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Improving Data with Models or Improving Models with Data

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Date and time:Ìý

Tuesday, October 7, 2014 - 10:30am

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Grandview Conference Room

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This talk will present recent results on an approach that we have been developing over the past few years to assimilate data into the solution of a partial differential equation.Ìý In particular, we will focus on the assimilation of echocardiographic particle imaging velocimetry (echo-PIV) data obtained using microbubbles in the left ventricle of the heart.Ìý The approximate solution to the Navier-Stokes equation is obtained using the least-squares finite element method (LSFEM) and this method has been shown to be very flexible when assimilating noisy echo-PIV data [1]. This flexibility is due to the ability of the method to close match accurate echo-PIV data and less accurately match noisy data. The LSFEM method with the assimilatiion of echo-PIV data is used to predict the 3-dimensional LV blood flow. Results from the current method clearly show the impact of assimilating echo-PIV data when visualizing the three-dimensional velocity field.Ìý Recent work in this area is focused on the type of finite element, h- vs. p-refinement, hybrid LSFEM, and alternative first-order systems for Navier-Stokes.