5 papers · 1 filter
Numerical approximation of the first -Laplace eigenpair
Hannah Potgieter, Razvan C. Fetecau, Steven J. Ruuth
We approximate the first Dirichlet eigenpair of the -Laplace operator for on both Euclidean and surface domains. We emphasize large values and discuss ho…
High-Order Meshfree Surface Integration, Including Singular Integrands
Daniel R. Venn, Steven J. Ruuth
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and…
Underdetermined Fourier Extensions for Surface Partial Differential Equations
Daniel R. Venn, Steven J. Ruuth
We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prov…
A Meshfree Method for Eigenvalues of Differential Operators on Surfaces, Including Steklov Problems
Daniel R. Venn, Steven J. Ruuth
We present and study techniques for investigating the spectra of linear differential operators on surfaces and flat domains using symmetric meshfree methods: meshfree methods that…
A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces
VÃctor Bayona, Argyrios Petras, Cécile Piret +1
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equat…