3 papers
math.NA2026
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…
math.NA2025
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…
math.NA2025
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…