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SUMMARY:Adaptive wavelet methods for PDEs and Integral equations\; Pro
 f. Dr. Mani Mehra (IIT Delhi)
UID:41ddae73-6fc5-4a38-b94d-c9548ebc971b
DESCRIPTION:ABSTRACT: Most of the times\, while dealing with the physi
 cal problems of real world such as climate modelling and numerical wea
 ther prediction etc. one ends up with PDEs on the sphere. The subject 
 of solving PDEs on the sphere using wavelets is not much developed. On
 e of the work in this direction is a dynamic adaptive numerical method
  for solving PDEs on the sphere [Mehra and Kevlahan\, 2008] using seco
 nd generation spherical wavelet. The main difficulty with second gener
 ation wavelet is that an initial mesh structure is required to approxi
 mate the manifold. This difficulty can be handled with meshfree method
 s. In this work\, we develop an adaptive meshfree diffusion wavelet me
 thod on the sphere (AMDWMS). Although the present work considers only 
 the sphere\, the strength of this method is that it can be easily exte
 nded to other manifolds. The beauty of the proposed method is that the
  diffusion operator is used both for the construction of the diffusion
  wavelet as well as for the approximation of the differential operator
  involved in the PDE at hand. Numerical results are given on couple of
  test problems. Moreover\, the problem of pattern formation on the sur
 face of the sphere (using Turing equations) is addressed to test the s
 trength of the method. The numerical results show that the method can 
 accurately capture the emergence of the localized patterns at all the 
 scales and the node arrangement is accordingly adapted.
DTSTART:20170608T141500Z
DTEND:20170608T151500Z
LOCATION:H13
DTSTAMP:20260726T130550Z
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