A globally convergent numerical method for coefficient inverse problems with time-dependent data. (English) Zbl 1278.65147
Beilina, Larisa (ed.), Applied inverse problems. Select contributions from the first annual workshop on inverse problems, Gothenburg, Sweden, June 2–3, 2011. New York, NY: Springer (ISBN 978-1-4614-7815-7/hbk; 978-1-4614-7816-4/ebook). Springer Proceedings in Mathematics & Statistics 48, 105-128 (2013).
Summary: In our terminology “globally convergent numerical method” means a numerical method whose convergence to a good approximation for the correct solution is independent of the initial approximation. A new numerical imaging algorithm is proposed to solve a coefficient inverse problem for an elliptic equation with the data generated by computer simulation. A convergence analysis shows that this method converges globally assuming the smallness of the asymptotic solution (the so-called tail function). A heuristic approach for approximating the “new tail function”, which is a crucial part (assuming the smallness of the tail function) of our problem, is utilized and verified in numerical experiments, so has the global convergence. Numerical experiments in the 2D time-domain optical property reconstruction are presented.
For the entire collection see [Zbl 1272.65001].
For the entire collection see [Zbl 1272.65001].
MSC:
| 65M32 | Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs |
| 35K10 | Second-order parabolic equations |
| 44A10 | Laplace transform |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
