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Detailed explanation of the principle of solving Poisson's equation using the two-dimensional finite element method:
The two-dimensional finite element method is a numerical solution method used to solve partial differential equation problems. When solving Poisson's equation, the two-dimensional finite element method divides the solution domain into multiple small areas (units), and uses a local function (finite element shape function) in each unit to approximate the solution of the original equation. By decomposing the entire domain into multiple units and establishing connection relationships between the units, a discrete equation system can be formed. Solving this discrete system of equations yields an approximate solution to Poisson's equation.
The underlying architecture flow chart:
The underlying architecture flow chart for solving the Poisson equation using the two-dimensional finite element method is as follows:
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| 网格生成和划分 |
| |
| |
| +---------------+ |
| | 单元刚度矩阵 | |
| | | |
| +---------------+ |
| | |
| v |
| +---------------+ |
| | 装配 | |
| | 矩阵和向量 | |
| +------