Análise Espectral de um Método Pseudo Espectral para Propagação de Onda com Condições de Fronteira Transparentes
DOI:
https://doi.org/10.5540/tema.2007.08.02.0201Abstract
Apresentamos uma análise espectral de um método para a simulação numérica de propagação de ondas unidimensionais, proposto recentemente por Jackiewicz e Renaut em [4]. Os resultados incluem uma fórmula fechada para o auto sistema do operador associado ao problema, um resultado teórico que corrige uma conclus˜ao errônea desses autores e um método numérico para calcular soluções aproximadas. Além disso, destacamos a importância da análise do pseudo espectro do operador do modelo contínuo, assim como o pseudo espectro das matrizes dos modelos discretos correspondentes.References
[1] P.C. Calegari, “Método Pseudo Espectral de Chebyshev para Problemas de Propagação de Ondas com Condições de Fronteira Absorventes”, Dissertação de Mestrado em Matemática e Computação Científica, Universidade Federal de Santa Catarina, Florianópolis 2007.
T.A. Driscol, L.N. Trefethen, Pseudospectra of the wave operator with an absorbing boundary, J. Comput. Appl. Math., 69 (1996), 125-142.
L. Halpern, A. Rahmouni, “One Way Operators, Absorbing boundary conditions and domain decomposition for wave propagation”, Modern Methods in Scientific Computing and Applications, 155-209. A. Bourliex et M.J.Gauder editeurs. Kluwer Academic Publishers, 2002.
Z. Jackiewicz, R.A. Renaut, A note on stability of pseudospectral methods for wave propagations, J. Comput. Appl. Math., 143 (2002), 127-139.
S.C. Reddy, L.N. Trefethen, Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues, Comput. Meth Appl. Mech. Eng., 80 (1990), 147-164.
S.C. Reddy, L.N. Trefethen, Stability of the method of lines, Num. Math., 62 (1992), 235-267.
R. Renaut, Stability of a Chebyshev pseudoespectral solution of the wave equation with absorbing boundaries, J. Comput. Appl. Math., 87 (1997), 243-259.
R.D. Richtmyer, K.W. Morton, “Difference Methods for Initial-value Problems”, 2nd ed., John Wiley, New York, 1967.
J.C. Strikwerda, “Finite Difference Schemes and Partial Differential Equations”, Wadsworth & Brooks, Califórnia, 1989.
L.N. Trefethen, “Spectral Methods in Matlab”, Society for Industrial and Applied Mathematics, Philadelphia, 2000.
L.N. Trefethen, M. Embree, “Spectra e Pseudospectra - The behavior of Nonnormal Matrices o Operators”, Princeton University Press, Princeton, 2005.
K. Veseli´c, On linear vibrational systems with one-dimensional damping, Applicable Anal., 29 (1988), 1-18.
T.G. Wright, “Matlab codes and graphical user interfaces for computation of pseudospectra”, available at http://www.comlab.ox.ac.uk/oucl/work/nick.trefethen
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.
