154 citations · 389 across the 16 of their papers we have counts for
16 papers
Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence
Sara Pollock, Leo Rebholz, Xuemin Tu +1
We analyze and test a simple-to-implement two-step iteration for the incompressible Navier-Stokes equations that consists of first applying the Picard iteration and then applying t…
Implicit Particle Filtering via a Bank of Nonlinear Kalman Filters
Iman Askari, Mulugeta A. Haile, Xuemin Tu +1
The implicit particle filter seeks to mitigate particle degeneracy by identifying particles in the target distribution's high-probability regions. This study is motivated by the ne…
Semantic Clustering based Deduction Learning for Image Recognition and Classification
Wenchi Ma, Xuemin Tu, Bo Luo +1
The paper proposes a semantic clustering based deduction learning by mimicking the learning and thinking process of human brains. Human beings can make judgments based on experienc…
BDDC Algorithms for Advection-diffusion problems with HDG Discretizations
Xuemin Tu, Jinjin Zhang
The balancing domain decomposition methods (BDDC) are originally introduced for symmetric positive definite systems and have been extended to the nonsymmetric positive definite sys…
Projected Shadowing-based Data Assimilation
Bart de Leeuw, Svetlana Dubinkina, Jason Frank +3
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refin…
Composing Scalable Nonlinear Algebraic Solvers
Peter R. Brune, Matthew G. Knepley, Barry F. Smith +1
Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A sim…
Sampling, feasibility, and priors in Bayesian estimation
Alexandre J. Chorin, Fei Lu, Robert N. Miller +2
Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it pos…
A FETI-DP type domain decomposition algorithm for three-dimensional incompressible Stokes equations
Xuemin Tu, Jing Li
The FETI-DP algorithms, proposed by the authors in [SIAM J. Numer. Anal., 51 (2013), pp.~1235--1253] and [Internat. J. Numer. Methods Engrg., 94 (2013), pp.~128--149] for solving i…
Limitations of polynomial chaos expansions in the Bayesian solution of inverse problems
Fei Lu, Matthias Morzfeld, Xuemin Tu +1
Polynomial chaos expansions are used to reduce the computational cost in the Bayesian solutions of inverse problems by creating a surrogate posterior that can be evaluated inexpens…
Parameter estimation by implicit sampling
Matthias Morzfeld, Xuemin Tu, Jon Wilkening +1
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of…
A unified FETI-DP approach for incompressible Stokes equations
Xuemin Tu, Jing Li
A unified framework of FETI-DP algorithms is proposed for solving the system of linear equations arising from the mixed finite element approximation of incompressible Stokes equati…
A non-overlapping domain decomposition method for incompressible Stokes equations with continuous pressure
Jing Li, Xuemin Tu
A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A contin…
A random map implementation of implicit filters
Matthias Morzfeld, Xuemin Tu, Ethan Atkins +1
Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This…
Implicit particle filters for data assimilation
Alexandre J. Chorin, Matthias Morzfeld, Xuemin Tu
Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles…
Interpolation and Iteration for Nonlinear Filters
Alexandre J. Chorin, Xuemin Tu
We present a general form of the iteration and interpolation process used in implicit particle filters. Implicit filters are based on a pseudo-Gaussian representation of posterior…
Non-Bayesian particle filters
Alexandre J. Chorin, Xuemin Tu
Particle filters for data assimilation in nonlinear problems use "particles" (replicas of the underlying system) to generate a sequence of probability density functions (pdfs) thro…