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Solving helmholtz equation with compressed sensing enhanced finite element methods

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dc.contributor.author Sharma, Pragya
dc.contributor.author Ram, Shobha Sundar (Advisor)
dc.date.accessioned 2015-12-07T09:23:30Z
dc.date.available 2015-12-07T09:23:30Z
dc.date.issued 2015-12-07T09:23:30Z
dc.identifier.uri https://repository.iiitd.edu.in/jspui/handle/123456789/380
dc.description.abstract The generalized nite element method (FEM) approach towards solving the Helmholtz equation involves a very high computational complexity of the order of O(n3) where n is the number of nodes of the FEM formulation. Prior research involved exploiting the special properties of FEM matrices for reducing the computation time and memory involved in solving the large FEM problems. These included both direct and iterative solvers. In more recent times, graphical processing units (GPUs) are being used to accelerate the solvers. In this work, we propose an alternative di erent approach for solving the Helmholtz equation with reduced memory requirements by incorporating compressed sensing (CS) techniques into the original FEM formulation. Our approach is based on the fundamental assumption that electromagnetic fields are continuous except at source locations and can be represented with sparse coeffcients in alternate transform domains such as wavelets or DCT. We present different practical aspects of this approach with respect to one-dimensional FEM problems and conclude by pointing out some open-ended questions with respect to this area of research. en_US
dc.language.iso en en_US
dc.subject Finite Element Method en_US
dc.subject Compressed Sensing en_US
dc.subject l1 minimization en_US
dc.subject Sparsity en_US
dc.title Solving helmholtz equation with compressed sensing enhanced finite element methods en_US
dc.type Thesis en_US


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