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• W2024401988 abstract "The sideways parabolic equation (SPE) is a model of the problem of determining the temperature on the surface of a body from the interior measurements. Mathematically it can be formulated as a noncharacteristic Cauchy problem for a parabolic partial differential equation. This problem is severely ill-posed in an $L_2$ setting. We use a preconditioned generalized minimum residual method (GMRES) to solve a two-dimensional SPE with variable coefficients. The preconditioner is singular and chosen in a way that allows efficient implementation using the FFT. The preconditioner is a stabilized solver for a nearby problem with constant coefficients, and it reduces the number of iterations in the GMRES algorithm significantly. Numerical experiments are performed that demonstrate the performance of the proposed method." @default.
• W2024401988 created "2016-06-24" @default.
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• W2024401988 date "2014-01-01" @default.
• W2024401988 modified "2023-10-18" @default.
• W2024401988 title "Solving an Ill-Posed Cauchy Problem for a Two-Dimensional Parabolic PDE with Variable Coefficients Using a Preconditioned GMRES Method" @default.
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• W2024401988 doi "https://doi.org/10.1137/130951166" @default.
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