Solving a Cauchy problem for a 3D elliptic PDE with variable coefficients by a quasi-boundary-value method
نویسندگان
چکیده
An ill-posed Cauchy problem for a 3D elliptic PDE with variable coefficients is considered. A well-posed quasi-boundary-value (QBV) problem is given to approximate it. Some stability error estimates are given. For the numerical implementation, a large sparse system is obtained from the discretizing the QBV problem using finite difference method (FDM). A LeftPreconditioner Generalized Minimum Residual (GMRES) method is used to solve the large system effectively. For the preconditioned system, a fast solver using the Fast Fourier Transform (FFT). Numerical results show that the method works well.
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