7 papers
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…
Simulation of the high Mach number motion for bubble collapse in a compressible Euler fluid using Basilisk
Daniels Krimans, Steven J. Ruuth, Seth Putterman
We examine an extreme case of experimentally realizable sonoluminescence, where spherical cavities have an initial radius that is to times their ambient radius and change…
Geodesic distance approximation using a surface finite element method for the -Laplacian
Hannah Potgieter, Razvan C. Fetecau, Steven J. Ruuth
We use the -Laplacian with large -values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's (2018) [1] computational…