CRG 2020- Synthetic data Driven Model reduction methods for Modal Analysis

Model Order Reduction for seismic imaging

Organization:


Funded by:

KAUST, Saudi Arabia

PhD

Abdul Halim

Supervisor:


Collaboration:

Dr. Daniele Boffi, Applied Mathematics and Computer Science, KAUST, Saudi Arabia

Description :

Eigenvalue problems associated with PDEs is an important and interesting problem in the field of applied mathematics and engineering. The general from of an eigen value problem is  , where L is a differential operator. The function u is called eigenvector and the number  is called eigenvalue. Simulation of PDE eigenvalue problems consists of three phases namely modeling of the PDE, discretizing and solving the PDEs and post processing of the solution like posteriori estimate. For discretization and solving the PDE we will use FEM because it is a consolidated technique for approximation of PDEs.

It has been seen that the numerical simulation of eigenvalue problem related to PDEs are challenging because it needs large amount of memory that is the complexity of these problems are very high. So, our one aim is to design strategy to simulate large scale problem in commonly available devices.

Our strategy is to used reduced order models to reduce the computational cost. Our plan is to investigate, implement and analyze Reduced Order Models (ROMs) for approximating eigenvalue problems arising from PDEs. We will start from eigenvalue problems without any parameters introducing fictitious quantities such as time-continuation parameter. Then we will consider the parameter-dependent problems, parameters may be deterministic or stochastic.

Another goal of this project is to use techniques from data science and machine learning to optimize the offline-stage and the choice of snapshots to compute. We will develop data-driven algorithms and take advantage of the advanced tools involving a priori and a posterior error analysis for the problems and input and output bounds for ROMs.

The outcomes of this project will be beneficial for the problems arising from Fluid dynamics, structural mechanics, electromagnetism, and in many industrial and medical applications.


Output:


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