313 citations · 704 across the 32 of their papers we have counts for
5 papers · 1 filter
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…
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
Han Gao, Matthew J. Zahr, Jian-Xun Wang
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more c…
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…