313 citations · 704 across the 32 of their papers we have counts for
21 papers · 1 filter
An -adaptive method for accurate resolution of shock-dominated viscous flow based on implicit shock tracking
Huijing Dong, Masayuki Yano, Tianci Huang +1
This work introduces an optimization-based -adaptive numerical method to approximate solutions of viscous, shock-dominated flows using implicit shock tracking and a high-order…
Model reduction of convection-dominated viscous conservation laws using implicit feature tracking and landmark image registration
Victor Zucatti, Matthew J. Zahr
Reduced-order models (ROMs) remain generally unreliable for convection-dominated problems, such as those encountered in hypersonic flows, due to the slowly decaying Kolmogorov -…
Neural network-based Godunov corrections for approximate Riemann solvers using bi-fidelity learning
Akshay Thakur, Matthew J. Zahr
The Riemann problem is fundamental in the computational modeling of hyperbolic partial differential equations, enabling the development of stable and accurate upwind schemes. While…
Preconditioned iterative solvers for constrained high-order implicit shock tracking methods
Jakob Vandergrift, Matthew J. Zahr
High-order implicit shock tracking (fitting) is a class of high-order numerical methods that use numerical optimization to simultaneously compute a high-order approximation to a co…
Symmetric, Optimization-based, Cross-element Compatible Nodal Distributions for High-order Finite Elements
Julian M. Kaufmann, Matthew J. Zahr
We present a general framework to construct symmetric, well-conditioned, cross-element compatible nodal distributions that can be used for high-order and high-dimensional finite el…
An adaptive model reduction method leveraging locally supported basis functions
Han Gao, Matthew J. Zahr
We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order mo…
A space-time high-order implicit shock tracking method for shock-dominated unsteady flows
Charles J. Naudet, Matthew J. Zahr
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features b…
Accelerated solutions of convection-dominated partial differential equations using implicit feature tracking and empirical quadrature
Marzieh Alireza Mirhoseini, Matthew J. Zahr
This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominat…
High-order implicit shock tracking boundary conditions for flows with parametrized shocks
Tianci Huang, Charles Naudet, Matthew J. Zahr
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features b…
An adaptive, training-free reduced-order model for convection-dominated problems based on hybrid snapshots
Victor Zucatti, Matthew J. Zahr
The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards us…
Model reduction of convection-dominated partial differential equations via optimization-based implicit feature tracking
Marzieh Alireza Mirhoseini, Matthew J. Zahr
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with impl…
Accurate quantification of blood flow wall shear stress using simulation-based imaging: a synthetic, comparative study
Charles J. Naudet, Johannes Toger, Matthew J. Zahr
Simulation-based imaging (SBI) is a blood flow imaging technique that optimally fits a computational fluid dynamics (CFD) simulation to low-resolution, noisy magnetic resonance (MR…
A robust, high-order implicit shock tracking method for simulation of complex, high-speed flows
Tianci Huang, Matthew J. Zahr
High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the c…
Implicit shock tracking for unsteady flows by the method of lines
Andrew Shi, Per-Olof Persson, Matthew Zahr
A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [41, 43] is extended to the un…
A globally convergent method to accelerate topology optimization using on-the-fly model reduction
Masayuki Yano, Tianci Huang, Matthew J. Zahr
We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate…
Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method
Matthew J. Zahr, Andrew Shi, Per-Olof Persson
A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuo…
Non-intrusive model reduction of large-scale, nonlinear dynamical systems using deep learning
Han Gao, Jian-Xun Wang, Matthew J. Zahr
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settin…
High-order partitioned spectral deferred correction solvers for multiphysics problems
Daniel Z. Huang, Will Pazner, Per-Olof Persson +1
We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing…
A high-order partitioned solver for general multiphysics problems and its applications in optimization
Daniel Z. Huang, Per-Olof Persson, Matthew J. Zahr
A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly sta…
High-order, linearly stable, partitioned solvers for general multiphysics problems based on implicit-explicit Runge-Kutta schemes
Daniel Z. Huang, Per-Olof Persson, Matthew J. Zahr
This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit-explicit Runge-Kutta…
An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions
Matthew J. Zahr, Per-Olof Persson
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inte…