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Adaptive Wavelet Collocation Method (Theory):

Invited and Feature Articles

  1. Vasilyev, O.V., Solving Multi-Dimensional Evolution Problems with Localized Structures Using Second Generation Wavelets.Int. J. Comp. Fluid Dyn., Special issue on High-Resolution Methods in Computational Fluid Dynamics, 17(2), pp. 151-168, 2003.

Articles in Refereed Journals

  1. Vasilyev, O.V., and Paolucci, S., and Sen, M., A Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain. J. Comp. Phys. 120, pp.33-47, 1995.
  2. Vasilyev, O.V., and Paolucci, S., A Dynamically Adaptive Multilevel Wavelet Collocation Method for Solving Partial Differential Equations in a Finite Domain. J. Comp. Phys., 125, pp. 498-512, 1996.
  3. Vasilyev, O.V., and Paolucci, S., A Fast Adaptive Wavelet Collocation Algorithm for Multi-Dimensional PDEsJ. Comp. Phys., 138, pp. 16-56, 1997.
  4. Vasilyev, O.V. and Bowman, C., Second Generation Wavelet Collocation Method for the Solution of Partial Differential Equations. J. Comp. Phys., 165, pp. 660-693, 2000.
  5. Vasilyev, O.V. and Kevlahan, N.K.-R., Hybrid Wavelet Collocation - Brinkman Penalization Method for Complex Geometry Flows. Int. J. Numer. Meth. in Fluids, 40, pp. 531-538, 2002.
  6. Kevlahan, N.K.-R. and Vasilyev, O.V., An adaptive Wavelet Collocation Method for Fluid-Structure Interaction, SIAM Journal on Scientific Computing, 26(6), pp. 1894-1915, 2005.
  7. Vasilyev, O.V. and Kevlahan, N.K.-R., An Adaptive Multilevel Wavelet Collocation Method for Elliptic Problems. Journal of Computational Physics, 206(2), pp. 412-431, 2005.
  8. Alam, J.M., Kevlahan, N.K.-R., and Vasilyev, O.V., Simultaneous space--time adaptive wavelet solution of nonlinear partial differential equations, Journal of Computational Physics, 214(2), pp. 829-857, 2006.
  9. Regele, J.D. and Vasilyev, O.V., An Adaptive Wavelet-Collocation Method for Shock Computations, International Journal of Computational Fluid Dynamics, 23(7), pp. 503-518, 2009.
  10. Nejadmalayeri, A., Vezolainen, A., Brown-Dymkoski, E., and Vasilyev, O.V., Parallel Adaptive Wavelet Collocation Method for PDEs, Journal of Computational Physics, 298, pp. 237–253, 2015.
  11. Souopgui, I., Scott A. Wieland, Hussaini, M.Y., and Vasilyev, O.V., Space-Time Adaptive Approach to Variational Data Assimilation Using Wavelets, Journal of Computational Physics, 306, pp. 253-268, 2016.
  12. Brown-Dymkoski, E. and Vasilyev, O.V., Adaptive-Anisotropic Wavelet Collocation Method on General Curvilinear Coordinate Systems, Journal of Computational Physics, 333, pp. 414-426, 2017.

Conference and Symposium Papers

  1. Kevlahan, N.K.-R., Vasilyev, O.V., and Cherhabili, A., An Adaptive Wavelet Method for Turbulence in Complex Geometries. In Proceedings of the 16th IMACS World Congress 2000, 411-39.pdf, Edited by M. Deville and R. Owens, IMACS, 2000.
  2. Vasilyev, O.V. and Kevlahan, N.K.-R.,  Hybrid Wavelet Collocation -Brinkman Penalization Method for Complex Geometry Flows. In M.J. Baines, editor, Numerical Methods for Fluid Dynamics VII, ICFD, Oxford, University Computing Laboratory, pp. 509-515, 2001.
  3. Kevlahan, N.K.-R. and Vasilyev, O.V. An adaptive wavelet method for fluid-structure interaction.  In Direct and Large-Eddy Simulation Workshop 4: University of Twente, ed. B. J. Geurts, R. Friedrich and O. Metais, pp. 253-260, 2001.
  4. Kevlahan, N.K.-R.,Vasilyev, O.V., Goldstein, D.E., anf Jay, A., A three-dimensional adaptive wavelet method for fluid-structure interaction. In Proceedings of Direct and Large-Eddy Simulation Workshop 5, Technical University of Munich, Germany, 2003.
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Dr. Oleg V. Vasilyev, Founder and CEO
Adaptive Wavelet Technologies LLC.
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Email: O.V.Vasilyev@AdaptiveWaveletTechnologies.com
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Last Updated: June 15, 2019