scholarly journals Kansa method for problems with multiple boundary conditions

2018 ◽  
Author(s):  
Artur Krowiak
Keyword(s):  
Boundary Conditions ◽  
Kansa Method ◽  
Multiple Boundary Conditions

A Noniterative Numerical Solution of Poisson’s and Laplace’s Equations With Applications to Slow Viscous Flow

1966 ◽  
Vol 88 (4) ◽  
pp. 725-733 ◽  
Author(s):  
M. L. Booy
Keyword(s):  
Boundary Conditions ◽  
Viscous Flow ◽  
Computational Effort ◽  
Linear Boundary ◽  
Simultaneous Solution ◽  
Slow Viscous Flow ◽  
Flow Problems ◽  
Engineering Problems ◽  
Iterative Procedures ◽  
Multiple Boundary Conditions

A noniterative finite-difference method for solution of Poisson’s and Laplace’s equations for linear boundary conditions is given. The method is simpler and more accurate than iterative procedures. It is limited in the number of meshes that can be used, but that number is adequate to obtain accurate solutions to many engineering problems. The computational effort is reduced vastly when one differential equation must be solved in a family of domains for the same boundary condition. The same applies to calculations of the integral of the function in the domain. Examples are given for simultaneous solution in Laplace’s and Poisson’s equations and for problems with multiple boundary conditions. The results of several slow viscous-flow problems are discussed.

A Meshless Method Based on Radial Basis and Spline Interpolation for 2-D and 3-D Inhomogeneous Biharmonic BVPs

2015 ◽  
Vol 70 (8) ◽  
pp. 673-682 ◽  
Author(s):  
Elyas Shivanian
Keyword(s):  
Boundary Conditions ◽  
Meshless Method ◽  
Spline Interpolation ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Poisson Equations ◽  
Second Derivatives ◽  
Radial Basis ◽  
Collocation Scheme ◽  
Multiple Boundary Conditions

AbstractThis paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of first derivatives. In the next step, our meshless approach uses two- and three-dimensional cubic spline interpolation to get smooth, approximate solutions for the 2-D and 3-D inhomogeneous biharmonic-type problem, respectively. Numerical experiments are included to demonstrate the reliability and efficiency of this method.

scholarly journals Optimal Generation Expansion Planning Model of a Combined Thermal-wind-PV Power System Considering Multiple Boundary Conditions: A Case Study in Xinjiang, China

2020 ◽  
Author(s):  
Yu Li ◽  
Mei Dai ◽  
Songtao Hao ◽  
Gang Qiu ◽  
Guoqing Li ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Power System ◽  
Boundary Conditions ◽  
Power Plants ◽  
Generation Expansion Planning ◽  
Total Cost ◽  
Expansion Planning ◽  
Generation Expansion ◽  
Photovoltaic Power ◽  
Multiple Boundary Conditions

Abstract Background The scarcity of fossil fuels and their high emissions impact on the environment have forced the rapid development of renewable energy. Wind and photovoltaic power play a more and more important role in today's power system because of their clean and renewable characteristics. However, with the large-scale grid connection of wind and photovoltaic power, the contradiction between renewable energy and thermal power is becoming more and more serious. The unreasonable planning of power generation resources has also caused a lot of waste of electric power.Methods To solve this problem, this paper comprehensively considers the construction and operation costs of power plants, and constructs an optimal generation expansion planning model of a combined thermal-wind-PV power system with the objective of minimizing total cost. The planning is calculated under the boundary conditions of ensuring the safe operation of the power grid and taking into account the share requirement, utilization requirements and construction requirements for renewable energy. The model is applied to the self-use and external power plants in Xinjiang.Results The results show that this generation expansion plan can reduce the total cost of the power plants while ensuring the load demand. The renewable energy has also received more consumption share and its abandonment rate has dropped significantly. Numerical examples show that the optimization model has good applicability.Conclusion The proposed optimization model can realize the coordinated development of three types of power sources under multiple boundary conditions, which can not only guarantee the economy of power construction, but also take into account the optimization of environmental benefits. Reasonable generation expansion planning can improve energy efficiency, achieve clean and low carbon in the process of power generation, and promote the sustainable development of society.

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