jacobi_poisson_1d_2011_fsu, "Solving the 1D Poisson Equation with Jacobi Iteration", investigate the use of the Jacobi iterative solver to compute approximate solutions to a discretization of Poisson's equation in 1D, written at Florida State University in 2011.
The document is intended as a record and guide for a particular investigation into this problem. Therefore, we specify a particular set of data that represents an instance of the Poisson equation; we discuss the form of a discretization of the equation which results in a linear system; we consider a specific implementation of the Jacobi iteration that was used to solve the linear system; we then consider the convergence behavior of the iterative method as the size of the grid increases and look for an alternative solution procedure that will give us the answer more efficiently. The expectation is that the multigrid method will enable us to solve the 1D problem more quickly, and to proceed to the 2D problems that are of greater interest.
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