Efficient solvers for the shallow water equations on a sphere

Ilya Tregubov, Thanh Tran


We present a finite element method using spherical splines to solve the shallow water equations on a sphere involving satellite data. We compare the proposed method with a meshless method using radial basis functions. The use of either radial basis functions or spherical splines leads to ill-conditioned systems of linear equations. To accelerate the solution process we use additive Schwarz and alternate triangular preconditioners. Some numerical experiments are presented to show the effectiveness of both preconditioners.

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Shallow Water Equations; radial basis function; spherical spline; preconditioning

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DOI: http://dx.doi.org/10.21914/anziamj.v54i0.6301

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