Spectral/hp element methods: Recent developments, applications, and perspectives

H Xu, CD Cantwell, C Monteserin, C Eskilsson… - Journal of …, 2018 - Springer
The spectral/hp element method combines the geometric flexibility of the classical h-type
finite element technique with the desirable numerical properties of spectral methods …

Solving PDEs with radial basis functions

B Fornberg, N Flyer - Acta Numerica, 2015 - cambridge.org
Finite differences provided the first numerical approach that permitted large-scale
simulations in many applications areas, such as geophysical fluid dynamics. As accuracy …

[图书][B] A primer on radial basis functions with applications to the geosciences

B Fornberg, N Flyer - 2015 - SIAM
This book is focused on a powerful numerical methodology for solving PDEs to high
accuracy in any number of dimensions: Radial Basis Functions (RBFs). During the past …

A guide to RBF-generated finite differences for nonlinear transport: shallow water simulations on a sphere

N Flyer, E Lehto, S Blaise, GB Wright… - Journal of Computational …, 2012 - Elsevier
The current paper establishes the computational efficiency and accuracy of the RBF-FD
method for large-scale geoscience modeling with comparisons to state-of-the-art methods …

Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations

MA Kopera, FX Giraldo - Journal of Computational Physics, 2014 - Elsevier
The resolutions of interests in atmospheric simulations require prohibitively large
computational resources. Adaptive mesh refinement (AMR) tries to mitigate this problem by …

[PDF][PDF] Radial basis function-generated finite differences: A mesh-free method for computational geosciences

N Flyer, GB Wright, B Fornberg - Handbook of geomathematics, 2014 - academia.edu
Radial basis function-generated finite differences (RBF-FD) is a mesh-free method for
numerically solving partial differential equations that emerged in the last decade and have …

[HTML][HTML] A robust fuzzy-fractional approach for the atmospheric internal wave model

PP Sartanpara, R Meher - Journal of Ocean Engineering and Science, 2023 - Elsevier
The study of internal atmospheric waves, also known as gravity waves, which are detectable
inside the fluid rather than at the fluid surface, is presented in this work. We have used the …

Partitioned and implicit–explicit general linear methods for ordinary differential equations

H Zhang, A Sandu, S Blaise - Journal of Scientific Computing, 2014 - Springer
Implicit–explicit (IMEX) time stepping methods can efficiently solve differential equations with
both stiff and nonstiff components. IMEX Runge–Kutta methods and IMEX linear multistep …

Discontinuous Galerkin scheme for the spherical shallow water equations with applications to tsunami modeling and prediction

B Bonev, JS Hesthaven, FX Giraldo… - Journal of Computational …, 2018 - Elsevier
We present a novel high-order discontinuous Galerkin discretization for the spherical
shallow water equations, able to handle wetting/drying and non-conforming, curved meshes …

High order implicit-explicit general linear methods with optimized stability regions

H Zhang, A Sandu, S Blaise - SIAM Journal on Scientific Computing, 2016 - SIAM
In the numerical solution of partial differential equations using a method-of-lines approach,
the availability of high order spatial discretization schemes motivates the development of …