New math framework could make AI weather models and simulations faster
Researchers have proven that three commonly used computational methods can reliably solve complex flow problems if properly calibrated—a finding that could accelerate everything from climate forecasting to financial modeling. The work removes a major barrier holding back adoption of faster, cheaper simulation techniques in industries that depend on real-time predictions.
Originaltitel: Stability estimates for radial basis function methods applied to linear scalar conservation laws
<p>We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) method, the RBF partition of unity method (RBF-PUM) and Kansa's (global) RBF method. We give the estimates in the discrete l(2)-norm 2-norm intrinsic to each of the three methods. The results show that Kansa's method and RBF-PUM can be l(2)-stable 2-stable in time under a sufficiently large oversampling of the discretized system of equations. The RBF-FD method in addition requires stabilization of the spurious jump terms due to the discontinuous RBF-FD cardinal basis functions. Numerical experiments show an agreement with our theoretical observations.</p>