Author(s)

EDWARD J. KANSA

Abstract

Meshfree transport calculations have been traditionally performed in the Lagrangian or particle velocity mode connected to an underlying distorting mesh. That is remapped (interpolated) onto a regular mesh. This primitive procedure was necessary with extremely primitive electronic computers that has extremely restrictive memory storage and execution speed. However, the meshless radial basis function approach allows points to move; without diffusive re-interpolation; one can choose to allow the motion at each interior point to convert the partial differential equation into an exact differential, thereby eliminating truncation errors. Given the proper tools to utilize extended arithmetic precision on computers, electronic computers can asymptotically approach the power of ideal academic mathematics and solve numerically problems approaching theoretical methods.

Keywords

hyperbolic partial differential equations, radial basis functions, exact solutions of time expansion coefficients, exponential convergence, meshless methods