Solving Poisson's Equation Using Finite Difference Method
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Resource Overview
This example demonstrates solving Poisson's equation using the finite difference method with SOR (Successive Over-Relaxation) iteration. The implementation models a square domain discretized into an 11×11 grid structure, where the grid density can be easily modified through parameter configuration.
Detailed Documentation
In this article, we employ the finite difference method to solve Poisson's equation, enhanced by the SOR (Successive Over-Relaxation) iterative technique for improved convergence efficiency. To effectively demonstrate the model's performance, we implement a square computational domain discretized using an 11×11 grid system. The implementation utilizes central difference approximation for spatial derivatives and incorporates a relaxation parameter (typically between 1 and 2) to accelerate iteration convergence. The grid resolution can be conveniently adjusted by modifying the grid parameter in the code, allowing users to adapt the model to specific accuracy requirements or computational constraints. Key implementation aspects include boundary condition handling, residual calculation, and convergence criteria monitoring through relative error thresholds.
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