scholarly journals Coupling of Point Collocation Meshfree Method and FEM for EEG Forward Solver

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Chany Lee ◽  
Jong-Ho Choi ◽  
Ki-Young Jung ◽  
Hyun-Kyo Jung
Keyword(s):  
Reproducing Kernel ◽  
Kernel Method ◽  
Current Source ◽  
Meshfree Method ◽  
Forward Problem ◽  
Least Square ◽  
Head Model ◽  
Source Modeling ◽  
Moving Least Square ◽  
Point Collocation

For solving electroencephalographic forward problem, coupled method of finite element method (FEM) and fast moving least square reproducing kernel method (FMLSRKM) which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed using meshfree method. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM adopts point collocation scheme. Suggested method is tested using simple equation using 1-, 2-, and 3-dimensional models, and error tendency according to node distance is studied. In addition, electroencephalographic forward problem is solved using spherical head model. Proposed hybrid method can produce well-approximated solution.

Two Implicit Meshless Finite Point Schemes for the Two-Dimensional Distributed-Order Fractional Equation

2019 ◽  
Vol 19 (4) ◽  
pp. 813-831
Author(s):  
Rezvan Salehi
Keyword(s):  
Reproducing Kernel ◽  
Point Method ◽  
Least Square ◽  
Computationally Efficient ◽  
Finite Point ◽  
Moving Least Square ◽  
Point Collocation ◽  
Finite Point Method ◽  
Distributed Order ◽  
Fractional Equation

AbstractIn this paper, the distributed-order time fractional sub-diffusion equation on the bounded domains is studied by using the finite-point-type meshless method. The finite point method is a point collocation based method which is truly meshless and computationally efficient. To construct the shape functions of the finite point method, the moving least square reproducing kernel approximation is employed. Two implicit discretisation of order{O(\tau)}and{O(\tau^{1+\frac{1}{2}\sigma})}are derived, respectively. Stability and{L^{2}}norm convergence of the obtained difference schemes are proved. Numerical examples are provided to confirm the theoretical results.

A Miniaturized Electron Beam Column Simulation by the Fast Moving Least Square Reproducing Kernel Point Collocation Method

2003 ◽  
Vol 42 (Part 1, No. 6B) ◽  
pp. 3842-3848 ◽  
Author(s):  
Do Wan Kim ◽  
Yongsik Kim ◽  
Young Chul Kim ◽  
Ho Seob Kim ◽  
Seungjoon Ahn ◽  
...  
Keyword(s):  
Electron Beam ◽  
Collocation Method ◽  
Fast Moving ◽  
Reproducing Kernel ◽  
Least Square ◽  
Moving Least Square ◽  
Point Collocation

An Efficient Meshfree Method for Fracture Analysis of Cracks in Bi-Materials

2006 ◽  
Author(s):  
B. Nandulal ◽  
B. N. Rao ◽  
C. Lakshmana Rao
Keyword(s):  
Computational Efficiency ◽  
Basis Function ◽  
Meshfree Method ◽  
Fracture Analysis ◽  
Least Square ◽  
Moving Least Square ◽  
Linear Elastic ◽  
Moving Least Square Approximation ◽  
Material Fracture ◽  
Element Free

This paper presents an enriched meshless method based on an improved moving least-square approximation (IMLS) method for fracture analysis of cracks in homogeneous, isotropic, linear-elastic, two-dimensional bimaterial solids, subject to mixed-mode loading conditions. The method involves an element-free Galerkin formulation in conjunction with IMLS and a new enriched basis functions to capture the singularity field in linear-elastic bi-material fracture mechanics. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill-conditioned system of equations. The proposed enriched basis function can be viewed as a generalized enriched basis function, which degenerates to a linear-elastic basis function when the bimaterial constant is zero. Numerical examples are presented to illustrate the computational efficiency and accuracy of the proposed method.

Upwinding Meshfree Point Collocation Method for Steady MHD Flow

2010 ◽  
Author(s):  
Xinghui Cai ◽  
Guanghui Su ◽  
Suizheng Qiu
Keyword(s):  
Magnetic Field ◽  
Collocation Method ◽  
Mhd Flow ◽  
Least Square ◽  
Good Convergence ◽  
Moving Least Square ◽  
Point Collocation ◽  
Coupled Equations ◽  
Meshless Collocation ◽  
Mls Approximation

In this paper, a meshfree point collocation method, with a upwinding scheme, is presented to obtain the numerical solution of the coupled equations in velocity and magnetic field for the fully developed magnetohydrodynamic (MHD) flow through a straight pipe of rectangular section with insulated walls. The moving least-square (MLS) approximation is employed to construct shape functions in conjunction with the framework of point collocation method. Computations have been carried out for different applied magnetic field orientations and different Hartmann numbers from 5 to 1,000,000. As the adaptive upwinding local support domain is introduced in the meshless collocation method, numerical results show that the method can compute MHD problems not only at low and moderate values but also at high values of the Hartmann number with high accuracy and good convergence.

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