Towards Stable Radial Basis Function Methods for Linear Advection Problems

01/24/2021
by   Jan Glaubitz, et al.
0

In this work, we investigate (energy) stability of global radial basis function (RBF) methods for linear advection problems. Classically, boundary conditions (BC) are enforced strongly in RBF methods. By now it is well-known that this can lead to stability problems, however. Here, we follow a different path and propose two novel RBF approaches which are based on a weak enforcement of BCs. By using the concept of flux reconstruction and simultaneous approximation terms (SATs), respectively, we are able to prove that both new RBF schemes are strongly (energy) stable. Numerical results in one and two spatial dimensions for both scalar equations and systems are presented, supporting our theoretical analysis.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/07/2022

Energy-stable global radial basis function methods on summation-by-parts form

Radial basis function methods are powerful tools in numerical analysis a...
09/29/2019

Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems

Many important initial value problems have the property that energy is n...
02/01/2021

Stabilizing Radial Basis Function Methods for Conservation Laws Using Weakly Enforced Boundary Conditions

It is well understood that boundary conditions (BCs) may cause global ra...
08/13/2021

Towards stability of radial basis function based cubature formulas

Cubature formulas (CFs) based on radial basis functions (RBFs) have beco...
06/20/2018

Radial Basis Function Approximations: Comparison and Applications

Approximation of scattered data is often a task in many engineering prob...
06/01/2018

SFA-GTM: Seismic Facies Analysis Based on Generative Topographic Map and RBF

Seismic facies identification plays a significant role in reservoir char...
03/29/2022

An extended range of energy stable flux reconstruction methods on triangles

We present an extended range of stable flux reconstruction (FR) methods ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.