Laplace-Beltrami Eigenfunctions for the Inverse Source/Design Problems
| Autor: | Balasubramaniam Shanker, A. M. A. Alsnayyan, A. Diaz |
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| Rok vydání: | 2020 |
| Předmět: |
Basis (linear algebra)
Computer science Mathematical analysis Boundary (topology) 020207 software engineering Harmonic (mathematics) 010103 numerical & computational mathematics 02 engineering and technology Eigenfunction 01 natural sciences Manifold Convexity Operator (computer programming) 0202 electrical engineering electronic engineering information engineering Subdivision surface 0101 mathematics |
| Zdroj: | 2020 IEEE International Symposium on Antennas and Propagation and North American Radio Science Meeting. |
| Popis: | The Laplace-Beltrami operator has a broad breadth and depth of application in the fields of engineering, machine learning, and computer graphics. In particular, the operator's salient feature of defining a spectral method, enabling the manipulation of its eigenfunctions as a basis set, has been driving its popularity in many fields. The eigenfunctions form a basis referred to as the manifold harmonic basis (MHB). MHB are constructed over $C^{2}$ subdivision surfaces, further enhancing its ability to capture very fine features such as convexity, edges, corners, etc., with relatively few eigenfunctions. MHB proves to be a great candidate for developing the inverse source/design framework due to their natural means of compressing data. We pose a shape optimization problem that aims to find the boundary, in terms of MHs, wherein sources are defined to produce the desired fields constrained. Numerical results are presented for validation. |
| Databáze: | OpenAIRE |
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