Sparse spectral methods on disk-slices, trapeziums and spherical caps

Benjamin Samuel Thomas Snowball
This thesis develops sparse spectral methods for solving partial differential equations (PDEs) on various multidimensional domains, with a specific focus on the disk-slice and trapezium in 2D, and the spherical cap in 3D. For the latter, the PDEs are surface PDEs involving Laplace-Beltrami operators, spherical gradients and other spherical operators. We begin with an introduction to sparse spectral methods via viewing spherical harmonics as multidimensional orthogonal polynomials in x, y, and z. We explain how...
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