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On the development of finite nodal point methods
27th Structures, Structural Dynamics and Materials Conference, 1986A new method for the numerical solution of ordinary or partial differential equations over one or several dimensional domains, developed jointly at the Engineering College at Kansas State University and the University of Mississippi, is presented. This method has the advantages of being flexible, and well suited for many engineering problems in which ...
K. HU, S. SWARTZ, P. KIRMSER, S. WANG
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An Alternate Formulation of the Nodal Expansion Method
Nuclear Science and Engineering, 2001An alternate formulation of the two-group transverse-integration-based nodal expansion method is presented. In this formulation, the two-group problem is formulated by using the relationship between the group fluxes derived from an analytical procedure. As a result, a simplified procedure for the thermal group is suggested. The numerical results of the
Keqiang Ruan, Xiaogang Xue, Xuedong Fu
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A CMFD Acceleration Method for SP3 Advanced Nodal Method
Nuclear Science and Engineering, 2016Flux-level-fixup (FF) coarse-mesh finite difference (CMFD) (FF-CMFD), which increases numerical stability during nonlinear iterations for the SP3 advanced nodal method, is proposed as an improved C...
Akio Yamamoto +2 more
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An Integral Form of the Variational Nodal Method
Nuclear Science and Engineering, 2004An integral form of the variational nodal method is formulated, implemented, and tested. The method combines an integral transport treatment of the even-parity flux within the spatial node with an odd-parity spherical harmonics expansion of the Lagrange multipliers at the node interfaces.
M. A. Smith +3 more
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Nodal Mimetic Finite Difference Methods
2018GDMs are obtained from the nodal mimetic finite differences methods, and also cover some DDFV schemes.
Jérôme Droniou +4 more
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Efficient nodal equation assembly method
Proceedings of the IEEE, 1969Using Branin and Wang's method of storing the incidence matrix, a general and efficient method of forming the nodal equations is presented.
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2017
For a truly meshfree technique, Galerkin meshfree methods rely chiefly on nodal integration of the weak form. In the case of Strong Form Collocation meshfree methods, direct collocation at the nodes can be employed. In this paper, performance of these node-based Galerkin and collocation meshfree methods is compared in terms of accuracy, efficiency, and
M. Hillman, J. S. Chen
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For a truly meshfree technique, Galerkin meshfree methods rely chiefly on nodal integration of the weak form. In the case of Strong Form Collocation meshfree methods, direct collocation at the nodes can be employed. In this paper, performance of these node-based Galerkin and collocation meshfree methods is compared in terms of accuracy, efficiency, and
M. Hillman, J. S. Chen
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A spatial rehomogenization method in nodal calculations
Annals of Nuclear Energy, 2006Abstract Infinite medium flux weighted cross-sections used in nodal calculations enable equivalence with the corresponding fine configuration if the following condition is satisfied: the flux shape inside the assembly in the core is close to the infinite medium flux shape (computed in lattice calculations).
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A Hennart Nodal Method for the Diffusion Equation
Nuclear Science and Engineering, 1995A modification of the Hennart nodal method for neutron diffusion problems is presented. The final system of equations obtained by this method is not positive definite. However, a flux elimination technique leads to a simple positive definite system, which can be solved by the traditional iterative methods.
P. Lesaint, S. Noceir, D. Verwaerde
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