Four-dimensional tomographic reconstruction by time domain decomposition

Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes this decades-old requirement of static samples. In the presented method, dynamic tomographic data sets are decomposed in the temporal domain using basis functions and deploying an L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We implemented the iterative algorithm for solving the regularization problem on modern GPU systems to demonstrate its practical use

A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems

Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of Krylov solvers for tomographic linear inversion problems. These advanced iterative methods feature fast convergence at the expense of a higher computational cost per iteration, causing them to be generally uncompetitive without the inclusion of a suitable preconditioner. Combining elements from standard multigrid (MG) solvers and the theory of wavelets, a novel wavelet-based multi-level (WMG) preconditioner is introduced, which is shown to significantly speed-up Krylov convergence. The performance of the WMG-preconditioned Krylov method is analyzed through a spectral analysis, and the approach is compared to existing methods like the classical Simultaneous Iterative Reconstruction Technique (SIRT) and unpreconditioned Krylov methods on a 2D tomographic benchmark problem. Numerical experiments are promising, showing the method to be competitive with the classical Algebraic Reconstruction Techniques in terms of convergence speed and overall performance (CPU time) as well as precision of the reconstruction.Comment: Journal of Computational and Applied Mathematics (2014), 26 pages, 13 figures, 3 table

Transient Analysis of High-Speed Channels via Newton-GMRES Waveform Relaxation

This paper presents a technique for the numerical simulation of coupled high-speed channels terminated by arbitrary nonlinear drivers and receivers. The method builds on a number of existing techniques. A Delayed-Rational Macromodel is used to describe the channel in compact form, and a general Waveform Relaxation framework is used to cast the solution as an iterative process that refines initial estimates of transient scattering waves at the channel ports. Since a plain Waveform Relaxation approach is not able to guarantee convergence, we turn to a more general class of nonlinear algebraic solvers based on a combination of the Newton method with a Generalized Minimal Residual iteration, where the Waveform Relaxation equations act as a preconditioner. The convergence of this scheme can be proved in the general case. Numerical examples show that very few iterations are indeed required even for strongly nonlinear termination

Algorithmic aspects of transient heat transfer problems in structures

It is noted that the application of finite element or finite difference techniques to the solution of transient heat transfer problems in structures often results in a stiff system of ordinary differential equations. Such systems are usually handled most efficiently by implicit integration techniques which require the solution of large and sparse systems of algebraic equations. The assembly and solution of these systems using the incomplete Cholesky conjugate gradient algorithm is examined. Several examples are used to demonstrate the advantage of the algorithm over other techniques