Nine-Point Nearest Neighbors Finite Difference Method
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Date: Fri, July 02, 2021
Time: 10:30am - 11:00am
Location: online, email for details
Speaker: Charles White, candidate for MS, advisor Dr. Gary Varner
The Finite difference method (FDM) is widely used in many applications such as the calculation of electric potential distribution in transmission lines where boundary conditions are known. For the two-dimensional (2D) Laplace Equation ( ), the common solution using the FDM is to use a 5-point equal arm grid in which the potential at the center point is expressed as the average of the surrounding four potentials. The Nearest Neighbor Finite difference method (NNFDM) is an extension of the FDM which uses the nearest 9 points of a mesh square grid. This work shows when a mesh grid is defined with 50 x 100 points or more then it is more accurate for the NNFDM as opposed to the FDM. In the case of a rectangular box with a 100V source on one edge the NNFDM showed an improvement with up to 5000 times more accuracy than the FDM when compared to the analytical solution while adding only a 0.7% difference in the total time executing the NNFDM solution.
Date: Fri, July 02, 2021
Time: 10:30am - 11:00am
Location: online, email for details
Speaker: Charles White, candidate for MS, advisor Dr. Gary Varner
The Finite difference method (FDM) is widely used in many applications such as the calculation of electric potential distribution in transmission lines where boundary conditions are known. For the two-dimensional (2D) Laplace Equation ( ), the common solution using the FDM is to use a 5-point equal arm grid in which the potential at the center point is expressed as the average of the surrounding four potentials. The Nearest Neighbor Finite difference method (NNFDM) is an extension of the FDM which uses the nearest 9 points of a mesh square grid. This work shows when a mesh grid is defined with 50 x 100 points or more then it is more accurate for the NNFDM as opposed to the FDM. In the case of a rectangular box with a 100V source on one edge the NNFDM showed an improvement with up to 5000 times more accuracy than the FDM when compared to the analytical solution while adding only a 0.7% difference in the total time executing the NNFDM solution.