Pseudospectral Solution Of Near-Singular Problems Using Numerical Coordinate Transformations Based On Adaptivity Export

@article{citeulike:5937931, abstract = {The work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions. The approach makes use of the adaptive finite difference method presented by Huang and Sloan [SIAM J. Sci. Comput., 15 (1994), pp. 776--797]. This method is applied on a coarse grid to obtain a rough approximation of the solution and a suitable adapted mesh. The adaptive finite difference solution permits the construction of a smooth coordinate transformation that relates the computational space to the physical space. The map between the spaces is based on Chebyshev polynomial interpolation. Finally, the standard pseudospectral (PS) method is applied to the transformed differential problem to obtain highly accurate, nonoscillatory numerical solutions. Numerical results are presented for steady problems in one and two space dimensions.}, author = {Mulholland, L. S. and Huang, W. Z. and Sloan, D. M.}, citeulike-article-id = {5937931}, citeulike-linkout-0 = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.8164}, journal = {SIAM J. SCI. COMPUT}, keywords = {pseudospectral}, pages = {1261--1289}, posted-at = {2009-10-13 23:36:10}, priority = {0}, title = {Pseudospectral Solution Of Near-Singular Problems Using Numerical Coordinate Transformations Based On Adaptivity }, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.8164}, volume = {19}, year = {1998} }

TY - JOUR ID - citeulike:5937931 L3 - citeulike-article-id:5937931 N2 - The work presented here describes a method of coordinate transformation that enables spectral methods to be applied efficiently to differential problems with steep solutions. The approach makes use of the adaptive finite difference method presented by Huang and Sloan [SIAM J. Sci. Comput., 15 (1994), pp. 776--797]. This method is applied on a coarse grid to obtain a rough approximation of the solution and a suitable adapted mesh. The adaptive finite difference solution permits the construction of a smooth coordinate transformation that relates the computational space to the physical space. The map between the spaces is based on Chebyshev polynomial interpolation. Finally, the standard pseudospectral (PS) method is applied to the transformed differential problem to obtain highly accurate, nonoscillatory numerical solutions. Numerical results are presented for steady problems in one and two space dimensions. JF - SIAM J. SCI. COMPUT EP - 1289 TI - Pseudospectral Solution Of Near-Singular Problems Using Numerical Coordinate Transformations Based On Adaptivity VL - 19 SP - 1261 KW - pseudospectral AU - Mulholland, LS AU - Huang, WZ AU - Sloan, DM PY - 1998/// UR - http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.8164 ER -