Fast and robust solvers for pressure-correction in bubbly flow problems
Journal of Computational Physics
The Lanczos Method for Parameterized Symmetric Linear Systems with Multiple Right-Hand Sides
SIAM Journal on Matrix Analysis and Applications
Accelerating the LSTRS Algorithm
SIAM Journal on Scientific Computing
A Regularized Gauss-Newton Trust Region Approach to Imaging in Diffuse Optical Tomography
SIAM Journal on Scientific Computing
Supporting dynamic parameter sweep in adaptive and user-steered workflow
Proceedings of the 6th workshop on Workflows in support of large-scale science
Low-Rank Tensor Krylov Subspace Methods for Parametrized Linear Systems
SIAM Journal on Matrix Analysis and Applications
Journal of Computational Physics
Accelerated GCRO-DR method for solving sequences of systems of linear equations
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
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We discuss the efficient solution of a long sequence of slowly varying linear systems arising in computations for diffuse optical tomographic imaging.The reconstruction of three-dimensional absorption and scattering information by matching computed solutions from a parameterized model to measured data leads to a nonlinear least squares problem that we solve using the Gauss--Newton method with a line search. This algorithm requires the solution of a long sequence of linear systems. Each choice of parameters in the nonlinear least squares algorithm results in a different matrix describing the optical properties of the medium. These matrices change slowly from one step to the next, but may change significantly over many steps. For each matrix we must solve a set of linear systems with multiple shifts and multiple right-hand sides.For this problem, we derive strategies for recycling Krylov subspace information that exploit properties of the application and the nonlinear optimization algorithm to significantly reduce the total number of iterations over all linear systems. Furthermore, we introduce variants of GCRO that exploit symmetry and that allow simultaneous solution of multiple shifted systems using a single Krylov subspace in combination with recycling. Although we focus on a particular application and optimization algorithm, our approach is applicable generally to problems where sequences of linear systems must be solved. This may guide other researchers to exploit the opportunities of tunable solvers.We provide results for two sets of numerical experiments to demonstrate the effectiveness of the resulting method.