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Full-Text Articles in Applied Mathematics
Source Optimization In Abstract Function Spaces For Maximizing Distinguishability: Applications To The Optical Tomography Inverse Problem, Bonnie Jacob
All Dissertations
The focus of this thesis is to formulate an optimal source problem for the medical imaging technique of optical tomography by maximizing certain distinguishability criteria. We extend the concept of distinguishability in electrical impedance tomography to the frequency-domain diffusion approximation model used in optical tomography.
We consider the dependence of the optimal source on the choice of appropriate function spaces, which can be chosen from certain Sobolev or Lp spaces. All of the spaces we consider are Hilbert spaces; we therefore exploit the inner product in several ways. First, we define and use throughout an inner product on the Sobolev …
High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang
High Accuracy Multiscale Multigrid Computation For Partial Differential Equations, Yin Wang
University of Kentucky Doctoral Dissertations
Scientific computing and computer simulation play an increasingly important role in scientific investigation and engineering designs, supplementing traditional experiments, such as in automotive crash studies, global climate change, ocean modeling, medical imaging, and nuclear weapons. The numerical simulation is much cheaper than experimentation for these application areas and it can be used as the third way of science discovery beyond the experimental and theoretical analysis. However, the increasing demand of high resolution solutions of the Partial Differential Equations (PDEs) with less computational time has increased the importance for researchers and engineers to come up with efficient and scalable computational techniques …