A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation II: Efficient algorithm for the discrete linear system
| Autor: | Taishan Zeng, Jian Chen, Minfan He |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Linear system
020207 software engineering 02 engineering and technology Mathematics::K-Theory and Homology Matrix splitting Integro-differential equation Product (mathematics) Signal Processing Convergence (routing) 0202 electrical engineering electronic engineering information engineering Media Technology Order (group theory) Applied mathematics 020201 artificial intelligence & image processing Computer Vision and Pattern Recognition Boundary value problem Electrical and Electronic Engineering Galerkin method Mathematics |
| Zdroj: | Journal of Visual Communication and Image Representation. 58:112-118 |
| ISSN: | 1047-3203 |
| DOI: | 10.1016/j.jvcir.2018.11.027 |
| Popis: | A multiscale Galerkin method (MGM) was proposed recently by the same authors in order to solve second-order boundary value problems of Fredholm integro-differential equation. Although, the numerical solution of MGM is always stable because of the multiscale bases properties, obligatory of considerable computational cost and huge memory for achieving great approximation accuracy, are the main draw backs. To overcome MGM problems, in this paper, a new multilevel augmentation method (MAM) in order to solve discrete linear system is proposed. Applying the special matrix splitting techniques, approximate solution is obtained by (1) solving a linear system only at an initial lower level; (2) compensating the error by directly computing the product of matrices and vectors at the higher level without any iterations. Theoretical and experimental results approve that MAM and MGM have similar and optimum convergence orders, though MAM is more efficient than MGM. |
| Databáze: | OpenAIRE |
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