Zobrazeno 1 - 10
of 81
pro vyhledávání: '"Zahr, Matthew J."'
Autor:
Wen, Tianshu, Zahr, Matthew J.
We present an augmented Lagrangian trust-region method to efficiently solve constrained optimization problems governed by large-scale nonlinear systems with application to partial differential equation-constrained optimization. At each major augmente
Externí odkaz:
http://arxiv.org/abs/2405.14827
Autor:
Vandergrift, Jakob, Zahr, Matthew J.
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 conservation law solution and align elements of the computational mesh w
Externí odkaz:
http://arxiv.org/abs/2402.18403
Autor:
Kaufmann, Julian M., Zahr, Matthew J.
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 elements. Starting from the inherent symmetries of an element geometry,
Externí odkaz:
http://arxiv.org/abs/2401.13209
Autor:
Gao, Han, Zahr, Matthew J.
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 models (ROMs) by incorporating solution-based adaptivity with locally su
Externí odkaz:
http://arxiv.org/abs/2310.05379
Autor:
Naudet, Charles J., Zahr, Matthew J.
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 by aligning elements of the computational mesh with non-smooth features
Externí odkaz:
http://arxiv.org/abs/2308.04065
This work introduces an empirical quadrature-based hyperreduction procedure and greedy training algorithm to effectively reduce the computational cost of solving convection-dominated problems with limited training. The proposed approach circumvents t
Externí odkaz:
http://arxiv.org/abs/2305.15661
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 by aligning elements of the computational mesh with non-smooth features
Externí odkaz:
http://arxiv.org/abs/2304.11427
Autor:
Zucatti, Victor, Zahr, Matthew J.
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 used to obtain a system of reduced complexity. Unfortunately, convection
Externí odkaz:
http://arxiv.org/abs/2301.01718
Autor:
Wen, Tianshu, Zahr, Matthew J.
We present a numerical method to efficiently solve optimization problems governed by large-scale nonlinear systems of equations, including discretized partial differential equations, using projection-based reduced-order models accelerated with hyperr
Externí odkaz:
http://arxiv.org/abs/2206.09942
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction techniques use an a
Externí odkaz:
http://arxiv.org/abs/2109.14694