We introduced a method presented in Information Field Theory (IFT) [Abramovich et al., 2007] to improve interpolation in Smoothed Particle Hydrodynamics (SPH) in cases of less smooth flow. The method makes use of wavelet theory combined with B-splines for interpolation. The idea is to identify any jumps a function may have and then reconstruct the smoother segments between the jumps. The results of our work demonstrated superior capability when compared to a particular challenging SPH application, to better conserve jumps and more accurately interpolate the smoother segments of the function. The results of our work also demonstrated increased computational efficiency with limited loss in accuracy as number of multiplications and execution time were reduced. Similar benefits were observed for functions with spikes analyzed by the same method. Lesser, but similar effects were also demonstrated for real life data sets of less smooth nature. SPH is widely used in modeling and simulation of flow of matters. SPH presents advantages compared to grid based methods both in terms of computational efficiency and accuracy, in particular when dealing with less smooth flow. The results we achieved through our research is an improvement to the model in cases of less smooth flow, in particular flow with jumps and spikes. Up until now such improvements have been sought through modifications to the models' physical equations and/or kernel functions and have only partially been able to address the issue. This research, as it introduced wavelet theory and IFT to a field of science that, to our knowledge, not currently are utilizing these methods, did lay the groundwork for future research ideas to benefit SPH. Among those ideas are further development of criteria for wavelet selection, use of smoothing splines for SPH interpolation and incorporation of Bayesian field theory. Improving the method's accuracy, stability and efficiency under more challenging conditions such as flow with jumps and spikes, will benefit applications in a wide area of science. Just in medicine alone, such improvements will further increase real time diagnostics, treatments and training opportunities because jumps and spikes are often the characteristics of significant physiological and anatomic conditions such as pulsatile blood flow, peristaltic intestine contractions and organs' edges appearance in imaging.


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Graduation Date





Wiegand, Rudolf


Master of Science (M.S.)


College of Sciences

Degree Program

Modeling and Simulation









Release Date

December 2016

Length of Campus-only Access


Access Status

Masters Thesis (Open Access)