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Publication 26-CNA-006

Constrained Optimization of Whitney Forms for Nonlinear Projection-Based Reduced Order Methods

Katherine Piper
Department of Civil and Environmental Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
kbpiper@andrew.cmu.edu

Lorenz Biegler
Department of Chemical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
lb01@cmu.edu

Nathaniel Trask
Department of Mechanical Engineering and Applied Mechanics
University of Pennsylvania
Philadelphia PA, USA
ntrask@seas.upenn.edu

Kaushik Dayal
Department of Civil and Environmental Engineering
Center for Nonlinear Analysis
Department of Mechanical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
Kaushik.Dayal@cmu.edu

Abstract: In this work, we present the NLP-ROM, a method for finding Machined-Learned Whitney forms for nonlinear model order reduction through constrained optimization. We first demonstrate the performance of the methods on the Poisson problem for a unit mesh, before demonstrating the applicability to free boundary linear elasticity on an unstructured mesh.

Get the paper in its entirety as  26-CNA-006.pdf

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