Combining existing numerical models with data assimilation using weighted least-squares finite element methods.

A new approach has been developed for combining and enhancing the results from an existing computational fluid dynamics model with experimental data using the weighted least-squares finite element method (WLSFEM). Development of the approach was motivated by the existence of both limited experimental blood velocity in the left ventricle and inexact numerical models of the same flow. Limitations of the experimental data include measurement noise and having data only along a two-dimensional plane.

Adaptive multigrid algorithm for the lattice Wilson-Dirac operator.

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.

First-order system least-squares (FOSLS) for modeling blood flow.

The modeling of blood flow through a compliant vessel requires solving a system of coupled nonlinear partial differential equations (PDEs). Traditional methods for solving the system of PDEs do not scale optimally, i.e.

Modeling 3-D compliant blood flow with FOSLS.

Blood flow in large vessels is typically modeled using the Navier-Stokes equations for the fluid domain and elasticity equations for the vessel wall. As the wall deforms, additional complications are introduced because the shape of the fluid domain changes, necessitating the use of a re-mapping or re-griding process for the fluid region. Typically, this system (fluid, solid, mapping) is solved using an iterative approach in which the fluid, elastic, and mapping equations are solved in series until the iterations converge.

First-order system least squares for elastohydrodynamics with application to flow in compliant blood vessels.

Mathematical modeling of compliant blood vessels generally involves the Navier-Stokes equations on the evolving fluid domain and constitutive structural equations on the tissue domain. Coupling these systems while accounting for the changing shape of the fluid domain is a major challenge in numerical simulation. Many techniques have been developed to model compliant vessels, but all suffer from disproportionate increase in computational cost as problem complexity increases (i.