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Cauchy-Riemann differential equations of the spherical geometry

Date: 
Friday 7th September 2012 - 10:00 to 11:00
Venue: 
INI Seminar Room 2
Abstract: 
A system of PDEs relating to the transformation of the latitude- longitude parameterisation of the sphere was described in the work of F. Schmidt[Sch77]. This system of PDEs is known in the Meteorological literature as Cauchy-Riemann equations of the sphere. However the connection between this form of PDEs and the complex analytic function theory is not known to be reported. This talk will describe the connection between complex analytic function theory and the differential geometry of the sphere. A class of variable separable solutions of the C-R equations are useful in creating variable mesh configurations. One such solution had been applied to create a variable resolution global spectral method on the sphere[JNM12]. Complex function theory provides some useful insights on the types of variable resolution mesh configurations that can be generated on the sphere.

References

[JNM12] S. Janakiraman, Ravi S. Nanjundiah, and A.S. Vasudeva Murthy, A novel variable resolution global spectral method on the sphere, Journal of Computational Physics 231 (2012), no. 7, 2794 2810.

[Sch77] F. Schmidt, Variable ne mesh in spectral global models, Beiträge zur Physik der Atmosphäre 50 (1977), no. 12, 211 217.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons