scholarly journals Reduced Step Point Collocation Interpolation Method for the Solution of Heat Equation

2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Sunday Babuba
Keyword(s):  
Heat Equation ◽  
Interpolation Method ◽  
Point Collocation

GEOMETRIC INTEGRATION BY SOLUTION INTERPOLATION

2009 ◽  
Vol 20 (02) ◽  
pp. 313-322
Author(s):  
PILWON KIM
Keyword(s):  
Differential Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Standard Method ◽  
Interpolation Method ◽  
Nonlinear Heat Equation ◽  
Geometric Integration ◽  
Numerical Schemes ◽  
New Class ◽  
Geometric Integrators

Numerical schemes that are implemented by interpolation of exact solutions to a differential equation naturally preserve geometric properties of the differential equation. The solution interpolation method can be used for development of a new class of geometric integrators, which generally show better performances than standard method both quantitatively and qualitatively. Several examples including a linear convection equation and a nonlinear heat equation are included.

A Meshfree Weak-Strong-Form Method for Magnetohydrodynamic Flow in a Pipe

2012 ◽  
Vol 490-495 ◽  
pp. 1883-1887
Author(s):  
Xing Hui Cai ◽  
Cheng Ying Shi ◽  
Peng Xu ◽  
Man Lin Zhu ◽  
Guo Liang Wang
Keyword(s):  
Interpolation Method ◽  
Weak Form ◽  
Strong Form ◽  
Quadrature Domain ◽  
Point Collocation ◽  
Function Point ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Local Weak Form ◽  
Natural Boundaries

In this paper, a meshfree weak-strong form method is presented to compute the fully developed magnetohydrodynmic flow in a pipe. The radial basis function point interpolation approximation is adopted to construct the shape functions. For the nodes whose local quadrature domain is intersect with the natural boundaries, a local weak form of radial point interpolation method is applied. Otherwise, a strong form of meshfree point collocation method is employed. Numerical simulations are carried out for fully developed magnetohydrodynmic flow in a rectangular pipe with arbitrary electrical conductivity.

A NONLINEAR INVERSE PHASE TRANSITION PROBLEM FOR THE HEAT EQUATION

1991 ◽  
Vol 01 (02) ◽  
pp. 167-182 ◽  
Author(s):  
L. PREZIOSI ◽  
L.M. DE SOCIO
Keyword(s):  
Phase Transition ◽  
Heat Equation ◽  
Space Dimension ◽  
Interpolation Method ◽  
Solution Procedure ◽  
Nonlinear Heat Equation ◽  
Moving Interface ◽  
First Case ◽  
Phase Transition Problem ◽  
Quantitative Results

This paper proposes a method for the solution of two inverse problems which are governed by the nonlinear heat equation in one space dimension. In the first case phase transition occurs at the moving interface which divides two media. In the second one a random heat source is placed at a moving point. In both cases the temperature is assigned, as a function of time and within a random error, at a given fixed point. The solution procedure leads to quantitative results and is based on the Stochastic Adaptative Interpolation method.

Bicubic B-spline interpolation method for two-dimensional heat equation

2015 ◽  
Author(s):  
Nur Nadiah Abd. Hamid ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail
Keyword(s):  
Heat Equation ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Two Dimensional ◽  
B Spline

scholarly journals Solving acoustic scattering problem by the meshless method based on radial basis function

2019 ◽  
Vol 288 ◽  
pp. 01008
Author(s):  
Weifang Liu ◽  
Sanfei Zhao ◽  
Cong Zhang ◽  
Huipo Qiao
Keyword(s):  
Meshless Method ◽  
Solid Mechanics ◽  
Interpolation Method ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Neumann Boundary ◽  
Convection Diffusion ◽  
Point Collocation ◽  
Solution Accuracy

In this paper, radial point collocation method (RPCM) is introduced to solve the acoustic scattering problem. This is a mathematically simple, easy-to-program and truly meshless method, which has been successfully applied to solve the solid mechanics and convection diffusion problems. However, application of this method to investigate acoustic problems, in particle the acoustic scattering problem is relatively new. The main advantage of this method is its mathematically simple, easy to program, and truly meshless. A Hermite-type interpolation method is employed to improve the solution accuracy while the Neumann boundary conditions exist. In addition, acoustic scattering problem is a typical unbounded domain problem, in order to solve it with RPCM, the domain is truncated to a finite region and an artificial boundary condition (ABC) is imposed. Finally, numerical example is presented to validate the accuracy and effectiveness of RPCM. In the future, the extension of RPCM to more complex and practical problems, especially the three-dimensional situations need to be investigated in more detail.

Ab initio band theory approach to electron energy loss near edge structures

1988 ◽  
Vol 46 ◽  
pp. 506-507
Author(s):  
Xudong Weng ◽  
O.F. Sankey ◽  
Peter Rez
Keyword(s):  
Ab Initio ◽  
Local Density ◽  
Interpolation Method ◽  
Atomic Orbital ◽  
Plane Waves ◽  
Large Set ◽  
Theory Approach ◽  
Band Theory ◽  
Atomic Orbitals ◽  
Pseudopotential Calculations

Single electron band structure techniques have been applied successfully to the interpretation of the near edge structures of metals and other materials. Among various band theories, the linear combination of atomic orbital (LCAO) method is especially simple and interpretable. The commonly used empirical LCAO method is mainly an interpolation method, where the energies and wave functions of atomic orbitals are adjusted in order to fit experimental or more accurately determined electron states. To achieve better accuracy, the size of calculation has to be expanded, for example, to include excited states and more-distant-neighboring atoms. This tends to sacrifice the simplicity and interpretability of the method.In this paper. we adopt an ab initio scheme which incorporates the conceptual advantage of the LCAO method with the accuracy of ab initio pseudopotential calculations. The so called pscudo-atomic-orbitals (PAO's), computed from a free atom within the local-density approximation and the pseudopotential approximation, are used as the basis of expansion, replacing the usually very large set of plane waves in the conventional pseudopotential method. These PAO's however, do not consist of a rigorously complete set of orthonormal states.

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