A stabilized radial basis-finite difference (RBF-FD) method with hybrid
kernels
release_hr5pw6um4fgrtmahyntso2bwwy
by
Pankaj K Mishra, Gregory E Fasshauer, Mrinal K Sen, Leevan Ling
2018
Abstract
Recent developments have made it possible to overcome grid-based limitations
of finite difference (FD) methods by adopting the kernel-based meshless
framework using radial basis functions (RBFs). Such an approach provides a
meshless implementation and is referred to as the radial basis-generated finite
difference (RBF-FD) method. In this paper, we propose a stabilized RBF-FD
approach with a hybrid kernel, generated through a hybridization of the
Gaussian and cubic RBF. This hybrid kernel was found to improve the condition
of the system matrix, consequently, the linear system can be solved with direct
solvers which leads to a significant reduction in the computational cost as
compared to standard RBF-FD methods coupled with present stable algorithms.
Unlike other RBF-FD approaches, the eigenvalue spectra of differentiation
matrices were found to be stable irrespective of irregularity, and the size of
the stencils. As an application, we solve the frequency-domain acoustic wave
equation in a 2D half-space. In order to suppress spurious reflections from
truncated computational boundaries, absorbing boundary conditions have been
effectively implemented.
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