Fast parallel-in-time quasi-boundary value methods for backward heat conduction problems

In this paper we propose two new quasi-boundary value methods for regularizing the ill-posed backward heat conduction problems. With a standard finite difference discretization in space and time, obtained all-at-once nonsymmetric sparse linear systems have desired block ? -circulant structure, which can be utilized to design an efficient parallel-in-time (PinT) direct solver that built upon explicit FFT-based diagonalization of time matrix. Convergence analysis is presented justify optimal choice regularization parameter under suitable assumptions. Numerical examples are reported validate our illustrate superior computational efficiency proposed PinT methods.