New Implementation Method for Essential Boundary Condition to Extended Element-Free Galerkin Method: Application to Nonlinear Problem

Ayumu SAITOH; Taku ITOH; Nobuyuki MATSUI; Atsushi KAMITANI; Hiroaki NAKAMURA

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New Implementation Method for Essential Boundary Condition to Extended Element-Free Galerkin Method: Application to Nonlinear Problem

机译：扩展自由元Galerkin方法的基本边界条件的新实现方法：在非线性问题中的应用

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A new method has been proposed for implementing essential boundary conditions to the Element-Free Galerkin Method (EFGM) without using the Lagrange multiplier. Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that, as interpolation functions become closer to delta functions, the accuracy of the solution is improved on the boundary. In addition, the accuracy of the proposed method is higher than that of the conventional EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem.

机译：已经提出了一种新方法，用于在不使用拉格朗日乘数的情况下将基本边界条件实现为无元素伽勒金方法（EFGM）。此外，已经针对非线性泊松问题研究了所提出方法的性能。计算结果表明，随着插值函数越来越接近增量函数，解的精度在边界上得到了提高。另外，所提出的方法的精度高于传统的EFGM。因此，可以得出结论，所提出的方法对于解决非线性泊松问题是有用的。

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《Plasma and Fusion Research》 |2011年第6期|共1页
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Ayumu SAITOH; Taku ITOH; Nobuyuki MATSUI; Atsushi KAMITANI; Hiroaki NAKAMURA;
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中图分类等离子体物理学;
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专利

1. A modified element-free Galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function [J] . Marcelo Krajnc Alves, Rodrigo Rossi International Journal for Numerical Methods in Engineering . 2003,第11期

机译：一种改进的无元素Galerkin方法，其基本边界条件由单位有限元权重函数的扩展分区实施
2. A Moving Least Squares weighting function for the Element-free Galerkin Method which almost fulfills essential boundary conditions [J] . Thomas Most, Christian Bucher Structural Engineering and Mechanics . 2005,第3期

机译：无元素Galerkin方法的移动最小二乘加权函数几乎满足基本边界条件
3. Application of Extended Element-Free Galerkin Method to Nonlinear Problem [J] . Saitoh A., Itoh T., Matsui N., Magnetics, IEEE Transactions on . 2012,第2期

机译：扩展无单元Galerkin方法在非线性问题中的应用
4. New Method for Implementing Essential BoundaryCondition to Element-Free Galerkin Method [C] . Ayumu Saitoh, Taku Itoh, Nobuyuki Matsui, International Conference on Numerical Analysis and Applied Mathematics . 2010

机译：实现无元素Galerkin方法的基本边界条件的新方法
5. THE MODELING OF GALVANIC CORROSION SYSTEMS USING NUMERICAL METHODS WITH PARTICULAR ATTENTION TO BOUNDARY CONDITIONS OF NONLINEAR POLARIZATION (ELECTROCHEMISTRY, FINITE-ELEMENT METHODS). [D] . MUNN, RAYMOND SHATTUCK. 1986

机译：电偶腐蚀系统的建模使用数值方法，特别注意非线性极化的边界条件（电化学，有限元方法）。
6. Implicit finite-difference schemes, based on the Rosenbrock method, for nonlinear Schrödinger equation with artificial boundary conditions [O] . Vyacheslav A. Trofimov, Evgeny M. Trykin 2012

机译：基于Rosenbrock方法的含人工边界条件的非线性Schrödinger方程的隐式有限差分格式
7. New Implementation Method for Essential Boundary Condition to Extended Element-Free Galerkin Method: Application to Nonlinear Problem [O] . Ayumu SAITOH, Taku ITOH, Nobuyuki MATSUI, 2011

机译：扩展元素Galerkin方法的基本边界条件的新实现方法：非线性问题的应用

New Implementation Method for Essential Boundary Condition to Extended Element-Free Galerkin Method: Application to Nonlinear Problem

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