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| Formato: | Artículo científico |
| Lenguaje: | en |
| Publicado: |
ECOPETROL S.A.
2019
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| Acceso en línea: | https://www.redalyc.org/articulo.oa?id=46570742002 https://www.redalyc.org/journal/465/46570742002/ https://www.redalyc.org/journal/465/46570742002/html/ https://www.redalyc.org/journal/465/46570742002/46570742002.epub https://www.redalyc.org/journal/465/46570742002/movil |
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| _version_ | 1866817137972084736 |
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| author | Mauricio-A Londoño |
| author_facet | Mauricio-A Londoño |
| contents | OPTIMAL SHAPE PARAMETER FOR MESHLESS SOLUTION OF THE 2D HELMHOLTZ EQUATION Mauricio-A Londoño Hebert Montegranario Ingeniería FD RBF Shape parameter pollution effect Helmholtz equation The solution of the Helmholtz equation is a fundamental step in frequency domain seismic imaging. This paper deals with a numerical study of solutions for 2D Helmholtz equation using a Gaussian radial basis function-generated finite difference scheme (RBFFD). We analyze the behavior of the local truncation error in approximating partial derivatives of the 2D Helmholtz equation solutions when the shape parameter of RBF varies. For discretization, we performed, by means of a classical numerical dispersion analysis with plane waves, a minimization of the error function to obtain local and adaptive near optimal shape parameters according to the local wavelength of the required solution. In particular, the method is applied to obtain a simple and accurate solver by using stencils which seven nodes on hexagonal regular grids, wich mitigate pollution-effects. We validated numerically that the stability and isotropy are enhanced with respect to Cartesian grids. Our method is tested with standard case studies and velocity models, showing similar or better accuracy than finite difference and finite element methods. This is an efficient way for interacting with inverse and imaging problems such as Full Wave Inversion 2019 artículo científico 0122-5383 https://www.redalyc.org/articulo.oa?id=46570742002 https://www.redalyc.org/journal/465/46570742002/ https://www.redalyc.org/journal/465/46570742002/html/ https://www.redalyc.org/journal/465/46570742002/46570742002.epub https://www.redalyc.org/journal/465/46570742002/movil 10.29047/01225383.178 en http://www.redalyc.org/revista.oa?id=465 CT&F Ciencia, Tecnología y Futuro application/pdf ECOPETROL S.A. CT&F Ciencia, Tecnología y Futuro (Colombia) Num.2 Vol.9 |
| format | Artículo científico |
| id | redalyc_46570742002 |
| language | en |
| publishDate | 2019 |
| publisher | ECOPETROL S.A. |
| spellingShingle | OPTIMAL SHAPE PARAMETER FOR MESHLESS SOLUTION OF THE 2D HELMHOLTZ EQUATION Mauricio-A Londoño Ingeniería FD RBF Shape parameter pollution effect Helmholtz equation OPTIMAL SHAPE PARAMETER FOR MESHLESS SOLUTION OF THE 2D HELMHOLTZ EQUATION Mauricio-A Londoño Hebert Montegranario Ingeniería FD RBF Shape parameter pollution effect Helmholtz equation The solution of the Helmholtz equation is a fundamental step in frequency domain seismic imaging. This paper deals with a numerical study of solutions for 2D Helmholtz equation using a Gaussian radial basis function-generated finite difference scheme (RBFFD). We analyze the behavior of the local truncation error in approximating partial derivatives of the 2D Helmholtz equation solutions when the shape parameter of RBF varies. For discretization, we performed, by means of a classical numerical dispersion analysis with plane waves, a minimization of the error function to obtain local and adaptive near optimal shape parameters according to the local wavelength of the required solution. In particular, the method is applied to obtain a simple and accurate solver by using stencils which seven nodes on hexagonal regular grids, wich mitigate pollution-effects. We validated numerically that the stability and isotropy are enhanced with respect to Cartesian grids. Our method is tested with standard case studies and velocity models, showing similar or better accuracy than finite difference and finite element methods. This is an efficient way for interacting with inverse and imaging problems such as Full Wave Inversion 2019 artículo científico 0122-5383 https://www.redalyc.org/articulo.oa?id=46570742002 https://www.redalyc.org/journal/465/46570742002/ https://www.redalyc.org/journal/465/46570742002/html/ https://www.redalyc.org/journal/465/46570742002/46570742002.epub https://www.redalyc.org/journal/465/46570742002/movil 10.29047/01225383.178 en http://www.redalyc.org/revista.oa?id=465 CT&F Ciencia, Tecnología y Futuro application/pdf ECOPETROL S.A. CT&F Ciencia, Tecnología y Futuro (Colombia) Num.2 Vol.9 |
| title | OPTIMAL SHAPE PARAMETER FOR MESHLESS SOLUTION OF THE 2D HELMHOLTZ EQUATION |
| topic | Ingeniería FD RBF Shape parameter pollution effect Helmholtz equation |
| url | https://www.redalyc.org/articulo.oa?id=46570742002 https://www.redalyc.org/journal/465/46570742002/ https://www.redalyc.org/journal/465/46570742002/html/ https://www.redalyc.org/journal/465/46570742002/46570742002.epub https://www.redalyc.org/journal/465/46570742002/movil |