87 citations · 303 across the 21 of their papers we have counts for
24 papers
Deep-Learning Solvers and Surrogates for Infinity and p-Laplace Problems
Tak Shing Au Yeung, Ka Chun Cheung, Hannah Potgieter +2
We investigate the use of neural network solvers for infinity and -Laplace problems, which are fundamental in nonlinear analysis and have practical applications. Our approach em…
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…
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…
A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces
Víctor 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…
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…
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…
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 Closest Point Method for PDEs on Manifolds with Interior Boundary Conditions for Geometry Processing
Nathan King, Haozhe Su, Mridul Aanjaneya +2
Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in or , such as curves or surfa…
Realistic pattern formations on surfaces by adding arbitrary roughness
Siqing Li, Leevan Ling, Steven J. Ruuth +1
We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, so…
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners
Ian C. T. May, Ronald D. Haynes, Steven J. Ruuth
The DD-CPM software library provides a set of tools for the discretization and solution of problems arising from the closest point method (CPM) for partial differential equations o…
A Convergence Analysis of the Parallel Schwarz Solution of the Continuous Closest Point Method
Alireza Yazdani, Ronald D. Haynes, Steven J. Ruuth
The discretization of surface intrinsic PDEs has challenges that one might not face in the flat space. The closest point method (CPM) is an embedding method that represents surface…
Linearly Stabilized Schemes for the Time Integration of Stiff Nonlinear PDEs
Kevin Chow, Steven J. Ruuth
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by…
Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws
Weifeng Zhao, Juntao Huang, Steven J. Ruuth
In \cite{ZH2019}, we developed a boundary treatment method for implicit-explicit (IMEX) Runge-Kutta (RK) methods for solving hyperbolic systems with source terms. Since IMEX RK met…
PDEs on moving surfaces via the closest point method and a modified grid based particle method
A. Petras, S. J. Ruuth
Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is…
Schwarz solvers and preconditioners for the closest point method
Ian May, Ronald Haynes, Steven Ruuth
The discretization of surface intrinsic elliptic partial differential equations (PDEs) poses interesting challenges not seen in flat space. The discretization of these PDEs typical…
Domain Decomposition for the Closest Point Method
Ian May, Ronald D. Haynes, Steven J. Ruuth
The discretization of elliptic PDEs leads to large coupled systems of equations. Domain decomposition methods (DDMs) are one approach to the solution of these systems, and can spli…
A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces
A. Petras, L. Ling, C. Piret +1
The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs…
An RBF-FD closest point method for solving PDEs on surfaces
Argyrios Petras, Leevan Ling, Steven J. Ruuth
Partial differential equations (PDEs) on surfaces appear in many applications throughout the natural and applied sciences. The classical closest point method (Ruuth and Merriman, J…
Solving variational problems and partial differential equations that map between manifolds via the closest point method
Nathan D. King, Steven J. Ruuth
Maps from a source manifold to a target manifold appear in liquid crystals, colour image enhancement, texture mapping, brain mapping, and many other…
Spatially partitioned embedded Runge-Kutta methods
David I. Ketcheson, Colin B. Macdonald, Steven J. Ruuth
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different p…
An Embedding Technique for the Solution of Reaction-Diffusion Equations on Algebraic Surfaces with Isolated Singularities
Parousia Rockstroh, Thomas März, Steven J. Ruuth
In this paper we construct a parametrization-free embedding technique for numerically evolving reaction-diffusion PDEs defined on algebraic curves that possess an isolated singular…
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Colin B. Macdonald, Jeremy Brandman, Steven J. Ruuth
Eigenvalue problems are fundamental to mathematics and science. We present a simple algorithm for determining eigenvalues and eigenfunctions of the Laplace--Beltrami operator on ra…
Molecular Dynamics Simulation of Sonoluminescence: Modeling, Algorithms and Simulation Results
Steven J. Ruuth, Seth Putterman, Barry Merriman
Sonoluminescence is the phenomena of light emission from a collapsing gas bubble in a liquid. Theoretical explanations of this extreme energy focusing are controversial and difficu…