numerical examples are given to confirm the good accuracy of the proposed methods.

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The Coupling of RBF and FDM for Solving Higher Order Fractional Partial Differential Equations

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.598.409 ◽

2014 ◽

Vol 598 ◽

pp. 409-413 ◽

Cited By ~ 3

Author(s):

Zakieh Avazzadeh ◽

Wen Chen ◽

Vahid Reza Hosseini

Keyword(s):

Partial Differential Equations ◽

Finite Difference ◽

Differential Equations ◽

Radial Basis Functions ◽

Basis Functions ◽

Discrete Solution ◽

Fractional Partial Differential Equations ◽

Partial Differential ◽

Time Direction ◽

Radial Basis

In this work, we describe the radial basis functions for solving the time fractional partial differential equations defined by Caputo sense. These problems can be discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. Numerical results accuracy the efficiency of the presented method.

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Heat Diffusion in Heterogeneous Bodies Using Heat-Flux-Conserving Basis Functions

Journal of Heat Transfer ◽

10.1115/1.3250480 ◽

1988 ◽

Vol 110 (2) ◽

pp. 276-282 ◽

Cited By ~ 6

Author(s):

A. Haji-Sheikh

Keyword(s):

Heat Flux ◽

Finite Difference ◽

Finite Difference Method ◽

Diffusion Equation ◽

Difference Method ◽

Solution Method ◽

Basis Functions ◽

Heat Diffusion ◽

Simple Geometry ◽

The Finite Difference Method

The generalized analytical derivation presented here enables one to obtain solutions to the diffusion equation in complex heterogeneous geometries. A new method of constructing basis functions is introduced that preserves the continuity of temperature and heat flux throughout the domain, specifically at the boundary of each inclusion. A set of basis functions produced in this manner can be used in conjunction with the Green’s function derived through the Galerkin procedure to produce a useful solution method. A simple geometry is selected for comparison with the finite difference method. Numerical results obtained by this method are in excellent agreement with finite-difference data.

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