514 citations · 1.7k across the 51 of their papers we have counts for
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Scheduled Relaxation Jacobi schemes for non-elliptic partial differential equations
Mohammad Shafaet Islam, Qiqi Wang
The Scheduled Relaxation Jacobi (SRJ) method is a linear solver algorithm which greatly improves the convergence of the Jacobi iteration through the use of judiciously chosen relax…
Space-split algorithm for sensitivity analysis of discrete chaotic systems with unstable manifolds of arbitrary dimension
Adam A. Sliwiak, Qiqi Wang
Accurate approximations of the change of system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory…
Aerodynamic Risk Assessment using Parametric, Three-Dimensional Unstructured, High-Fidelity CFD and Adaptive Sampling
Runda Ji, Qiqi Wang
We demonstrate an adaptive sampling approach for computing the probability of a rare event for a set of three-dimensional airplane geometries under various flight conditions. We de…
A trajectory-driven algorithm for differentiating SRB measures on unstable manifolds
Adam A. Sliwiak, Qiqi Wang
SRB measures are limiting stationary distributions describing the statistical behavior of chaotic dynamical systems. Directional derivatives of SRB measure densities conditioned on…
Differentiating densities on smooth manifolds
Adam A. Sliwiak, Qiqi Wang
Lebesgue integration of derivatives of strongly-oscillatory functions is a recurring challenge in computational science and engineering. Integration by parts is an effective remedy…
Efficient computation of linear response of chaotic attractors with one-dimensional unstable manifolds
Nisha Chandramoorthy, Qiqi Wang
This paper presents the space-split sensitivity or the S3 algorithm to transform Ruelle's linear response formula into a well-conditioned ergodic-averaging computation. We prove a…
Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems
Adam A. Sliwiak, Nisha Chandramoorthy, Qiqi Wang
An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and th…