This paper presents a new forward-in-time advection method for nearly incompressible ow, MU, and its application to an adaptive multilevel ow solver for atmospheric ows. MU is a modi cation of Leonard et al.'s (1993) UTOPIA scheme. MU, like UTOPIA, is based on third-order accurate semiLagrangian multidimensional upwinding for constant velocity ows. For varying velocity elds, MU is a second-orde...

This paper develops a class of meshless methods that are well-suited to statistical inverse problems involving partial differential equations (PDEs). The methods discussed in this paper view the forcing term in the PDE as a random field that induces a probability distribution over the residual error of a symmetric collocation method. This construction enables the solution of challenging inverse...

Seismic full waveform inversion (FWI) uses the gradient of the objective function for computing model updates. This requires computation of the forward and adjoint wavefields on the current model estimate. Calculating the gradient on the full computational domain is wasteful when it is only required in a limited region of interest, as is the case in 4D seismic and salt boundary estimation, for ...

Electrical impedance tomography (EIT) has the potential to provide a low cost and safe imaging modality for clinically monitoring patients being treated with mechanical ventilation. Variations in reconstruction algorithms at different clinical settings, however, make interpretation of regional ventilation across institutions difficult, presenting the need for a unified algorithm for thoracic EI...

Traditionally, solving the adjoint equation for unsteady problems involves solving a large, structured linear system. This paper presents a variation on this technique and uses a Monte Carlo linear solver. The Monte Carlo solver yields a forward-time algorithm for solving unsteady adjoint equations. When applied to computing the adjoint associated with Burgers’ equation, the Monte Carlo approac...

An efficient matrix solver is critical to the analytical placement. As the size of the matrix becomes huge, the multilevel methods tum out to be more efficient and more scalable. Algebraic Multigrid (AMG) is a multilevel technique to speedup the iterative matrix solver [lo]. We apply the algebraic multigrid method to solve the linear equations that arise from the analytical placement. A layout ...