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Presented By: Aerospace Engineering

AE585 Graduate Seminar Series - Towards reliable and automated solution of partial differential equations: error estimation, adaptation, and model reduction

Masayuki Yano, Assistant Professor, University of Toronto, Institute for Aerospace Studies

Masayuki Yano, Assistant Professor, University of Toronto, Institute for Aerospace Studies

We present work towards the development of reliable and automated computational tools for partial differential equations (PDEs) in continuum mechanics. Here, reliability refers to the ability to quantify and control the two sources of error in numerical predictions: the model error that arises from mathematical modeling of the true physics; the discretization error that arises from numerical approximation of the mathematical model. Autonomy refers to the ability to complete the analysis with minimal user intervention.

In the first part, we focus on single- or few-query scenarios and develop an adaptive finite element solver for conservation laws with emphasis on aerodynamic flows. The solver consists of three key ingredients: a high-order discontinuous Galerkin method; an output error estimate; and a mesh optimization strategy. We demonstrate the effectiveness of the strategy for aerodynamic flows.

In the second part, we focus on many-query and real-time scenarios and develop model reduction strategies for rapid and reliable solution of parametrized PDEs. We in particular address model reduction challenges associated with reliable and efficient treatment of problems that exhibit a wide range of scales and strong nonlinearities. We demonstrate the method for parametrized problems in solid and fluid mechanics.


About the speaker...

Masayuki Yano is an assistant professor at the University of Toronto Institute for Aerospace Studies (UTIAS). His research focuses on the development of computational methods for problems in aerospace sciences and engineering. Specifically, his research interests lie in numerical methods, scientific computation, and numerical analysis for partial differential equations (PDEs) with applications in aerodynamics, continuum mechanics, acoustics, and transport.

He obtained his PhD in Aeronautics and Astronautics from MIT in 2012, working on adaptive high-order methods for aerodynamic flows. He was then a post-doctoral associated at MIT, working on model reduction and data assimilation techniques for parametrized PDEs. He joined UITAS in 2015.

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