Analysis of a one-dimensional model for the immersed boundary method
SIAM Journal on Numerical Analysis
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
A variational level set approach to multiphase motion
Journal of Computational Physics
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A front-tracking method for the computations of multiphase flow
Journal of Computational Physics
Numerical approximations of singular source terms in differential equations
Journal of Computational Physics
A Lagrangian particle level set method
Journal of Computational Physics
The numerical approximation of a delta function with application to level set methods
Journal of Computational Physics
A variational approach to path planning in three dimensions using level set methods
Journal of Computational Physics
Threshold dynamics for the piecewise constant Mumford-Shah functional
Journal of Computational Physics
Fourth order partial differential equations on general geometries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Level Set Calculations for Incompressible Two-Phase Flows on a Dynamically Adaptive Grid
Journal of Scientific Computing
On Boundary Condition Capturing for Multiphase Interfaces
Journal of Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Geometric integration over irregular domains with application to level-set methods
Journal of Computational Physics
High order numerical methods to a type of delta function integrals
Journal of Computational Physics
A kernel-free boundary integral method for elliptic boundary value problems
Journal of Computational Physics
Short Note: A proof that a discrete delta function is second-order accurate
Journal of Computational Physics
A balanced force refined level set grid method for two-phase flows on unstructured flow solver grids
Journal of Computational Physics
Redistancing by flow of time dependent eikonal equation
Journal of Computational Physics
Journal of Computational Physics
A convergence rate theorem for finite difference approximations to delta functions
Journal of Computational Physics
Journal of Computational Physics
Superposition of Multi-Valued Solutions in High Frequency Wave Dynamics
Journal of Scientific Computing
A New Ghost Cell/Level Set Method for Moving Boundary Problems: Application to Tumor Growth
Journal of Scientific Computing
On the Numerical Approximation of the Length of (Implicit) Level Curves
Journal of Scientific Computing
Journal of Computational Physics
Finite difference methods for approximating Heaviside functions
Journal of Computational Physics
Discretizing delta functions via finite differences and gradient normalization
Journal of Computational Physics
Journal of Scientific Computing
High order numerical methods to two dimensional delta function integrals in level set methods
Journal of Computational Physics
A sharp interface finite volume method for elliptic equations on Cartesian grids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A level set approach for dilute non-collisional fluid-particle flows
Journal of Computational Physics
Numerical Method for Interaction Among Multi-particle, Fluid and Arbitrary Shape Structure
Journal of Scientific Computing
High Order Numerical Methods to Three Dimensional Delta Function Integrals in Level Set Methods
SIAM Journal on Scientific Computing
A conservative level set method suitable for variable-order approximations and unstructured meshes
Journal of Computational Physics
Spectral collocation and radial basis function methods for one-dimensional interface problems
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
A level-set continuum method for two-phase flows with insoluble surfactant
Journal of Computational Physics
Optimal reconstruction of material properties in complex multiphysics phenomena
Journal of Computational Physics
Journal of Scientific Computing
Hi-index | 31.59 |
Discretization of singular functions is an important component in many problems to which level set methods have been applied. We present two methods for constructing consistent approximations to Dirac delta measures concentrated on piecewise smooth curves or surfaces. Both methods are designed to be convenient for level set simulations and are introduced to replace the commonly used but inconsistent regularization technique that is solely based on a regularization parameter proportional to the mesh size. The first algorithm is based on a tensor product of regularized one-dimensional delta functions. It is independent of the irregularity relative to the grid. In the second method, the regularization is constructed from a one-dimensional regularization that is extended to multi-dimensions with a variable support depending on the orientation of the singularity relative to the computational grid. Convergence analysis and numerical results are given.