Fast Krylov subspace methods for geostatistical inverse problems
Abstract/Contents
- Abstract
- Inverse problems are part of a mathematical framework used to estimate parameters that characterize a physical system but are difficult to measure directly. An example application is hydraulic tomography which is a method of imaging the subsurface. Water is pumped at designated pumping wells and the measured pressure response is recorded at corresponding observation wells. These noisy measurements of pressure are then used to obtain tomographic reconstructions of important hydrogeological parameters such as hydraulic conductivity and storage. Inverse problems of this type are particularly challenging both mathematically as they are ill-posed, and computationally as they generally require repeated solutions of large-scale partial differential equations. In this dissertation, we discuss in detail a method of imaging based on oscillatory pumping tests. We discuss methods to extract the signal from the noise and examine the duration of the transient. For this class of inverse problems, solving shifted systems of linear equations is a major computational bottleneck. In the dissertation, we describe an iterative algorithm for solving shifted linear systems. Krylov subspace methods are particularly appealing because of their shift-invariant property. By exploiting this property, only a single Krylov basis is computed and the solution for multiple shifts can be obtained at a cost that is nearly equal to the cost of solving a single system. We then show how the time dependent inverse problems can be accelerated using these Krylov subspace solvers using a Laplace-transform approach.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Bakhos, Tania |
|---|---|
| Associated with | Stanford University, Institute for Computational and Mathematical Engineering. |
| Primary advisor | Kitanidis, P. K. (Peter K.) |
| Thesis advisor | Kitanidis, P. K. (Peter K.) |
| Thesis advisor | Poulson, Jack Lesly |
| Thesis advisor | Saunders, Michael A |
| Advisor | Poulson, Jack Lesly |
| Advisor | Saunders, Michael A |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Tania Bakhos. |
|---|---|
| Note | Submitted to the Institute for Computational and Mathematical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Tania Bakhos
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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